How to calculate linear momentum
Momentum combines mass with velocity and has direction. In one-dimensional problems, choose one direction as positive before using the signs.
What the formula is saying
Multiply mass by signed velocity: p = mv. This differs from kinetic energy, which squares speed and includes one half.
Read the symbols in plain language
- m
- Masskg
- v
- Velocitym/s
Sort out the units first
kg × m/s = kg·m/s, also equivalent to N·s. Use m/s, and state the chosen positive direction when interpreting a sign.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- m · Mass
- 10 kg
- v · Velocity
- 3 m/s
Identify the moving mass
Use mass in kilograms, not weight in newtons. Weight includes gravity; momentum does not.
(10) = 10 kgMultiply by velocity
The momentum points in the velocity direction for positive mass.
(10) × (3) = 30 kg·m/s
Does this worked answer make sense?
With the same velocity, doubling mass doubles momentum. The example gives 30 kg·m/s in the chosen positive direction.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- m · Mass
- 4 kg
- v · Velocity
- 5 m/s
Find: linear momentum
A hint, not the answer
Multiply mass by signed velocity: p = mv. This differs from kinetic energy, which squares speed and includes one half.
kg × m/s = kg·m/s, also equivalent to N·s. Use m/s, and state the chosen positive direction when interpreting a sign.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the moving mass
Use mass in kilograms, not weight in newtons. Weight includes gravity; momentum does not.
(4) = 4 kgMultiply by velocity
The momentum points in the velocity direction for positive mass.
(4) × (5) = 20 kg·m/s
Avoid the common trap
Do not square velocity: that would be part of an energy calculation. Add momenta with signs or vector components, not just magnitudes.
When this method applies — and when it does not
Classical linear momentum. Conservation of a system’s momentum requires the appropriate external-force conditions.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.