FORMULA SHELF 370 of 370

The workhorse of farm measurement: field areas, yard areas, floor areas and the size of a sheet of plywood. Multiply the two sides, then convert.

Round water tanks, silos, drums, milk churns, water troughs and fuel drums. The single most useful tank calculation there is.

The standard way to compare machines. Fill the tank, work all day, refill and measure. Divide litres by kilometres and multiply by 100.

Stocking rates, feed weights, seed rates and older books in pounds. Multiply by 2.2046.

Oven temperatures, animal temperatures, weather and old American books. Multiplication and addition beat a table every time.

Old manuals, old recipes and old spray tables are all in imperial gallons. Divide litres by 4.546.

Old books are in acres, new ones in hectares, and field maps in acres. Learn both. A hectare is about 2.5 acres, which is close enough for a rough job but not for a rent calculation.

Used for round tanks, silage pits, feed bins, pipe ends and round bales. Measure the diameter, halve it for the radius.

Trailer load volume, feed bin capacity, water tank volume, concrete for a footing.

Turn a heap into tonnes. Water is 1 kg per litre. Wheat is about 0.75 kg per litre, fertiliser about 1.1, soil about 1.3-1.5, sand about 1.6, concrete about 2.4.

A field with one square end, a yard that narrows, the cross section of a ditch bank, a hipped roof panel.

For wedges, gussets, triangular yard patches, roof end bays and the spread of a spray boom on a slope.

Cutting circles from sheet, sizing a round pen, measuring belt length round a pulley, the girth of a bale.

The number that decides whether a job is worth doing. Measure litres per hour by running the machine for an hour with a full tank and a full tank afterwards.

For spanners, tyres, pipe sizes and imported parts. Divide by 25.4. 12.7 mm is half an inch, 25.4 mm is an inch, 19.05 mm is three quarters.

Salt in a brine, protein in a feed, moisture in a crop, discount on a sale. Divide the percentage by 100 and multiply.

Tyre pressures, sprayer pressures, grease guns and air tools. Modern tyres quote bar; old manuals quote psi. 30 psi = 2.07 bar, which is roughly a car tyre.

For land drainage, roof pitch, silage clamp faces, ramps, and whether a load will get up the yard. A 1 in 10 slope is 10%.

Work out how fast you are actually travelling. A hectare in a day, a round of the field in an afternoon, or whether a load of sheep will get to the market in time.

Grain heaps, fertiliser heaps, sand and gravel cones, and conical feed piles. A third of the cylinder of the same base and height.

The only sane way to scale a bread recipe, and the way professional bakers write them. Change the flour and everything scales with it.

More water means a more open crumb and a wetter dough that is harder to handle. A change of 5% hydration changes the dough a lot.

Colour is not proof. A meat thermometer costs almost nothing and settles every argument about dinner. See Cooking Temperatures.

Weigh the salt and the water, or measure the water and use the figure for the salt. Ice brine is 20-25% for a fast pickle. See Curing Bacon And Sausages.

A boiling thermometer is worth the money. Overcook the jam and it goes tough, undercook it and it runs. See Jam Jelly And Preserves.

Roast the bones first for a deeper flavour, and add the vegetables for the last hour so they do not turn to mush. See Making Stock.

A rough check on a ferment. If the drink is not as strong as the sugar suggested, the yeast ran out of food or something else ate the sugar. See Cider And Perry.

Double acting powder works twice, once in the mix and once in the oven, so it is more forgiving. Do not mix baking powder and bicarbonate of soda together.

The way to know if your cider is fermenting and if your wine is ready. Sugar is the fuel for the yeast, and the falling reading tells you it is running out. See Cider And Perry.

The number to check a cream job against. See Butter And Cheese.

Cheddar and hard farmhouse cheeses need about 9-10 litres of milk a kilo. A cream cheese or a cottage cheese needs far less. See Butter And Cheese.

For working out what to charge at a gate sale or a market stall, and for seeing which dish actually earns.

A warm kitchen gives you a fast loaf and a sour one. The dough temperature at mixing decides how long you wait, not the clock on the wall.

For planning a dehydrator run and for expecting how much you will have in the jar at the end of it.

Weighing the eggs is the only reliable way, because the sizes in one box vary. A big egg in a cake is a wetter cake.

The number that tells you whether a mill is worth setting up. See Home Milling.

The whole of food safety in one line. See Food Safety In The Kitchen.

The honest test of whether you need a bigger freezer or fewer chickens.

