FORMULA SHELF
35 of 370
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
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
3 formulas
The honest test of whether you need a bigger freezer or fewer chickens.
A 60 kg dressed chicken is about 120 portions of 0.4 L each, so 48 L of freezer space.
Good tempering gives a snap and a shine. A bad one gives a grey dull surface and blooms later. See Working With Chocolate.
Dark chocolate at 45 C cooled to 31 C and worked back to 32 C sets with a shine.
The acid does the preserving. If you cannot get a 5% vinegar, make a brine pickle instead. See Kraut And Kimchi.
500 ml of 5% vinegar covers 1 kg of vegetables, but submerge them fully.
Agronomy
2 formulas
The language of every irrigation schedule. 25 mm is a proper soaking for a root crop, 5 mm is just keeping the surface damp.
Applying 40 m3/ha is a depth of 4 mm, which is too little to reach the roots in a loam.
Before you harvest, work out where the crop is going to go, and whether the bin will hold it all.
60 tonnes of barley at 0.70 t/m3 = 86 m3, plus 15% = 99 m3 of bin space needed.
Growing
4 formulas
Bed planning. Work out how many plants you want, divide the bed area by the number, and that is the space each one gets.
Brassicas at 60 cm: 1 / 0.6 x 0.6 = 2.8 plants a square metre, so about 0.4 m2 each.
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.
A 10 m bed, 30 cm rows, 25 cm plants: 10 / 0.25 = 40 plants a row.
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.
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.
A 3 m2 bed of radishes at 5 cm squares gives 120 plants, or 40 a sowing for three sowings.
Workshop
2 formulas
Order the bar in lengths that avoid joints in the worst places, and bend a hook at the ends. See Mixing Concrete.
A 12 mm bar lapped 480 mm and a 25 mm cover at each end needs 530 mm of bar per lap.
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
3 formulas
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.
Air at 20 C holds about 17 g of water a kg; cooled to 5 C it can only hold 7 g, so 10 g of water comes out of every kg of air.
A blocked sump floods the yard and the smell reaches the house. Keep the grate clear and the outlet clear.
A 2 x 2 x 1.5 m pit with 20% free space holds 3.6 m3.
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
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
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.
A 300 mm and a 100 mm pulley at 500 mm centres needs about 2,110 mm of belt.
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.
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.
Chemistry
2 formulas
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.
1 g per tonne = 1 ppm.
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.
25 g of powder in 1 litre of water is about 2.4% w/v.
Geometry
6 formulas
Diamond-shaped panels, paving patterns and braces. Multiply the diagonals and halve.
Diagonals 4 m and 6 m give 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.
Any three-sided run: gable ends, braces, triangular beds and roof bays.
Sides 3 m, 4 m and 5 m give a 12 m perimeter.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Roofs, hoppers and conical covers. Slant height is the distance up the slope.
A 2 m radius cone with 3 m slant = 31.42 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Paint and insulation for tanks, silos and drums, including both ends.
A 1 m radius, 3 m tall tank has 25.13 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Paint, coating and insulation on spherical or domed tanks.
A 1 m radius sphere has 12.57 m2 of surface.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Trigonometry
2 formulas
The 3-4-5 rule for square corners, diagonal braces and roof lengths.
Rise 3 m, run 4 m: the brace is 5 m.
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.
Advanced maths
2 formulas
Adding evenly spaced quantities: fence posts, rows, payments and wear allowances.
First term 2, difference 3, 10 terms: S = 155.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Area of an irregular field or a pond from equally spaced offsets.
Offsets 0, 2, 4, 2, 0 at 10 m spacing give 700 m2.
Surveying
3 formulas
The shoelace method for an irregular field boundary from surveyed coordinates.
A four-point paddock can be computed directly from its corners.
Placing a contour line between two surveyed levels on a plan.
Levels 8.2 and 9.0 m at 10 m apart: the 8.5 m contour is 3.75 m from the low point.
Converting a compass bearing to a map or grid bearing. Declination changes with place and year.
Magnetic 30 degrees with 5 degrees east declination is true 35 degrees.
Weather
1 formulas
Sizing a tank, drain or dam from roof or yard runoff.
20 mm on a 100 m2 roof at 0.9 = 1.8 m3.
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.