Momentum Calculator
Linear momentum from mass and velocity in SI and imperial units.
What it does
Momentum measures motion as mass times velocity. It decides how hard moving things are to stop and how they share motion in collisions, growing in direct proportion to both mass and speed.
The tool above takes mass and velocity in metric or imperial. It returns SI momentum with pound force seconds beside it, plus the speed converted for an input check.
The default of 1000 kg at 20 m/s carries 20,000 kg·m/s, about 4,496 lbf·s at 72 km/h. Unlike energy, doubling the speed only doubles this number instead of quadrupling it.
The p = mv form follows NASA motion references with the same conservation treatment in Khan Academy physics units. Both separate it cleanly from kinetic energy, which squares the velocity instead.
How to use
- Pick metric or imperial for your numbers.
- Enter the moving mass in kg or lb.
- Enter the velocity in m/s or mph.
- Read SI momentum first for the standard answer.
- Use lbf·s and the speed check for shop math.
Formula
- p
- Linear momentum carried by the motion.
- mass
- Kilos or converted pounds in motion.
- velocity
- Speed with direction (magnitude used here).
Direction is ignored here; collisions need signs per axis with the total conserved. Zero velocity always reads zero momentum at any mass.
Worked example
Example: 1000 kg at 20 m/s
Metric defaults: 1000 kg, 20 m/s.
- Multiply: 1000 x 20 = 20,000 kg·m/s.
- Imperial: 20,000 x 0.224809 = 4,496 lbf·s.
- Speed check: 20 x 3.6 = 72 km/h.
- Energy contrast: same motion holds 200,000 J, which squares speed.
- Tool shows 20,000 kg·m/s, 4,496 lbf·s, 72 km/h.
Reference table
| Speed | Momentum | Kinetic energy |
|---|---|---|
| 36 km/h (10 m/s) | 10,000 kg·m/s | 50,000 J |
| 72 km/h (20 m/s) | 20,000 kg·m/s | 200,000 J |
| 144 km/h (40 m/s) | 40,000 kg·m/s | 800,000 J |
Limits
- Magnitude only; collision directions need signs.
- Classical speeds only.
- Point mass assumed.
- External impulses during impact sit outside.
Common mistakes
- Squaring velocity like kinetic energy.
- Mixing mph with kilos without converting.
- Adding momenta pointing different ways as plain sums.
- Reading momentum as force (needs per second).
- Forgetting direction signs in recoil math.
Try it yourself
Quick checks. Answers sit tucked under each question.
5 kg at 10 m/s?
50 kg·m/s, about 11 lbf·s.
Double 20 to 40 m/s at 1000 kg?
40,000 kg·m/s: doubled, not quadrupled.
Stopped car momentum?
Zero at zero velocity, whatever the mass.
Questions
What is the momentum formula?
Mass times velocity. 1000 kg at 20 m/s is 20,000 kg·m/s.
Momentum vs kinetic energy?
Momentum scales linearly with speed, energy squares it. Both grow with mass.
What are the units?
kg·m/s in SI, lbf·s imperial. Multiply SI by 0.224809.
Is momentum conserved?
Total holds in collisions without external impulses; pieces trade shares.
Why does direction matter?
Opposite motions cancel in sums. Signs per axis keep crash math honest.
Can momentum be negative?
With signs, yes along an axis. Magnitudes here stay zero or above.