Ghee keeps for months in a warm kitchen, which is why it is the useful one. See Butter And Cheese.

The rules that decide what goes in the freezer. Label everything with the date and what it is.

Anything more and the extra sugar sits at the bottom of the jar. For a simple syrup, dissolve equal weights of sugar and water and stop there.

Weight is the only honest way to judge a rise, because a warm kitchen and a cold one both look different. Mark the bowl or use the scale.

Lime makes the maize release its niacin, which is the whole point of treating it. See Flint Corn And Popcorn.

How to work out how much fat ends up in a pie crust, and how to make it flaky instead of short. See Pastry And Pies.

The test of a good flint variety, and the reason some maize will not pop at all. See Flint Corn And Popcorn.

A 1:5:5 feed doubles in 4-6 hours at 24 C. A 1:10:10 takes 8-12 hours and tastes less sour.

Resting lets the juice spread back into the meat. Cut it early and the juice ends up on the board.

Weigh the rice and the water and the result is the same every time. Salt the water, and let it rest before you cook it.

Weigh the vegetables, then weigh the salt. Too much salt stops the ferment, too little lets mould in. See Kraut And Kimchi.

More salt does not mean better bread, it means a firmer crumb and a slower rise. Never add salt straight onto a wild yeast starter.

The quickest kitchen arithmetic. Divide by the factor for a smaller batch, and remember that a double batch does not cook in double the time.

Smoking is about getting the smoke into the meat and holding the temperature. See Curing Bacon And Sausages.

Honey is about 80% sugar and 20% water, and it is stickier, so cakes brown more and keep longer. Reduce the liquid in any recipe where you swap it in.

High pectin fruits like gooseberries and redcurrants need less sugar. Soft fruit such as strawberries need more, and more sugar means a firmer set.

Good tempering gives a snap and a shine. A bad one gives a grey dull surface and blooms later. See Working With Chocolate.

The acid does the preserving. If you cannot get a 5% vinegar, make a brine pickle instead. See Kraut And Kimchi.

Warm the milk to 45 C, cool to 40 C, add the starter and keep it warm. See Yoghurt And Kefir.

Feed price moves, growth rate, water use, milk yield, a price rise at the mart. Always state the direction with a sign.

The workhorse of farm arithmetic. Seed rate per hectare scaled to your patch, fertiliser from the label, spray mix from a test plot, feed per animal per day.

Average daily milk yield, average egg weight, average tractor hours a week, average weight at weaning.

On a loan, an investment, or a hire-purchase agreement. The difference from simple interest is that the interest itself earns interest.

For compound growth, interest, scaling up a feed rate, and working out how many times a treatment covers a flock.

They are the reverse of powers. They are how you find a compound interest time, a half-life, a pH, a decibels level or a Richter magnitude.

Bracing a gate, checking a diagonal, setting out a rectangle, working the length of a rafter, checking that a frame is square.

Mixing feed, splitting a bale, scaling a recipe, dividing a field between two crops, blending a concentrate with a home-grown protein.

How long money takes to double, and how long a debt takes to double as well. Rough, and right to within a few months at normal rates.

For very small and very large numbers: soil test results in parts per million, feed analysis in milligrams per kilogram, money in the billions.

The old hire-purchase and the short-term loan. Easy to check by hand against the paperwork.

For a roof pitch, a drain run, a graph of growth against time, or checking whether a field really does slope the way you think.

Before you buy pigs, take on a shed, or start selling eggs. If the margin per unit is negative, the answer is no, however many units you sell.

Margin is measured against the selling price, markup against the cost. They are not the same number and confusing them is how people lose money. A 50% markup is a 33% margin.

How long before the machine pays for itself. A payback under three years is usually good for a working tool.

For a flock, a herd, a customer list or a tree that is being improved each year. Shows the real rate behind a rising number.

The only way to compare two crops, or two fields, fairly. Divide the whole year's cost by the area, not just the variable bits.

The number that decides what you plant next year. Always leave the fixed costs out of this figure and add them back at the whole-farm level, or you will chase the wrong crop.

Working out whether a bulk buy of feed, fuel or seed is cheaper than the retail price, including the delivery.

Compare a new freezer, a new shed or a flock of sheep against what they actually return each year.

The proper way to buy seed. A bag says 80% germination, so you must buy 20% more seed than the target population needs, and more again for field losses.

Turn a spacing into a population, then into a seed rate. Work out what you want first, and the drill setting second.

