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Momentum calculator

GCSEA-level Motion

Momentum is mass multiplied by velocity. It is a vector, so direction matters.

p = m v

This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

18000 kg m/s

Working

  1. Write the equation
    p = m v
  2. Substitute the values
    p = 1500 × 12
  3. Calculate
    p = 18000 kg m/s
  4. Give the answer to 3 significant figures
    p = 18000 kg m/s
    In standard form: 1.80 × 104 kg m/s

Worked example

Find p, the momentum. Given: mass m = 1500 kg; velocity v = 12.0 m/s.

  1. Write the equation
    p = m v
  2. Substitute the values
    p = 1500 × 12
  3. Calculate
    p = 18000 kg m/s
  4. Give the answer to 3 significant figures
    p = 18000 kg m/s
    In standard form: 1.80 × 104 kg m/s

Symbols and units

SymbolQuantitySI unit
pMomentumkg m/s
mMasskg
vVelocitym/s

Momentum: rearranged

  • To find momentum: p = m v
  • To find mass: m = p / v
  • To find velocity: v = p / m

Exam tip

In collision questions, give opposite directions opposite signs.

Common questions

What is the formula for momentum?

The equation is p = m v, where p is the momentum (kg m/s); m is the mass (kg); v is the velocity (m/s).

What units should I use for momentum?

In SI units: momentum in kg m/s, mass in kg, velocity in m/s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange p = m v?

Rearranging gives these forms: to find momentum: p = m v. to find mass: m = p / v. to find velocity: v = p / m.

Practise momentum questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

Read the full explanation on the Momentum formula page. More motion equations: Speed, distance and time, Acceleration, Final velocity, Velocity squared, Displacement under constant acceleration, Displacement from average velocity, Force and change in momentum, Centripetal force. See the full list on the physics equation calculator page.