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
Workshop
41 formulas
The clamp force is what you actually want, and it is torque that gives it. Use a torque wrench on head bolts and wheel nuts, and never a guess on anything that matters.
A 10 mm bolt needing 8 kN of clamp: (0.20 x 8,000 x 10) / 1000 = 16 N.m.
For a footing, a step, a post hole or a slab. A 1:2:4 mix is for footings and paths, 1:2:5 for a mass base and 1:1.5:3 for a stronger mix. See Mixing Concrete.
A 1 m x 1 m x 0.15 m pad needs 0.15 m3, so about 1 bag of cement, 0.1 m3 of sand and 0.15 m3 of stone.
The wire needs to be tight and the post needs to be firm. See Setting Fence Posts and Fencing Wire And Straining.
A 100 m fence with posts at 2.5 m needs 41 posts.
How timber is sold in the trade, and how you check a delivery. A rough conversion is 1 board foot about 0.0024 m3.
A 25 x 150 x 4.8 m board is (1 x 6 x 15.7) / 12 = 7.8 board feet.
For sizing a water butt or a tank for the yard and the animals. See Water Troughs And Algae.
A 10 m x 10 m roof in a 20 mm storm collects 2,000 litres, which is a full water butt and a bit.
Multiply thickness x width x length, then divide by 12. This is how sawn timber is measured and sold. A 2-inch plank 8 inches wide and 10 feet long is 13.3 board feet.
2 x 8 x 10 / 12 = 13.3 board feet.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Divide the fence length by the post spacing, then add one for the end post. Round up to the next whole post. Add strainer posts at corners and gates separately.
100 m fence at 3 m spacing: 100 / 3 + 1 = 34 posts.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Chain pitch is stamped on the drive link or the bar. Multiply the pitch in inches by 25.4 to get the matching round file diameter in millimetres. Common: 3/8 inch pitch = 9.5 mm file; 0.325 inch = 8.3 mm file; 0.404 inch = 10.3 mm file.
3/8 inch = 0.375 x 25.4 = 9.5 mm round file.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Drying grain needs moving air, not hot air. If the fan is sized for the empty bin it will not cope with a full one. See Storing Grain.
A 400 mm fan at 10 m/s: 1.3 x 10 x 0.126 = 1.6 m3/s, about 80 W of heat capacity.
For a V-belt or a flat belt on a machine you have built. Add about 5% for tension and stretch, then cut to the nearest standard size.
C = 400, D = 200, d = 80: 800 + 440 + 14 = 1,254 mm, so buy a 1,300 mm belt.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Measure from the edge of the hole to the edge of the flange, not to where you think the bend goes. Add the allowance to the flat length before cutting.
A 10 mm radius bend at 90 degrees in steel: 1.57 x 10 = 15.7 mm of extra metal.
For ordering. Always order 5% more than the calculation for cuts and breakages.
440 x 215 blocks: 1 / (0.45 x 0.225) = 9.9, so 10 blocks a square metre.
Long runs need bigger cable, not bigger fuses. Measure the run, use the table, and check the breaker size next.
A 30 m run at 16 A on 2.5 mm2: (2 x 30 x 16 x 11.7) / 1000 = 11.2 V, which is 5% of 230 V.
For chain wear, sprocket sizing and the speed of a bicycle. Multiply by 3.6 for km/h.
A 48 tooth sprocket at 100 rpm on 12.7 mm pitch: 0.0127 x 48 x 100 / 60 = 1.02 m/s.
Set posts in concrete for a gate, a fence or a sign. A quick-setting post mix works in cold weather. See Setting Fence Posts.
A 250 mm hole 1 m deep = 0.049 m3, which is about 2.5 bags of post mix.
Set the speed from the tool material and the work, then let the chips tell you if you are wrong. Blue chips mean too fast.
Cutting 20 mm steel at 25 m/min: (1000 x 25) / (pi x 20) = 398 rpm.
For working out the cost of a job and whether a machine is worth keeping. Idle burn is a surprising share of a small engine's fuel.