Every sprayer book starts with this. Get the volume right and the dose per hectare is right. Measure a nozzle with a jug, and time the pass over 100 m.

The calculation behind a fertiliser plan. Subtract what the soil and the manure already give you, then convert to the product you are actually buying.

The language of every irrigation schedule. 25 mm is a proper soaking for a root crop, 5 mm is just keeping the surface damp.

To know how much grain is in the barn before you sell it, and to check a silo is big enough. Measure the heap or the bin and multiply.

For checking whether there is enough hay for the winter, and for working out how many bales to book in.

Catch the output from one nozzle for one minute to get flow. Measure your forward speed and the nozzle spacing on the boom. This tells you how many litres per hectare you are putting down, so you can mix the right amount of chemical in the tank.

For converting the old imperial yields into today's tonnes a hectare, and for reading the old books on the shelf. A bushel is a volume, so the weight depends on the crop.

The rule that makes a heap work. Too much carbon and it sits there for a year; too little nitrogen and it goes sour and smells. See Compost Heap.

Grain dried too fast or too hot goes cracked, and the cracks cost you in the mill. See Storing Grain.

Comparing a field of grass with a field of hay, and working out how much feed a field really gives. The green weight is mostly water.

The two numbers that tell you whether the drill or the seed is at fault. A poor emergence with a good germination test means a drilling problem, not a seed problem.

The way to work out what a crop is worth before you have even got the harvester in the field. Combine it with a per hectare count of plants and ears.

Whether the cover crop is a real feed or just a cover. It depends on the dry matter, not the green weight, and on how much you leave behind.

The basic scheduling method. Multiply the daily water use by the crop stage, take off the rain, and divide by how well your system actually delivers.

Lime is the one thing you cannot take back once it is spread, so use a buffer test rather than a pH test. See Soil Ph And Lime.

Oilseed rape and grass are hungry for sulphur. Too little sulphur and the crop cannot use the nitrogen you have paid for, so the response to extra N is poor.

The part of the manure spreadsheet that matters. A load of manure looks like a big pile of nitrogen on the yard, and only a fraction of it is available to the crop this year.

To check that the pump and the pipes can deliver. A 1 hectare block needing 25 mm in 4 hours needs 17 L/s.

To work out how long it takes to drill a field, how much fuel you will burn, or how much fertiliser to put on through the drill.

Convert your target plants per square metre into kg per hectare (check the seed bag or the seed-rate table), then multiply by the area in hectares. This gives total kilograms of seed to buy. See also the Seed Saving depot for saving your own seed.

The setting that goes on the drill. Work it out from the seed rate, then check it over a measured 10 m and count.

Work out the fill for the area you are about to spray, then measure the product with a proper jug. Over-application is expensive, illegal and dangerous.

Before you harvest, work out where the crop is going to go, and whether the bin will hold it all.

The single number that tells you if a ration or a system is working. Weigh the animals, do it again in 30 days, and divide.

How much feed you get back for every kilo you put in. A higher number means more feed per kilo of meat, and a bigger feed bill.

The fair way to compare a flock, a herd and a paddock. It also tells you whether you are about to overgraze.

To size a ration. Get this wrong in either direction and the animal is either hungry or overfed, and you will not see which from the ration sheet.

Multiply the animal's liveweight by the ration percentage, then divide by 100. A 600 kg cow on a 2.5% ration needs 15 kg of feed a day. Split between forage and concentrate as the ration sheet says.

Measure around the chest just behind the front legs (heart girth) and from the point of shoulder to the pin bone (body length), both in centimetres. Square the girth, multiply by length, divide by 300. Best for cattle; less accurate for very fat or very thin stock.

A condition score tells you more than a weight, and it takes ten seconds. Handle the animal and look at the hooks, the hips, the tailhead and the ribs.

Measure it, and aim to get it under 380. A long interval usually means the cow is losing condition before the bull goes in.

The price of your stock depends on it. A heavy animal with a poor dressing percentage is not worth much more than a lighter one, and the killing sheet tells you which you have.

Two different questions. Conception tells you about the bull and the condition score; calving rate tells you about the calving shed and the hard cases.

For working out whether a flock of hens is worth keeping. The feed per dozen is the number to watch, and it gets worse in winter when the birds are burning energy to stay warm.

The practical version of the stocking rate. It tells you when to move the herd on, and how long a paddock lasts.

