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FORMULA SHELF 8 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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Agronomy 2 formulas

Sprayer litres per hectare MOST USED
L/ha = (nozzle output in L/min x 600) / (speed in km/h x boom width in m)
SYMBOLS · 600 = 60 minutes in an hour x 1,000 m in a kilometre, divided by 100 to change hectares to square metres
UNITS · L/ha
HOW TO USE

Every sprayer book starts with this. Get the volume right and the dose per hectare is right. Measure a nozzle with a jug, and time the pass over 100 m.

EXAMPLE

A 2 L/min nozzle at 8 km/h on a 6 m boom: (2 x 600) / (8 x 6) = 250 L/ha.

sprayer nozzle volume rate boom herbicide
Sprayer output calibration MOST USED
O = (F x 600) / (S x W)
SYMBOLS · O = output (litres per hectare); F = flow per nozzle (litres per minute); S = speed (km per hour); W = nozzle spacing (metres)
UNITS · litres per hectare
HOW TO USE

Catch the output from one nozzle for one minute to get flow. Measure your forward speed and the nozzle spacing on the boom. This tells you how many litres per hectare you are putting down, so you can mix the right amount of chemical in the tank.

EXAMPLE

1.5 L/min x 600 / (8 km/h x 0.5 m) = 225 L/ha.

QUICK CALCULATOR O = result
Enter values above.

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

sprayer calibration spraying chemical agronomy

Workshop 4 formulas

Efficiency of a machine
efficiency % = (useful output / input) x 100
SYMBOLS · a gearbox is 95-98%, a chain drive 96-98%, a screw jack 20-40%, an electric motor 85-95%
UNITS · %
HOW TO USE

Friction and heat are the losses. A lower efficiency means more fuel, more electricity and more heat to shift away.

EXAMPLE

A 1 kW motor driving a 400 W pump is 40% efficient, which means something is rubbing.

efficiency losses friction machine
Gear ratio and overall ratio
ratio = teeth on the driven gear / teeth on the driving gear ; overall ratio = the product of each ratio
SYMBOLS · a ratio above 1 turns the output slower and stronger
UNITS · ratio
HOW TO USE

Whether you are rebuilding a gearbox, a mixer or a seedling thinner. Work it out on paper before you order the gears.

EXAMPLE

A 16 tooth pinion driving a 48 tooth gear is a 3:1 reduction.

gear ratio gearbox pinion reduction
Roof area for covering
area = footprint x sqrt(1 + pitch2) for each slope
SYMBOLS · the footprint is the length x width of the building; add 10-15% for the waste at the edges and the ridge
UNITS · m2
HOW TO USE

For ordering felt, tiles, battens and underlay. Always order the underlay and never skimp on it.

EXAMPLE

A 10 m x 6 m building at a pitch of 0.7: 60 x 1.22 = 73 m2 a slope, so 147 m2 for both.

roof area felt tiles underlay
Saw teeth per inch
TPI = 1 / (2 x gullet depth in inches)
SYMBOLS · for a rip cut in hardwood use 4-6 TPI, for a crosscut 8-12 TPI, for a hand saw 10-14 TPI
UNITS · teeth per inch
HOW TO USE

The difference between a saw that cuts along the grain and one that cuts across it. A rip saw has few deep teeth; a crosscut saw has many fine ones.

EXAMPLE

A 3/32 in gullet gives 1 / (2 x 0.094) = 5.3 TPI, a rip saw.

saw tpi teeth rip cut crosscut

Energy 2 formulas

Solar array output MOST USED
P = irradiance x area x efficiency
SYMBOLS · irradiance in W/m2 - about 1,000 at midday on a clear summer day, 200 on an overcast winter day; efficiency typically 0.15 to 0.22 for a panel
UNITS · watts (W)
HOW TO USE

For sizing a solar array for the electric fence, the lights or a small freezer. Multiply the panel area by the irradiance you can count on, not the best case.

EXAMPLE

2 m2 of panel at 800 W/m2 and 20% gives 320 W.

solar panel irradiance electric fence power
Heat pump coefficient of performance
COP = heat output (W) / electrical input (W)
SYMBOLS · a good heat pump has a COP of 3 to 4; an electric heater has a COP of 1
UNITS · dimensionless
HOW TO USE

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.

EXAMPLE

A 500 W heat pump with a COP of 3.5 gives 1,750 W of heat.

heat pump cop efficiency heating electricity
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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.