The newton - Derived from SI Base Units (2024)

The newton (N) from mass (kg), length (m) and time (s)

This page contains a calculator for working out force in newtons (N) from the SI base units of mass (kg), length (m) and time (s), as well as calculators with the equation rearranged to make kg, m and s the subject. The formulas are shown together with other useful information and examples to try. The newton is the unit of force. The newton is a derived unit. Note that when written out fully the unit has a lower case n, i.e. newton, to distinguish it from the person it is named after: Isaac Newton (1643 - 1727). However, the letter denoting the unit is upper case, i.e. N. Enter all figures without commas. For example, enter 2,400 as 2400.

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Calculate force (N) from mass (kg), length (m) and time (s)

The equation for force derived from SI base units is given on the right. Example: A small passenger jet with a mass of 12,000 kg is accelerating along a runway at 3.2 metres per second. What is the force acting on the jet? In this case we simply enter the mass (12,000 kg) and the distance (3.2 m) covered in the time given (1 second) into the calculator and click Calculate, to show that the answer is 38,400 newtons. Note that mass / time squared (m/s 2 ) is acceleration.

Calculate mass (kg) from force (N), distance (m) and time (s)

The equation for mass is given above right. Example: We are told an object is moved with a force of 200 newtons for 4 seconds and in doing so covered a distance of 20 metres. What was the mass of the object? Entering the force (200 N), time (4 s) and distance (20 m) and clicking Calculate tells us that the mass was 160 kilograms.

The equation for mass is: Where: kg = the mass (kilograms) F = the force (newtons, N) s 2 = the time (seconds, squared) m = the distance (metres)

Quick Facts 1 tonne (t) = 1,000 kilograms (kg) 1 ton (US) = 907.185 kilograms 1 ton (UK) = 1016.05 kilograms 1 kilonewton (kN) = 1,000 newtons (N) So 1 newton is 0.001 kN

Calculate distance (m) from force (N), time (s) and mass (kg)

The equation for distance is given above right. Example: A car with a mass of 1,200 kg is driven with a force of 2 kN for 8 seconds. How far did it travel? The answer can be obtained by entering the force (2,000 N), the time (8 s) and the mass (1,200 kg) into the calculator and clicking Calculate. Doing so shows that the answer is 106.67 metres.

The equation for distance is: Where: m = the distance (metres) F = the force (newtons, N) s 2 = the time (seconds, squared) kg = the mass (kilograms)

The equation for force is: Where: F = the force (newtons, N) kg = the mass (kilograms) m = the distance (metres) s 2 = the time (seconds, squared)

Calculate time (s) from mass (kg), distance (m) and force (N)

The equation for time is given above right. Example: An object is moved with a force of 1.6 kN a distance of 80 m. The object has a mass of 62 kg. How long did it take? The answer can be obtained by entering the force (1,600 N), the distance (80 m) and the mass (62 kg) into the calculator and clicking Calculate. Doing so shows that the answer is 1.76 seconds.

The equation for time is: Where: s = the time (seconds) F = the force (newtons, N) m = the distance (metres) kg = the mass (kilograms)

Putting it into context From the example given, an average adult weighs about 62kg, and the result showed that the speed was 80m / 1.76s = 45.5 metres per second. This is close to 102 mph, i.e. about as fast as a fast train, so a person on that train is moving with a force of about 1,600 newtons.

- As derived from SI base units -

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