Measure the bale in metres, multiply length x width x height to get cubic metres, then multiply by density. A small square bale is about 100-150 kg/m3; a big round bale is denser, about 200-250 kg/m3.

For planning how many hives you can keep, how much equipment you need and what the honey is worth. See Keeping Bees.

The measure of the whole system - rams, condition, feed, scanning and lambing. It is the number to write down every year.

The number that shows whether the land or the cow is the limiting factor, and the reason a good dairy farmer looks at the forage first.

The honest measure of the system. Write it down every year; it tells you whether the problem is the housing, the feed or the lambing.

Size the troughs. A trough that is too small for a hot day is the reason a cow stops eating. See Water Troughs And Algae.

Write the treatment date and the withdrawal date on the animal or in the book, and check the milk before it goes in the tank. See Vaccinating And Cold Chain.

For working out the wool income from a flock, and for judging whether the condition of the sheep at shearing was right.

Bed planning. Work out how many plants you want, divide the bed area by the number, and that is the space each one gets.

For a watering can shift or a hose timer. A 10 L can covers about 2 m2 a day, and a hose sprinkler covers about 20 m2.

Work out the total area in square metres, then divide by the area each plant needs (row spacing x in-row spacing). This tells you how many plants to order for a plot or field.

How much compost to barrow across the plot. One wheelbarrow is about 60 litres, so a 10 m2 bed at 5 cm needs about 5 barrows.

Ten minutes and it tells you whether a packet is worth sowing. Old or badly stored seed is the most common reason a row does not come up.

Every bed plan starts with this. A 10 m bed with rows 30 cm apart has 33 rows, and at 25 cm in the row that is about 1,300 plants.

Only worth it if you grow one variety at a time, or if the neighbours are not growing the same crop. Otherwise you will save a hybrid.

A plant that goes out too early loses a fortnight. Harden it off properly and it will lose a week of growth instead of a month of plants.

The quickest way to plan a bed or a border. Onions at 10 cm square give 100 a square metre; potatoes at 30 cm give 11.

For beans, beetroot, carrots and onions sown in a drill in a bed. Sowing three seeds in a station and taking the best one is often more reliable.

The halving rule: seed loses half its life each year, so freshness doubles the years it lasts. Buy fresh seed for the crops that go over quickly.

A cover crop is worth nothing if it is too thin to shade the soil and hold the rain. See Cover Crops.

How to keep a small bed productive all season. Sow little and often, and swap a fast crop for a slow one when the space frees up.

The clamp force is what you actually want, and it is torque that gives it. Use a torque wrench on head bolts and wheel nuts, and never a guess on anything that matters.

For a footing, a step, a post hole or a slab. A 1:2:4 mix is for footings and paths, 1:2:5 for a mass base and 1:1.5:3 for a stronger mix. See Mixing Concrete.

The wire needs to be tight and the post needs to be firm. See Setting Fence Posts and Fencing Wire And Straining.

How timber is sold in the trade, and how you check a delivery. A rough conversion is 1 board foot about 0.0024 m3.

For sizing a water butt or a tank for the yard and the animals. See Water Troughs And Algae.

Multiply thickness x width x length, then divide by 12. This is how sawn timber is measured and sold. A 2-inch plank 8 inches wide and 10 feet long is 13.3 board feet.

Divide the fence length by the post spacing, then add one for the end post. Round up to the next whole post. Add strainer posts at corners and gates separately.

Chain pitch is stamped on the drive link or the bar. Multiply the pitch in inches by 25.4 to get the matching round file diameter in millimetres. Common: 3/8 inch pitch = 9.5 mm file; 0.325 inch = 8.3 mm file; 0.404 inch = 10.3 mm file.

Drying grain needs moving air, not hot air. If the fan is sized for the empty bin it will not cope with a full one. See Storing Grain.

For a V-belt or a flat belt on a machine you have built. Add about 5% for tension and stretch, then cut to the nearest standard size.

Measure from the edge of the hole to the edge of the flange, not to where you think the bend goes. Add the allowance to the flat length before cutting.

For ordering. Always order 5% more than the calculation for cuts and breakages.

Long runs need bigger cable, not bigger fuses. Measure the run, use the table, and check the breaker size next.

For chain wear, sprocket sizing and the speed of a bicycle. Multiply by 3.6 for km/h.

Set posts in concrete for a gate, a fence or a sign. A quick-setting post mix works in cold weather. See Setting Fence Posts.

