The weight equation

The weight equation is W = mg: weight (N) = mass (kg) × gravitational field strength (N/kg). Weight is the force of gravity on an object, so it is measured in newtons, while mass is the amount of matter, measured in kilograms. On Earth, g is about 9.8 N/kg, so a 55 kg person weighs 55 × 9.8 = 539 N. On the Moon, where g is smaller, the same person has the same mass but a smaller weight.

The weight equation, W = mg

AQA's GCSE Physics specification defines weight as the force acting on an object due to gravity, and says that the weight of an object depends on the gravitational field strength at the point where the object is. It gives W = mg as an equation to recall and apply, and it is also on AQA's equations sheet. In any calculation, the value of g will be given: at GCSE this is usually 9.8 N/kg.

Rearranging the weight equation

Weight vs mass

AQA's specification states that weight and mass are directly proportional, W ∝ m, and that weight is measured using a calibrated spring balance, a newtonmeter. Double the mass and the weight doubles, as long as g stays the same. In everyday speech people say "weight" when they mean mass, as in "I weigh 55 kilograms", but in physics weight is always a force in newtons.

Weight equation worked examples

Example 1: finding weight

A student has a mass of 55 kg. Find their weight on Earth. Use g = 9.8 N/kg.

Example 2: finding mass

A suitcase weighs 196 N on Earth. Find its mass. Use g = 9.8 N/kg.

Example 3: mass in grams

An apple has a mass of 250 g. Find its weight. Use g = 9.8 N/kg.

Convert: 250 g = 0.25 kg.

Example 4: finding g

A 4.0 kg rock weighs 14.8 N on another planet. Find the gravitational field strength there.

Example 5: on the Moon

NASA's fact sheet gives the Moon's surface gravity as 1.62 m/s², so g on the Moon is about 1.6 N/kg. Find the weight of a 12 kg rover on the Moon and on Earth.

On the Moon: W = 12 × 1.6 = 19.2 N. On Earth: W = 12 × 9.8 = 117.6 N. The rover's mass is 12 kg in both places; only its weight changes. Our guide to gravitational field strength gives g on other planets and explains where it comes from.

Now sort some quantities into mass and weight, then press Mark to check them in the course.

Weight and the newtonmeter

A newtonmeter is a spring balance marked in newtons. Hang an object from it, and the spring stretches until its upward force balances the object's weight. A 300 g mass hanging from a newtonmeter on Earth reads 0.3 × 9.8 = 2.94 N. Because weight is proportional to mass, the same newtonmeter would read about a sixth as much on the Moon, while a balance comparing the mass with standard masses would give the same answer anywhere.

Weight acts at the centre of mass

AQA's specification says the weight of an object may be considered to act at a single point, its centre of mass. For a uniform, regular object such as a ruler or a block, that is its centre. This is why the weight arrow on a free body diagram is drawn from the middle of the object, and why a uniform beam's weight is treated as acting at its midpoint in moments problems. Our guide to centre of mass covers irregular shapes.

Weight and Newton's second law

When an object falls freely, the only force on it is its weight, and its acceleration is g. Putting these into Newton's second law, F = ma, gives W = mg: the weight equation is F = ma for a falling object. That is why, without air resistance, heavy and light objects fall with the same acceleration. Their weights differ, but so do their masses, in the same proportion. Our guide to Newton's second law explains more. The Force Calculator works out weight from mass and g, as well as F = ma.

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Force Calculator

Use F = ma to find force, mass, acceleration and weight

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Common mistakes

• Giving weight in kg. Weight is a force, in newtons. Mass is in kg.
• Mass in grams. Convert to kg first: 250 g is 0.25 kg.
• Saying mass changes on the Moon. Mass stays the same; weight changes because g changes.
• Using the wrong value of g. Use the value the question gives; different questions use 9.8, 9.81 or 10 N/kg.
• Confusing g with grams. In W = mg, g is the gravitational field strength, not grams.

Practise forces in a short timed paper

GCSE Physics Foundation and GCSE Physics Higher each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so weight and forces turn up regularly but not in every paper.

Read next

Physics · MechanicsForce calculator: F = ma, weight and mass with stepsFind force, mass or acceleration from F = ma, and weight from W = mg on Earth, the Moon or Mars, with unit conversions and worked examples.