About the Momentum Calculator
Momentum measures how hard it is to stop a moving object. A lorry rolling slowly and a bullet flying fast can both be hard to stop — one because of its large mass, the other because of its high speed. Momentum combines the two: it is mass multiplied by velocity. It is one of the most important quantities in physics because it is conserved: in any collision or explosion, the total momentum before equals the total momentum after.
This momentum calculator finds momentum from mass and velocity, or mass or velocity from momentum. It also gives the object's kinetic energy, and uses the idea of impulse to show the average force needed to stop it in a chosen time, which is the key to understanding car crashes, sports equipment and safety design.
How to Use the Momentum Calculator
Choose Find momentum, Find mass or Find velocity.
Enter the two known values. Mass can be in kg, g, tonnes, lb or oz, and velocity in m/s, km/h, mph, ft/s or knots. Momentum is entered in kg·m/s.
Optionally, enter a stopping time in seconds to see the average force needed to bring the object to rest.
The Formulas
momentum p = m × v (kg·m/s, equivalent to N·s)
kinetic energy KE = ½ m v² = p² ÷ 2m
impulse F × t = Δp
stopping force F = p ÷ tStep-by-Step Examples
A car. A 1,500 kg car travels at 20 m/s (72 km/h).
p = 1,500 × 20 = 30,000 kg·m/s
KE = ½ × 1,500 × 20² = 300,000 J (300 kJ)
stopping in 1 s: F = 30,000 ÷ 1 = 30,000 N
stopping in 0.1 s: F = 30,000 ÷ 0.1 = 300,000 NA baseball. A 0.145 kg ball thrown at 40 m/s.
p = 0.145 × 40 = 5.8 kg·m/s
KE = ½ × 0.145 × 40² = 116 JVelocity from momentum. A 1,500 kg object with 30,000 kg·m/s of momentum moves at 30,000 ÷ 1,500 = 20 m/s.
Conservation of Momentum
When objects collide or push apart, the forces between them are equal and opposite, by Newton's third law, and act for the same time. The momentum one gains is exactly the momentum the other loses, so the total momentum of the system is unchanged, as long as no outside force acts. This explains recoil: when a gun fires a bullet forward, the gun moves backward with equal and opposite momentum. It explains rocket propulsion: a rocket pushes exhaust gas backward at high speed and gains forward momentum in return, even in the vacuum of space. And it lets investigators work out the speeds of vehicles before a crash from how they moved afterwards.
Impulse and Stopping Force
Changing an object's momentum requires an impulse: a force applied for a time. The same change in momentum can come from a large force for a short time or a small force for a long time. That is the principle behind many safety features. Crumple zones make a car's front collapse over a fraction of a second longer; airbags and seat belts stretch the time it takes a passenger to stop; helmets and gym mats compress on impact. In each case, making the stop take longer reduces the average force. In the car example, stopping in 0.1 seconds instead of 1 second means ten times the force.
Momentum in Sport
Athletes use momentum all the time. A cricket or baseball catcher draws the hands back as the ball arrives, lengthening the catch and softening the force. A boxer rolls with a punch for the same reason. In rugby and American football, a heavier player running at the same speed carries more momentum and is harder to stop. A golfer or batter follows through to keep the club or bat in contact with the ball for longer, increasing the impulse and the ball's speed.
Momentum and Kinetic Energy
Momentum and kinetic energy both depend on mass and speed, but in different ways. Momentum is proportional to speed, while kinetic energy is proportional to the square of speed: doubling a car's speed doubles its momentum but quadruples its kinetic energy, which is one reason higher speeds make crashes so much more damaging. Momentum has a direction and is always conserved in collisions. Kinetic energy has no direction and is conserved only in perfectly elastic collisions; in most real collisions some is turned into heat, sound and deformation.
Momentum in Two Dimensions
In real collisions, objects often move at angles to each other. Momentum is then conserved separately in each direction: the total momentum east–west and the total momentum north–south are both unchanged. Snooker players rely on this when they cut a ball into a pocket, and accident investigators use it to reconstruct crashes at junctions.
Understanding Your Result
The headline is the momentum, mass or velocity you asked for.
The values line restates mass, velocity and momentum in SI units.
The kinetic energy line gives the energy of motion in joules and kilojoules.
The stopping force line shows the average force needed to stop the object in your chosen time, and in a tenth of that time.
When Should You Use This Calculator?
Use it for physics homework on momentum, impulse and collisions.
Use it to understand why safety devices lengthen stopping times.
Use it to compare the momentum of vehicles, balls or athletes.
Common Mistakes
Mixing units. Momentum in kg·m/s needs mass in kg and velocity in m/s; the calculator converts other units.
Forgetting direction. Momentum is a vector, so opposite directions have opposite signs.
Confusing momentum with kinetic energy. They grow differently with speed.
Assuming energy is conserved in every collision. Only momentum always is.