Momentum Calculator
Calculate linear momentum from mass and velocity (p = mv), or from force and time (p = F × t).
What Is Momentum?
Momentum (p) measures how hard it is to stop a moving object. p = mass × velocity. A heavy truck at low speed can have the same momentum as a bullet at high speed.
Choose your calculation method
Use "p = mv" if you know mass and velocity. Use "p = F × t" if you know force and time.
Enter the known values
Input mass (kg) and velocity (m/s), or force (N) and time (s).
Calculate momentum
The calculator shows momentum in kg·m/s with the formula used.
| Object | Mass | Velocity | Momentum |
|---|---|---|---|
| Baseball (pitched) | 0.145 kg | 40 m/s | 5.8 kg·m/s |
| Car (city driving) | 1500 kg | 15 m/s | 22,500 kg·m/s |
| Bullet (rifle) | 0.01 kg | 900 m/s | 9 kg·m/s |
| Person (running) | 70 kg | 5 m/s | 350 kg·m/s |
Momentum is a vector quantity—it has both magnitude and direction. The direction of momentum is the same as the direction of velocity.
Conservation of Momentum
In a closed system, total momentum before a collision equals total momentum after. This principle explains why a gun recoils when fired—the bullet gains forward momentum, the gun gains equal backward momentum.
Impulse-Momentum Theorem
Impulse (F × t) equals change in momentum. A small force applied for a long time can produce the same momentum change as a large force applied briefly. This is why airbags work—they extend the time of impact, reducing the force.
Elastic vs Inelastic Collisions
In elastic collisions, both momentum and kinetic energy are conserved (billiard balls). In inelastic collisions, only momentum is conserved—some energy becomes heat or deformation (car crashes).
What's the difference between momentum and inertia?
Inertia is an object's resistance to changes in motion—it depends only on mass. Momentum depends on both mass and velocity. A stationary object has inertia but zero momentum.
Can momentum be negative?
Yes. Momentum is a vector. If you define right as positive, an object moving left has negative momentum. In 1D problems, sign indicates direction.
How is impulse related to momentum?
Impulse equals change in momentum: J = Δp = F × t. Pushing a shopping cart for 5 seconds with 10 N gives an impulse of 50 N·s, changing its momentum by 50 kg·m/s.
Why do fielders pull their hands back when catching a ball?
Pulling back increases the time of impact. Since F = Δp/t, increasing t reduces the force on their hands. Same momentum change, less painful force.
Is momentum conserved in real collisions?
Yes, if you include all objects involved. A car hitting a wall transfers momentum to the Earth through the wall. The Earth's huge mass means its velocity change is imperceptible, but momentum is still conserved.
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