The equation W = m g links three quantities: weight W in newtons (N), mass m in kilograms (kg) and gravitational field strength g in N/kg. If you know two of them you can find the third by rearranging:
- weight = mass × g
- mass = weight ÷ g
- g = weight ÷ mass
Worked examples. An object with a weight of 360 N on Earth, where g is 10 N/kg, has a mass of 360 ÷ 10 = 36 kg. An object of mass 5 kg that weighs 8 N on the Moon is in a field of strength 8 ÷ 5 = 1.6 N/kg.
The equation also shows how the quantities change together. If the mass doubles in the same field, the weight doubles. If g is halved for the same object, its weight is halved. A probe of mass 80 kg has a weight of 800 N on Earth. On the Moon, where g is 1.6 N/kg, its mass is still 80 kg but its weight falls to 128 N.