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
Kitchen
1 formulas
The number that tells you whether a mill is worth setting up. See Home Milling.
100 kg of clean wheat gives about 72 kg of white flour and 28 kg of bran and germ.
Agronomy
4 formulas
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.
A 6 m diameter, 4 m deep bin holds about 113 m3, which is 85 tonnes of wheat.
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.
Wheat at 2,400 lb/acre: 2,400 / 60 = 40 bushels.
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.
Target 350 plants/m2 and you count 245: 70% emergence.
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.
250,000 plants/ha, 1.6 ears, 60 grains, 45 g: (250,000 x 1.6 x 60 x 45) / 1,000,000 = 108 t/ha.
Livestock
1 formulas
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.
A calf eats 8 kg of feed to gain 2 kg: FCR 4:1.
Growing
1 formulas
A cover crop is worth nothing if it is too thin to shade the soil and hold the rain. See Cover Crops.
A vetch and rye mix at 40 + 50 kg/ha gives a canopy in eight weeks.
Workshop
1 formulas
Measure the wall, not the tin. Two coats on new plaster need a primer first. See Painting And Prep.
A 4 m x 2.5 m wall with a 1 m2 window: 10 - 1 = 9 m2, so 1 L of paint for two coats.
Construction
1 formulas
Rushing a render is how it cracks. Two coats, and let the first one set before the second.
A 10 m2 wall at 15 mm needs 0.15 m3 of render, about 3 bags of cement and 0.6 m3 of sand.
Energy
1 formulas
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.
A 500 W heat pump with a COP of 3.5 gives 1,750 W of heat.
Physics
3 formulas
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.
Doubling the depth of a beam reduces its sag by 16 times.
Convenience only. Double-check the result against the worked example or a second method before you use it.
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.
A 1 m3 of wood in water gets 9,810 N of lift, which is 1,000 kg of weight.
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.
Statistics
12 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.
Whether two things move together. Correlation is not proof of cause.
r = 0.8 is a strong positive relationship.
Fitting a straight line through data to predict one value from another.
Feed in versus weight gain can give gain = 0.2 + 0.8 x feed.
The everyday average. Sensitive to outliers, so check the median as well.
Yields 4, 5, 6 and 9 t/ha average 6 t/ha.
A fairer average when one very high or low reading would distort the mean.
4, 5, 6, 9 has a median of 5.5.
The most common size, score or category in a batch.
Sizes 2, 3, 3, 4 have a mode of 3.
Smoothing noisy daily readings such as milk, rainfall or prices.
A 7-day average smooths the weekly milk curve.
How many samples you need before an average is trustworthy.
SD 10 and margin 2 needs about 96 samples at 95%.
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.
How spread out the readings are. The square root is the standard deviation.
Values 2, 4, 4, 10 have a sample variance of 12.
How many standard deviations a reading sits from the average. Useful for grading and outliers.
A 70 kg lamb in a 60 kg flock with SD 5 has z = 2.
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.