Set the speed from the tool material and the work, then let the chips tell you if you are wrong. Blue chips mean too fast.

For working out the cost of a job and whether a machine is worth keeping. Idle burn is a surprising share of a small engine's fuel.

Friction and heat are the losses. A lower efficiency means more fuel, more electricity and more heat to shift away.

For working out whether a supply will carry a heater, a welder or a three-phase motor. See Three Phase And Single Phase.

Work out the whole foundation before ordering, and add 10% for the lumps. Dig in a straight line, and set the pegs before the mixer arrives.

The standard way to compare a van, a tractor and a car. Keep a running total between fills.

Whether you are rebuilding a gearbox, a mixer or a seedling thinner. Work it out on paper before you order the gears.

Water on a level yard is water that never leaves. Get the fall right with a laser level or a long spirit level and a pegged board. See Underground Pipe And Trenches.

Why a door jams in a wet winter, why a solid wooden worktop cups, and why a gate needs a gap. Plan for the movement.

Measure the wall, not the tin. Two coats on new plaster need a primer first. See Painting And Prep.

The right pilot hole lets the screw pull the two parts together instead of just splitting the timber.

To check whether a motor, an engine or a hand tool has the power for the job, and to compare an electric motor with a petrol one.

The belt and pulley rules for a lathe, a compressor or a sander. A small pulley on a shaft with a big one on the belt gives speed and torque.

Order the bar in lengths that avoid joints in the worst places, and bend a hook at the ends. See Mixing Concrete.

For ordering felt, tiles, battens and underlay. Always order the underlay and never skimp on it.

The pitch decides the tile angle, the felt laps and how much water the roof throws off the building. The run is half the span for a normal gable.

The number that decides whether a second machine, a bigger one, or hiring it in makes sense.

Mixing by bucket. A wheelbarrow of sand is about 0.07 m3, so a bucket is roughly 0.014 m3. See Mixing Concrete.

The difference between a saw that cuts along the grain and one that cuts across it. A rip saw has few deep teeth; a crosscut saw has many fine ones.

A 300 ml cartridge of a 6 mm bead does about 10 m; a 10 mm bead does about 3.5 m. Get the bead size right or you will run out halfway along the shed roof.

For a shed, a fence charger or a small system. Size for the dark weeks of winter, not the bright ones. See Solar And Battery Storage.

Set the height of the first step from the finished floor and the landing, then work down. See Building A Step.

Concrete gains most of its strength in the first week. Keep it damp for the first three days and cover it if it is hot or frosty.

Water is the enemy of concrete strength. Never add water to make it easier to work; add cement or use a plasticiser instead. See Mixing Concrete.

Strain each wire to the same tension, lowest wire first, and keep the strainer run at the same place on every wire. See Fencing Wire And Straining.

The physics behind leverage. A bar is a machine: it does not change the work, only the force and the distance.

Multiply length x width x depth in metres. Add 5-10% for waste and over-excavation. A cubic metre of concrete weighs about 2.4 tonnes, so plan your delivery and your wheelbarrows.

For a round tank: area of the circle (pi x radius squared) times height, then multiply by 1000 to get litres from cubic metres. A 2-metre diameter tank 2 metres high holds about 6,283 litres.

Order 5% extra. A half block per row is needed at every corner and opening, and people always run out.

Condensation on the roof sheets means the warm moist air is meeting a cold surface and there is no way out. Vent the building at both ends. See Venting The Workshop.

A drain that does not fall will block, and the smell will find its way into the shed. See Underground Pipe And Trenches.

A foundation that is too shallow gets lifted by a hard frost and pushes the building out of square. See Building A Step.

An undersized gutter overflows in a storm and wets the foundation. See Draining Water Pipes.

For a yard or a track. Compact in layers of 100-150 mm or the bottom will go soft. See Building A Step.

For comparing a shed, a workshop and a house, and for working out what a stove has to make up. Bigger U-value means more heat going out.

A suspended timber floor over a cold ventilated void loses a lot of heat. See Insulating A Workshop.

For working out how much insulation to buy. Rule of thumb: 100 mm of mineral wool is about R2.5, and a well insulated roof wants R4 or better.

Before the trucks arrive, work out how much hard core or soil you need. The average of the high and low spots is the honest way to do it.

The strength comes from the sand being sharp and clean and the joints being filled. Lime in the mix makes it work better.

Rushing a render is how it cracks. Two coats, and let the first one set before the second.

Digging a hole the right width makes the job ten times quicker, and the post is stronger. See Setting Fence Posts.

