How much momentum is in motion.
Enter a mass and a velocity to get momentum from p = m x v, or solve backward for the mass or velocity you need. See the force it takes to stop, the kinetic energy for comparison, and why airbags save lives.
The motion
Add a force and a time, or a stopping time, to explore impulse = force x time = change in momentum.
What this momentum means
Momentum grows with velocity
Momentum vs velocity at this mass
Stopping scorecard
Momentum at different speeds
Same mass, different velocities. Notice momentum rises in a straight line while kinetic energy climbs far faster.
| Velocity (m/s) | Velocity | Momentum (kg m/s) | Kinetic energy (J) | Force to stop in 1 s (N) |
|---|
Momentum, explained
Conservation of Momentum
In a closed system with no external forces, total momentum is conserved. This is why a small bullet can knock back a heavy target: the bullet's momentum (m × v) transfers to the target. Recoil from firing a gun, ice skater pushing off a wall, and rocket propulsion all follow the same conservation law.
Momentum vs Kinetic Energy
Both depend on mass and velocity, but they scale differently. Momentum (p = mv) doubles when velocity doubles. Kinetic energy (KE = 0.5mv²) quadruples when velocity doubles. Two objects can have equal momentum but very different kinetic energies, heavy slow vs light fast.
Real-World Momentum Examples
A 9mm bullet (8 g) at 350 m/s has momentum of 2.8 kg·m/s. A baseball (145 g) at 40 m/s pitched at 90 mph has momentum of 5.8 kg·m/s, over twice the bullet's. A 1500 kg car at 30 m/s has 45,000 kg·m/s. Mass matters as much as velocity at the everyday scale.
Impulse and Momentum Change
Impulse = Force × Time = Change in Momentum. To stop something with a lot of momentum, you either apply huge force briefly (catching a baseball bare-handed hurts) or apply moderate force over more time (catching with the glove gives more travel time, lower force).
Common questions
What is the unit of momentum?
The SI unit is kg·m/s. There is no special name like joule for momentum, it is always expressed as mass times velocity.
How is momentum different from kinetic energy?
Momentum (p = mv) scales linearly with velocity. Kinetic energy (KE = 0.5mv²) scales with velocity squared. Both depend on mass and velocity but in different ways.
Can momentum be negative?
Yes, when velocity is negative (opposite direction). The sign indicates direction, not magnitude. Total momentum of a system can sum to zero if equal opposing momenta exist.
Why doesn't a bullet knock a target backward like in movies?
Newton's third law says the bullet's recoil on the shooter equals its momentum transfer to the target. Since the target absorbs much more than just the bullet's mass (clothing, body), the visible knockback is much less than movies show.
Is angular momentum the same thing?
No, angular momentum is for rotating systems and equals moment of inertia × angular velocity (L = Iω). This calculator handles only linear (translational) momentum.
Educational estimates using idealized physics. Real collisions involve deformation, friction, rotation and many-body effects. Figures assume linear (translational) motion in a single direction.