A 30 kW engine at 240 g/kWh uses (30 x 240) / 840 / 1,000 = 8.6 L/h.
Friction and heat are the losses. A lower efficiency means more fuel, more electricity and more heat to shift away.
A 1 kW motor driving a 400 W pump is 40% efficient, which means something is rubbing.
For working out whether a supply will carry a heater, a welder or a three-phase motor. See Three Phase And Single Phase.
A 3 kW heater at 230 V draws 13 A, so a 13 A circuit is at its limit.
Work out the whole foundation before ordering, and add 10% for the lumps. Dig in a straight line, and set the pegs before the mixer arrives.
10 m x 0.4 m x 0.5 m = 2.0 m3 of concrete.
The standard way to compare a van, a tractor and a car. Keep a running total between fills.
60 L over 400 km = 15 L/100km.
Whether you are rebuilding a gearbox, a mixer or a seedling thinner. Work it out on paper before you order the gears.
A 16 tooth pinion driving a 48 tooth gear is a 3:1 reduction.
Water on a level yard is water that never leaves. Get the fall right with a laser level or a long spirit level and a pegged board. See Underground Pipe And Trenches.
A 20 m yard falling 1 in 80 drops 250 mm from end to end.
Why a door jams in a wet winter, why a solid wooden worktop cups, and why a gate needs a gap. Plan for the movement.
A 1,000 mm fence rail moving 8% in moisture: 1,000 x 0.08 x 0.03 = 2.4 mm.
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.
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.
To check whether a motor, an engine or a hand tool has the power for the job, and to compare an electric motor with a petrol one.
200 N.m at 720 rpm: (200 x 2 x pi x 720) / 60 = 15,080 W, or 15 kW.
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.
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.
For ordering felt, tiles, battens and underlay. Always order the underlay and never skimp on it.
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.
The pitch decides the tile angle, the felt laps and how much water the roof throws off the building. The run is half the span for a normal gable.
A 3 m rise over a 4 m run is 36.9 degrees.
The number that decides whether a second machine, a bigger one, or hiring it in makes sense.
A 12,000 euro tractor working 500 hours a year at 9 L/h and 1.60 a litre burns about 7,200 euro a year in fuel alone.
Mixing by bucket. A wheelbarrow of sand is about 0.07 m3, so a bucket is roughly 0.014 m3. See Mixing Concrete.
A 0.5 m3 batch of 1:2:4 needs 0.1 m3 of cement, 0.2 m3 of sand and 0.4 m3 of stone.
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.
A 3/32 in gullet gives 1 / (2 x 0.094) = 5.3 TPI, a rip saw.
A 300 ml cartridge of a 6 mm bead does about 10 m; a 10 mm bead does about 3.5 m. Get the bead size right or you will run out halfway along the shed roof.
300 ml at a 10 mm bead: 300 / 79 = 3.8 m.
For a shed, a fence charger or a small system. Size for the dark weeks of winter, not the bright ones. See Solar And Battery Storage.
A 200 W panel for 4 hours of sun gives 800 Wh a day; for three dark days on a 12 V battery at 50% depth: (800 x 3) / (12 x 0.5 x 0.9) = 444 Ah.
Set the height of the first step from the finished floor and the landing, then work down. See Building A Step.
A 900 mm rise with 180 mm steps gives 5 steps, so the going can be 270 mm.
Concrete gains most of its strength in the first week. Keep it damp for the first three days and cover it if it is hot or frosty.
A gate post in concrete should stand for 48 hours before the gate goes on.
Water is the enemy of concrete strength. Never add water to make it easier to work; add cement or use a plasticiser instead. See Mixing Concrete.
A footing with 40 litres of water and 50 kg of cement has a 0.8 ratio, so about 10 MPa, which is fine for a post.
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.
The physics behind leverage. A bar is a machine: it does not change the work, only the force and the distance.
Lifting 500 N through 0.3 m is 150 J of work whatever lever you use.
SOURCES & PROVENANCE
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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.