The sand bed is what makes the blocks sit flat. A slabbed area that wobbles has not enough compacted sand under it.

A blocked sump floods the yard and the smell reaches the house. Keep the grate clear and the outlet clear.

Mould on the same corner every winter is not bad luck. Look for the cold spot with a thermal camera or the back of your hand.

The number that decides whether a workshop, a stable or a grain store is workable. See Venting The Workshop.

The first number for any insulation job. Measure every wall and subtract the openings, and buy 10% extra for the cutting.

For a header tank and a trough system, and for a yard where the mains cannot keep up. See Water Troughs And Algae.

Windows are the weak point of any old building. A secondary glazing frame on the inside of a single glazed window is cheap and effective.

The way to sell an idea to whoever holds the purse. Half the cost of an insulation job often comes back in fuel in the first winter.

For sizing a solar array for the electric fence, the lights or a small freezer. Multiply the panel area by the irradiance you can count on, not the best case.

The starting point for any electrical fault finding. If the voltage is right and the lamp is dim, the current is low, so the resistance is too high. See Electrical Fault Finding.

For working out what a heater, a motor or a charger really uses. 1 hp is about 746 W, so a 1.5 kW heater is 2 hp of heat going into the room.

For choosing a battery, and for working out how long a generator or a mains charger will take. A 12 V 100 Ah battery on a 10 A charger is about 10 hours, less the losses.

What the meter on the wall measures. Everything electric in the farm is counted in kilowatt hours, and a 1,000 W heater running for ten hours uses 10 kWh.

How many units of heat you get for each unit of electricity. A COP of 3.5 means the heat pump heats three and a half times more than the resistance heater it replaced.

For a string of lights, a trailer board, or when you are adding a second battery. Parallel adds power and series adds voltage.

For the three-phase supply to a barn, a grain dryer, a milking parlour or a welder. The root 3 is the bit people forget.

For a welder, a battery charger, a lamp on a long lead, and any step-down or step-up. Power is roughly conserved, so a step-up gives you less current for the same watts.

Count the rope, not the pulleys. A block and tackle with the load on a four-part reeve has an advantage of about 4, less the friction in every sheave.

For a gearbox, a quad final drive, a mower gearbox or a winch. A 3:1 reduction triples the torque and drops the speed to a third. The power stays the same, less the losses.

For a shed, a polytunnel, a cold room or a house. Insulation works by lowering U, and a door left open works by raising it again every time.

Why a fence rail sags, why a steel beam needs to be deep rather than wide, and why a long trailer bed needs cross members. Depth beats width every time.

For a drive belt on a tractor, a mower, a compressor or a bandsaw. Measure the old belt and copy it, or use the formula for a different pulley set.

Why a boat floats, why a tractor wheel floats in mud, and why you cannot lift a submerged post out of a hole by pulling on it.

Loading a trailer, tipping a wheelbarrow, setting a ladder, and why a tall stack of bales topples. Keep the load low and forward.

Converts a volume of something into a weight. Water is 1 kg per litre. Milk is about 1.03, oil 0.92, honey 1.42, fertiliser 1.1, wheat 0.75, chopped straw 0.25.

How much more than the job the part can take. Check it when you weld something load bearing - a gate bracket or a trailer chassis - and never design a lifting point yourself.

Why a ramp needs enough grip, why oil makes a bolt easier to undo, and why a ladder needs its feet on level ground.

The energy stored by lifting something. It is why a raised bale or a full water tank is dangerous, and why a ramp gains you the power to lift a load higher.

The energy of something that is moving. Double the speed and you have four times the energy, which is why a braking problem gets serious very quickly above a certain speed.

A lever, a block and tackle, a ramp, a screw jack. You trade distance for force, and no machine beats 100% efficiency. A ramp 4 m long and 1 m high has a theoretical advantage of 4.

Why a soft bag of sand and a hard block hit differently at the same speed, and why you roll with a fall. Doubling the speed doubles the momentum and quadruples the stopping force.

The force needed to move a mass. The tractor pulling a trailer, the ramp lifting a load, a horse pulling a plough. Double the mass and you double the force, for the same acceleration.

The jack, the brake press, the loader bucket and the post hole rammers. A 10 cm piston moved with 100 N will lift 1,000 kg on a 1 m piston.

How fast work gets done. 1 hp = 746 W, so a 50 hp engine is 37 kW. A machine doing the same work in half the time has twice the power.

