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    Weight Calculator (W = mg)

    GCSE PhysicsAQAEdexcelOCRFoundation & Higher

    Find weight, mass or gravitational field strength using W = m × g. g is set to 9.8 N/kg; change it for the Moon or another planet.

    Quick answer

    Weight = mass × gravitational field strength. Use mass in kg and g in N/kg to get newtons. For example, a 65 kg student on Earth (g = 9.8 N/kg) has a weight of 65 × 9.8 = 637 N. Weight is a force; mass is not.

    By Engr. Mehmood Kakar · Updated

    W = m × g
    Find:

    On Earth g is about 9.8 N/kg. Use the value the question gives (for example 1.6 N/kg on the Moon).

    Simulation

    Same mass, different weight

    Hang a mass on a newtonmeter and change where you are. The mass stays the same; the weight changes with the gravitational field strength.

    2 kg

    Mass (kg) is the amount of matter and doesn’t change. Weight (N) is the force of gravity on it, so it depends on where you are.

    Put these numbers in the calculator above

    How to calculate weight

    Weight is the force of gravity on an object. It depends on the object's mass and on the gravitational field strength where it is:

    weight = mass × gravitational field strength

    • W is weight in newtons (N)
    • m is mass in kilograms (kg)
    • g is gravitational field strength in newtons per kilogram (N/kg)

    A 65 kg student on Earth, where g is about 9.8 N/kg, has a weight of 65 × 9.8 = 637 N.

    Mass and weight are not the same thing. Mass is the amount of matter in an object, in kilograms, and it is the same everywhere. Weight is a force, in newtons, and it changes with g. The same student on the Moon, where g is about 1.6 N/kg, would weigh 65 × 1.6 = 104 N but still have a mass of 65 kg.

    Weight is measured with a newtonmeter (a calibrated spring balance). Weight and mass are directly proportional: double the mass and the weight doubles.

    Common mistakes that cost marks

    1. Giving weight in kilograms. Weight is a force, so its unit is newtons (N). Mass is in kilograms.
    2. Not converting grams. 500 g is 0.5 kg.
    3. Using 10 instead of 9.8. Use the value of g the question gives you.
    4. Saying mass changes on the Moon. Mass stays the same; only weight changes, because g is smaller.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A student has a mass of 65 kg. g = 9.8 N/kg. Calculate her weight.[2 marks]
    1. W = m × g
    2. W = 65 × 9.8
    3. W = 637 N
    Q2A crate has a weight of 490 N. g = 9.8 N/kg. Calculate its mass.[3 marks]
    1. Rearrange: m = W ÷ g
    2. m = 490 ÷ 9.8
    3. m = 50 kg
    Q3A 20 kg probe on Mars has a weight of 74 N. Calculate the gravitational field strength on Mars.[3 marks]
    1. Rearrange: g = W ÷ m
    2. g = 74 ÷ 20
    3. g = 3.7 N/kg

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation for weight?

    Weight = mass × gravitational field strength (W = mg). Weight is in newtons (N), mass in kilograms (kg) and g in newtons per kilogram (N/kg).

    What is the difference between mass and weight?

    Mass is the amount of matter in an object, measured in kilograms, and it is the same everywhere. Weight is the force of gravity on that mass, measured in newtons, and it depends on the gravitational field strength.

    What value of g should I use?

    Use the value given in the question. On Earth it is about 9.8 N/kg; some questions use 10 N/kg.

    What is weight measured with?

    A newtonmeter, which is a calibrated spring balance.