Units of force and their equivalents
| Unit | Symbol | In newtons |
|---|---|---|
| Newton | N | 1 Nbase unit |
| Kilonewton | kN | 1,000 N |
| Kilogram-force | kgf | 9.80665 N |
| Pound-force | lbf | 4.44822 N |
| Dyne | dyn | 0.00001 N |
| Ounce-force | ozf | 0.278014 N |
| Tonne-force | tf | 9,807 N |
Frequently asked questions
How many newtons in a kilogram?
A kilogram is not made of newtons, it is a mass. But it weighs 9.80665 newtons under standard gravity, and that is exactly what a kilogram-force is. A 70 kg person therefore presses on the ground with 686.5 newtons. On the Moon the same mass would press with only 114 newtons, one sixth, while its mass would not have changed by a gram.
Why does a scale show kilograms?
Because it measures a force and divides it by 9.80665 before showing you the result. The load cell knows only the force crushing it, the display assumes terrestrial gravity. That is why a scale calibrated in Europe reads slightly off at the equator, where gravity is 9.78 against 9.83 at the poles, and would be out by a factor of six on the Moon.
Is torque given in N·m or in kgf·m?
In newton-metres in any recent documentation, but older manuals and some Japanese and Italian equipment still use the kilogram-force-metre. One kgf·m is 9.80665 N·m: a torque of 10 kgf·m calls for 98 N·m. American torque wrenches are graduated in pound-feet, and one pound-foot is 1.3558 N·m, so 50 lbf·ft is 67.8 N·m.
How much force is a 2-tonne jack?
19.6 kilonewtons. The tonnage of a jack, a press or a hoist counts in tonnes-force, and one tonne-force is a thousand kilograms-force, that is 9.80665 kilonewtons. A workshop press rated at 20 tonnes therefore delivers 196 kN. The trap comes from North America, where the short ton as a force is 2,000 pounds-force, or 8.896 kilonewtons: a 20-ton press there produces 178 kN, nine per cent less than its European twin at the same figure.
Why can you push a car you could never lift?
Because what holds it back is not its weight but its rolling resistance. A 1,500 kilogram car weighs 14.7 kilonewtons, yet on the flat and on properly inflated tyres one to one and a half per cent of that weight is enough to keep it moving, that is 150 to 220 newtons, the effort of lifting 15 to 22 kilograms. Getting it going costs more than keeping it going. On a five per cent slope you must add five per cent of the weight, 735 newtons, which is why a badly braked car rolls away on its own and is never caught.
The newton is only seventy-five years old
The unit of force has borne its name only since 1948, when the ninth General Conference on Weights and Measures christened it. Before that, engineers worked in kilograms-force, which is why pre-war factory drawings are in kgf where today's are in N. The newton is not a base unit but a combination: one kilogram-metre per second squared, that is the force that accelerates one kilogram by one metre per second every second.
The dyne, meanwhile, survives where you would not expect it. It is ten micronewtons, useless in mechanics, but surface tension is still measured in dynes per centimetre in printing and in plastic film treatment. A film must reach about thirty-eight dynes per centimetre for ink to stick rather than bead, and the test pens sold to printers carry that scale. One dyne per centimetre is one millinewton per metre: the value has not changed, only the trade's vocabulary held on.