Force Calculator

How to use the force calculator

1. Fill in the fields — they start with a worked example.
2. Read the answer, and the arithmetic shown beneath it.
3. Copy the results, or adjust the inputs to compare scenarios.

About this tool

Force is mass times acceleration, and the formula is the easy part. What goes wrong is the units, because two of the words involved mean different things in different systems and nobody says which they meant.

A kilogram is mass. A pound, in ordinary use, is also mass — but a pound-force is the weight of that mass under standard gravity, and the two are written the same way in most documents. Newtons are unambiguous, which is why the answer here leads with them and gives the others alongside: a figure that is nine and a bit times larger or smaller than expected is almost always this confusion rather than an arithmetic slip.

Weight is the case people actually want most of the time. An object's weight is the force gravity exerts on it, so it is mass times 9.80665 metres per second squared at the Earth's surface. A 70-kilogram person weighs about 687 newtons, and that number surprises people precisely because everyday speech uses the mass figure for weight.

Gravity is not constant across the Earth either — it varies by about half a per cent between the poles and the equator, and more with altitude. That rarely matters, but it is the reason the standard value is defined rather than measured, and the reason precision scales are calibrated where they are used.

Common uses

• Converting a mass to the force it exerts under gravity.
• Working out the force needed to accelerate a known mass.
• Checking a specification given in pounds-force against one in newtons.

Frequently asked questions

What is the difference between a pound and a pound-force?

A pound is mass; a pound-force is the weight of one pound under standard gravity, about 4.448 newtons. They are written identically in most documents, which is the usual source of confusion.

How much does a 70 kg person weigh in newtons?

About 687 newtons, being 70 × 9.80665. Everyday speech uses the mass figure for weight, which is why the number looks unfamiliar.

Is gravity the same everywhere?

No. It varies by roughly half a per cent between the poles and the equator, and falls with altitude. The 9.80665 figure is a defined standard rather than a local measurement.