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Force and change in momentum calculator

GCSEA-level Motion

The resultant force equals the rate of change of momentum. This is Newton’s second law written with momentum.

F = Δp / Δt

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

FResultant force to find 3000 N

ΔpChange in momentum

ΔtTime taken

Significant figures

Working

Write the equation
F = Δp / Δt
Substitute the values
F = 60 ÷ 0.02
Calculate
F = 3000 N
Give the answer to 3 significant figures
F = 3000 N

Worked example

Find F, the resultant force. Given: change in momentum Δp = 60.0 kg m/s; time taken Δt = 0.0200 s.

Write the equation
F = Δp / Δt
Substitute the values
F = 60 ÷ 0.02
Calculate
F = 3000 N
Give the answer to 3 significant figures
F = 3000 N

Symbols and units

Symbol	Quantity	SI unit
F	Resultant force	N
Δp	Change in momentum	kg m/s
Δt	Time taken	s

Force and change in momentum: rearranged

To find resultant force: F = Δp / Δt
To find change in momentum: Δp = F Δt
To find time taken: Δt = Δp / F

Exam tip

A longer collision time means a smaller force for the same change in momentum. That is how crumple zones and airbags work.

Common questions

What is the formula for force and change in momentum?

The equation is F = Δp / Δt, where F is the resultant force (N); Δp is the change in momentum (kg m/s); Δt is the time taken (s).

What units should I use for force and change in momentum?

In SI units: resultant force in N, change in momentum in kg m/s, time taken in s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange F = Δp / Δt?

Rearranging gives these forms: to find resultant force: F = Δp / Δt. to find change in momentum: Δp = F Δt. to find time taken: Δt = Δp / F.

Practise force and change in momentum questions

Include unit conversions (km, g, minutes…)

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

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