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FORMULA SHELF 20 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.

Quick calculators. A calculator appears where the formula is a single, clean equation with clear symbols. It is a convenience, not an authority: double-check every result yourself, especially doses, loads, torque and safety-critical settings.
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Measurement 20 formulas

Area of a rectangle MOST USED
A = L x W
SYMBOLS · A = area; L = length; W = width
UNITS · m2, hectares, acres
HOW TO USE

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.

EXAMPLE

A 40 m x 25 m yard = 1,000 m2, which is 0.1 hectare.

QUICK CALCULATOR A = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

area rectangle length width field
Volume of a cylinder MOST USED
V = pi x r2 x h
SYMBOLS · V = volume; r = radius; h = height (or length)
UNITS · m3, litres
HOW TO USE

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

EXAMPLE

A 1.5 m diameter, 2 m tall tank holds 3,534 litres.

QUICK CALCULATOR V = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

volume cylinder tank silo trough
Fuel consumption (litres per 100 km) MOST USED
L/100km = (fuel used / distance) x 100
SYMBOLS · fuel used in litres; distance in km
UNITS · L/100km, or litres per hour
HOW TO USE

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

EXAMPLE

25 litres over 10 km = 25 L/100km.

fuel diesel consumption tractor
Kilograms to pounds MOST USED
lb = kg x 2.20462
SYMBOLS · kg = kilograms; lb = pounds
UNITS · kg, lb
HOW TO USE

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

EXAMPLE

500 kg of fertiliser = 1,102 lb.

QUICK CALCULATOR lb = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

conversion kilograms pounds weight
Celsius to Fahrenheit MOST USED
F = (C x 9 / 5) + 32 (C = (F - 32) x 5 / 9)
SYMBOLS · C = degrees Celsius; F = degrees Fahrenheit
UNITS · degrees
HOW TO USE

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

EXAMPLE

200 C = 392 F, the usual temperature for a hot oven.

QUICK CALCULATOR F = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

conversion temperature celsius fahrenheit oven
Litres to imperial gallons MOST USED
gallons = litres / 4.54609
SYMBOLS · 1 imperial gallon = 4.54609 litres; 1 US gallon = 3.785 litres
UNITS · litres, gallons
HOW TO USE

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

EXAMPLE

20 L of fuel = 4.4 imperial gallons.

conversion litres gallons fuel
Acres and hectares MOST USED
acres = m2 / 4046.86 ; hectares = acres x 0.404686 ; m2 = hectares x 10,000
SYMBOLS · 1 hectare = 10,000 m2 = 2.471 acres; 1 acre = 4046.86 m2
UNITS · m2, hectares, acres
HOW TO USE

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.

EXAMPLE

5 acres = 2.023 hectares.

conversion acres hectares field area
Area of a circle MOST USED
A = pi x r2
SYMBOLS · A = area; pi = 3.14159; r = radius (half the diameter)
UNITS · m2, cm2, mm2
HOW TO USE

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

EXAMPLE

A tank of 2 m diameter: r = 1 m, A = 3.14 m2 of base.

QUICK CALCULATOR A = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

area circle tank round
Volume of a box MOST USED
V = l x w x h
SYMBOLS · V = volume; l = length; w = width; h = height
UNITS · m3, litres (1 m3 = 1000 litres)
HOW TO USE

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

EXAMPLE

A 3 x 1.5 x 1.2 m trailer = 5.4 m3 = 5,400 litres.

QUICK CALCULATOR V = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

volume box trailer tank
Mass from volume and density MOST USED
m = V x rho
SYMBOLS · m = mass; V = volume; rho = density
UNITS · kg, tonnes; m3; kg/m3 or kg/litre
HOW TO USE

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.

EXAMPLE

A 10 m3 heap of wheat at 750 kg/m3 = 7.5 tonnes.

QUICK CALCULATOR m = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

mass density volume tonnage weight
Area of a trapezoid
A = ((a + b) / 2) x h
SYMBOLS · A = area; a = short parallel side; b = long parallel side; h = perpendicular height
UNITS · m2
HOW TO USE

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

EXAMPLE

A field 30 m at the top, 50 m at the bottom, 60 m deep = 2,400 m2.

QUICK CALCULATOR A = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

area trapezoid field
Area of a triangle
A = (b x h) / 2
SYMBOLS · A = area; b = base; h = perpendicular height
UNITS · m2, cm2
HOW TO USE

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

EXAMPLE

A 10 m base with 4 m of height = 20 m2.

QUICK CALCULATOR A = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

area triangle gusset
Circumference of a circle
C = 2 x pi x r (or C = pi x d)
SYMBOLS · C = circumference; r = radius; d = diameter
UNITS · m, mm, ft
HOW TO USE

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

EXAMPLE

A 600 mm disc: C = 1,885 mm, so a 1,885 mm belt fits it.

QUICK CALCULATOR C = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

circle circumference belt
Fuel cost per hour
cost/hour = (litres per hour x price per litre)
SYMBOLS · litres per hour from the engine spec or a tank test; price per litre from the pump
UNITS · currency per hour
HOW TO USE

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.

EXAMPLE

18 L/h at 1.60 per litre = 28.80 per hour.

fuel cost machine rate
Millimetres to inches
inches = mm / 25.4
SYMBOLS · mm = millimetres; 25.4 = exact mm in one inch
UNITS · mm, inches
HOW TO USE

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.

EXAMPLE

A 19 mm spanner = 0.75 inch.

QUICK CALCULATOR inches = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

conversion millimetres inches spanner
Percentage of a quantity
amount = (percentage / 100) x quantity
SYMBOLS · percentage = the part per hundred; quantity = the whole
UNITS · varies
HOW TO USE

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

EXAMPLE

2.5% salt on 10 kg of meat = 250 g of salt.

QUICK CALCULATOR amount = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

percentage concentration salt moisture
Pounds per square inch to bar
bar = psi / 14.5038 (psi = bar x 14.5038)
SYMBOLS · psi = pounds per square inch; bar = 1 bar = 100,000 Pa
UNITS · psi, bar, kPa
HOW TO USE

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.

EXAMPLE

A sprayer at 3 bar = 43.5 psi.

QUICK CALCULATOR bar = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

conversion pressure psi bar tyre
Slope and gradient
gradient = rise / run ; slope % = (rise / run) x 100
SYMBOLS · rise = vertical change; run = horizontal distance
UNITS · m/m, %, degrees
HOW TO USE

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%.

EXAMPLE

1 m rise over 20 m = a gradient of 1 in 20, or 5%.

QUICK CALCULATOR gradient = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

slope gradient drainage roof ramp
Speed from distance and time
v = d / t
SYMBOLS · v = speed; d = distance; t = time
UNITS · km/h, m/s, mph
HOW TO USE

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.

EXAMPLE

12 km in 3 hours = 4 km/h.

QUICK CALCULATOR v = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

speed distance time
Volume of a cone
V = (1/3) x pi x r2 x h
SYMBOLS · V = volume; r = radius; h = perpendicular height
UNITS · m3, litres
HOW TO USE

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

EXAMPLE

A 3 m radius, 2 m high heap of grain = 18.85 m3 = 18,850 kg at 750 kg/m3.

QUICK CALCULATOR V = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

volume cone heap grain fertiliser
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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.

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Formulas collected and indexed with AI. The calculators are convenience tools; double-check every result before using it.