Why a spade is sharp and a boot is not, and why a dam holds back a growing force. A 1 m column of water pushes 9,810 Pa on every square metre at the bottom.

To work out a pulley size for a different speed, and to check whether a driven machine is running at the speed it was designed for.

Why a stick looks bent in a pond, why a greenhouse bends the light, and how a lens focuses.

How much fuel or electricity a heater needs. Water needs far more energy per kilo than steel, which is why a hot water cylinder takes so long.

The stiffness of a material. Steel is nearly twenty times stiffer than oak, which is why a steel frame sags less and lasts longer than a timber one of the same size.

Ramps, loading ramps, the screw jack, the post hole auger and the cider press. Work in always equals work out, so a gentle ramp just means more walking.

Why a long fence rail buckles in a heatwave, why a steel tank needs a sliding bearing, and why a concrete slab needs expansion joints.

The whole of the spanner, the jack, the pump handle and the gate hinge. Torque depends on where you put your hand, not on how hard you pull. A 100 N push at 0.3 m gives 30 N m.

Sound, water, light and radio. Also the drum length of a pipe organ and the spacing of ripples on a pond.

Mass is how much there is, weight is how hard it presses. A sack of fertiliser has the same mass everywhere and a different weight on the moon. Lifting power is usually quoted in kilograms, which is really a mass in disguise.

Work only happens when the force is in the direction of the movement. Lifting a load 2 m and pushing a barrow 100 m are different amounts of work.

The rule that lets you scale up a gas reaction - a bottle of gas and a cylinder of gas behave the same way.

Each one holds the other two constant. A cold bottle warms in the sun and the pressure goes up, which is why a bottle left in a hot shed can go off.

How a milk, a must, or a soil stays at a steady pH while things are added to it. A brine is a buffer, and so is the lime in a soil.

Every time you mix a concentrate with water, for a spray, a disinfectant or a test solution. Always add the concentrate to the water, never the other way round.

Why a compost heap gets hot, why a lime slurry in a slurry tank warms, and why a soaking cold feed makes the animal cold.

Why salt melts ice on a road, why a brine freezes below zero, and why a freezer with a brine tank is colder than one with water.

The rule behind a pressure cooker, a tyre, a gas cylinder and a fermenting barrel. Pressure rises with temperature and with the amount of gas, and falls as the volume grows.

The reason a sealed compost bin gains mass (it gains the carbon dioxide that leaves) and the reason a fire seems to lose mass - the carbon dioxide and water vapour have left the shed.

The standard way to say how strong a solution is. A 1 mol/L solution of sodium hydroxide is 40 g of it in a litre of water.

The bridge between grams and reactions. Every recipe that uses chemicals is really counting molecules.

For trace elements in soil and feed, nitrate in water, and anything described as 'trace'. A soil test of 30 ppm copper is very different from 30 percent.

For a 2% milk replacer mix, a 1% iodine solution, a 5% bleach mix or a salt brine. Note that the denominator is the solution, not the water.

How well a process actually ran. A lime neutralisation that only reaches 80% means you need more lime than the label says.

For making a solution of a known strength, for a lime neutralisation calculation, and for anything where the reaction has to be right rather than roughly right.

For working out the strength of a bought solution, and for checking a soil or water test against the method. The end point is the colour change, so get it right before you read the burette.

To decide whether a borehole needs a softener, and why soap will not lather and the kettle furs up.

Soil, water, antacids and preserves. A change of one unit is ten times more or less acid, which is why a small pH change matters so much. See Soil Ph And Lime.

For checking that a caustic solution is strong enough, and for understanding why a wash and a rinse need different strengths.

For any medicine given by weight. First work out the animal's weight, then multiply, then convert to millilitres using the concentration on the label. Always confirm the dose with your vet before the first use.

To plan the yard, the lambing shed, the farrowing crate and the calving pen. Add a few days to the average for a first-time animal, because first pregnancies run long.

A rough guide for people, and a reminder that a weight without a condition score is only half a judgement. Use body condition scoring for stock, and the tape for pigs.

Almost every medicine error is a unit error. Learn the ladder by heart and write the unit next to every number you copy off a label.

Sunken eyes, tight skin and a tacky mouth in a calf or a dog mean a percentage of body weight has gone. A 5% loss in a 40 kg calf is 2 L to put back.

Feed energy is quoted in megajoules of net energy, and food labels in kilocalories. The conversion lets you compare the two. A megajoule is 239 kcal.

