FORMULA SHELF
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The arithmetic behind the work: what to measure, what to type in, and what the answer comes out as. Every formula says what the symbols mean and gives a worked example, so you can check it against a job you have already done.
SHELVES
Measurement
2 formulas
Stocking rates, feed weights, seed rates and older books in pounds. Multiply by 2.2046.
500 kg of fertiliser = 1,102 lb.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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%.
1 m rise over 20 m = a gradient of 1 in 20, or 5%.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Kitchen
1 formulas
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.
Cider at 8 Brix that falls to 2 Brix has used about 6% of its sugar, and at 15% alcohol it is nearly done.
Maths
2 formulas
Bracing a gate, checking a diagonal, setting out a rectangle, working the length of a rafter, checking that a frame is square.
A 3 m by 4 m rectangle has a 5 m diagonal.
Convenience only. Double-check the result against the worked example or a second method before you use it.
For very small and very large numbers: soil test results in parts per million, feed analysis in milligrams per kilogram, money in the billions.
0.00042 kg/m3 = 4.2 x 10(-4) kg/m3.
Agronomy
2 formulas
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.
Target 300,000 plants/ha, peas at 0.25 g a seed, 95% germination, 90% establishment: (300,000 x 0.25) / (0.95 x 0.90) / 1,000,000 = 87.7 kg/ha.
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.
2 ha at 35 plants per m2 (about 200 kg/ha): 2 x 200 = 400 kg of seed.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Livestock
1 formulas
The measure of the whole system - rams, condition, feed, scanning and lambing. It is the number to write down every year.
120 lambs from 100 ewes = 120% lambing.
Workshop
1 formulas
Set the height of the first step from the finished floor and the landing, then work down. See Building A Step.
A 900 mm rise with 180 mm steps gives 5 steps, so the going can be 270 mm.
Construction
2 formulas
Digging a hole the right width makes the job ten times quicker, and the post is stronger. See Setting Fence Posts.
A 150 mm radius hole 600 mm deep = 0.042 m3.
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.
A 2 m2 single glazed window at 12 K: 2 x 5.0 x 12 = 120 W, which is a small heater running all winter.
Physics
8 formulas
Why a ramp needs enough grip, why oil makes a bolt easier to undo, and why a ladder needs its feet on level ground.
A 500 N ladder on a wet floor with mu = 0.3 slips at 150 N of sideways push.
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.
A 100 kg load lifted 3 m stores 2,943 J.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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.
A block and tackle with 4 supporting parts needs a quarter of the force.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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.
A 1,500 kg trailer accelerating at 1 m/s2 needs 1,500 N.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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.
A 100 N push on a 10 cm2 piston lifts 1,000 kg on a 1,000 cm2 piston.
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.
A 10 mm steel bar pulled by 5 kN across 78.5 mm2 = 64 MPa.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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.
A 2 m ramp at 500 mm high gives an advantage of 4.
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.
A 200 kg sack weighs about 1,962 N.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Chemistry
1 formulas
The bridge between grams and reactions. Every recipe that uses chemicals is really counting molecules.
36 g of water is 2 moles, because H2O is 18 g/mol.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Health
3 formulas
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.
A drug at 10 mg/kg for a 400 kg cow = 4,000 mg, which is 4 mL of a 1,000 mg/mL solution.
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.
2.5 g = 2,500 mg = 2,500,000 micrograms.
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.
A 600 kg lactating cow at 1.2 g/kg needs 720 g of digestible protein a day.
Geometry
4 formulas
Sloping panels, lean-to roofs and fields with parallel sides. Use perpendicular height, not the sloping side.
A 6 m base and 2 m height = 12 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Checking a frame is square, ordering a diagonal brace and setting out a building.
A 6 m by 8 m shed has a 10 m diagonal.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Fencing, skirting, edging and the length of timber round a frame. Add the two sides and double it.
A 12 m by 8 m pen needs 40 m of fence.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Grain heaps, gravel piles and pyramidal roofs. A third of the box it sits in.
A 4 m x 4 m base and 3 m height = 16 m3.
Trigonometry
3 formulas
Working out a ramp, roof pitch or the slope to a drain from two measurements.
A 1 m rise over 4 m run is 14 degrees.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Roof pitches, ramps, braces and setting out any right-angle triangle.
A 10 m rafter at 30 degrees rises 5 m.
Solving any triangle when you know an angle and its opposite side. Surveying and roof framing.
a = 5 m, A = 30 degrees, B = 60 degrees gives b = 8.66 m.
SOURCES & PROVENANCE
1 listed
This page is an AI-organised index. The label means the grouping and cross-links were compiled with AI; the information itself comes from the public-domain books, reports and manuals listed below. Open any source to read the local copy or follow the link to the original publication.