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
1 formulas
Grain heaps, fertiliser heaps, sand and gravel cones, and conical feed piles. A third of the cylinder of the same base and height.
A 3 m radius, 2 m high heap of grain = 18.85 m3 = 18,850 kg at 750 kg/m3.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Kitchen
4 formulas
Lime makes the maize release its niacin, which is the whole point of treating it. See Flint Corn And Popcorn.
1 kg of maize and 1 L of water with 15 g of lime makes about 1.1 kg of nixtamal.
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.
500 g of rice with 750 ml of water makes about 1.6 kg of cooked rice.
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.
A recipe for 6 with 300 g of flour, baked for 25 minutes: for 4, multiply by 0.67, so 200 g of flour and about 20 minutes.
Warm the milk to 45 C, cool to 40 C, add the starter and keep it warm. See Yoghurt And Kefir.
5 L of milk at 45 C with 100 ml of starter, kept at 45 C for 8 hours, gives about 5 kg of yoghurt.
Money
1 formulas
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.
Bought at 2 and sold at 3: a 50% markup, a 33% margin.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Growing
2 formulas
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.
Saving brassica seed on a smallholding usually needs an agreement with the neighbours.
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.
Carrots at 5 cm in 15 cm rows: 1 / (0.15 x 0.05) = 133 a square metre.
Workshop
3 formulas
The right pilot hole lets the screw pull the two parts together instead of just splitting the timber.
A 6.5 mm screw wants a 5 mm pilot in softwood.
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.
A 100 rpm motor on a 100 mm pulley driving a 400 mm pulley: 100 x (100/400) = 25 rpm.
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.
A 100 m fence with a strainer run 200 mm gives 1/500 of stretch in the wire.
Construction
1 formulas
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.
Damp at the base of a cold wall is condensation, not a leak, unless it moves when it rains.
Energy
1 formulas
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.
Stepping 230 V down to 24 V gives about ten times the current for the same power.
Physics
7 formulas
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.
A 12-tooth pinion driving a 36-tooth gear is 3:1.
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.
A 2 kg tool at 5 m/s has 10 kg m/s of momentum.
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.
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.
37 kW (50 hp) = 74,000 W.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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.
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 rule that lets you scale up a gas reaction - a bottle of gas and a cylinder of gas behave the same way.
Double the moles in a fixed vessel and you double the pressure.
Data
1 formulas
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.
Readings 98, 100, 102, 100 give a mean of 100 and a standard deviation of about 1.6.
Statistics
4 formulas
The range the true average is likely to lie in. Use 2.58 for 99%.
Mean 50 and SE 2 gives 46.1 to 53.9.
Comparing variability between groups with different averages, such as two flocks.
SD 2 kg on a 40 kg mean is 5% CV.
Smoothing noisy daily readings such as milk, rainfall or prices.
A 7-day average smooths the weekly milk curve.
How precisely a sample mean estimates the true mean. More samples, smaller error.
SD 10 with 25 samples gives SE 2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Finance
1 formulas
How long before a machine, shed or solar array pays for itself. Ignore interest for a quick check.
A 6000 machine saving 1500 a year pays back in 4 years.
Electrical
1 formulas
A low power factor means more current for the same useful work. It matters for pumps and motors.
8 kW from 10 kVA is a power factor of 0.8.
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.