The starting point for how much water or IV fluid an animal needs. Add losses for fever, heat, exercise and any diarrhoea. A cow drinking less than this is a cow that will go down.

To check a ration against a feed table. Growers and lactating stock need more protein than dry stock, and the tables are always in digestible protein.

Average feed analysis across different batches, average yield across fields of different sizes, average price across different volumes sold.

How spread out a set of readings is. A 500 litre herd with a standard deviation of 20 is steady; one with 120 is not. It is how you tell a genuinely consistent flock from a lucky average.

Averages lie when one reading is odd. The median tells you the typical day; the range tells you how variable the month was. Use both for milk records, daily temperatures and yields.

For a sprayer that does not deliver its rated volume, a scale that reads light, or a soil test that is out by a tenth of a point. Know the error and you can correct for it.

Bending strip, curved edging and the length of a curved wall.

Pie-shaped concrete, a curved header bank, or part of a round tank lid.

Sloping panels, lean-to roofs and fields with parallel sides. Use perpendicular height, not the sloping side.

Hexagonal pens, octagonal silos and regular paving. For a hexagon the multiplier is 2.598.

Diamond-shaped panels, paving patterns and braces. Multiply the diagonals and halve.

Oval beds, elliptical tank ends and oval pipe openings.

Setting out curved yards and checking whether a point falls inside a round pen.

Checking a frame is square, ordering a diagonal brace and setting out a building.

Fencing, skirting, edging and the length of timber round a frame. Add the two sides and double it.

Any three-sided run: gable ends, braces, triangular beds and roof bays.

Scaling a drawing, finding an inaccessible height from a shadow, and setting out a roof.

Roofs, hoppers and conical covers. Slant height is the distance up the slope.

Paint and insulation for tanks, silos and drums, including both ends.

Paint, coating and insulation on spherical or domed tanks.

When you can measure the three sides but not the height. Useful for odd yard patches.

Tapered tanks, silage pits, hoppers and the volume of a truncated cone.

Grain heaps, gravel piles and pyramidal roofs. A third of the box it sits in.

Round tanks, ballast, domes and spherical stock waterers.

The 3-4-5 rule for square corners, diagonal braces and roof lengths.

Working out a ramp, roof pitch or the slope to a drain from two measurements.

Converting a survey line into a bearing. Adjust to 0-360 degrees.

Setting out a curved gate, an arch or a circular saw cut.

The third side of any triangle when two sides and the included angle are known.

Any calculation that uses angles in code, physics or engineering formulas.

Checking a survey, setting out a fence or measuring between two points on a plan.

Finding the centre of a span, a gate opening or a surveyed line.

Turning a calculator or spreadsheet result back into an angle you can set out.

Roof pitches, ramps, braces and setting out any right-angle triangle.

Solving any triangle when you know an angle and its opposite side. Surveying and roof framing.

Odd-shaped plots and roof panels where the height is awkward to measure.

Adding evenly spaced quantities: fence posts, rows, payments and wear allowances.

Compound annual growth for a herd, a woodlot, a business or an investment.

Expanding repeated multiplication in engineering, statistics and compound growth.

Counting selections where order does not matter: feed mixes, teams, sample plots.

Rates of change: how fast a tank empties, a crop grows or cost rises.

Checking whether two equations have a unique solution; used in surveying and transformations.

When one quantity doubles, the other doubles: seed to area, feed to animals, paint to wall.

Tells you whether a quadratic has two, one or no real solutions before you solve it.

Checking a diagonal in a building, a pipe run or a 3D survey.

Cooling, spoilage, radioactive decay, drug clearance and declining yields.

Populations, investments, fermentation and anything that grows by a percentage each period.

Counting arrangements, combinations and probability. 0! is defined as 1.

Compound growth, repeated dilution and doubling problems.

Finding total volume, distance or energy from a rate. The reverse of a derivative.

When one goes up and the other goes down: speed and time, men and days, pressure and volume.

Light, sound, radio and spray coverage fall off with the square of distance.

Straight-line relationships: cost per hour, fuel use against load, yield against rainfall.

When a calculator only has log base 10 or natural log but the problem uses another base.

Growth and decay, half-life and the inverse of the exponential function.

Solving an equation that cannot be rearranged neatly. Iterate until the answer settles.

Checking a scale, a meter, a yield estimate or a mixing measurement.

Counting ordered arrangements: jobs in a sequence, routes, rotations.