What this calculator does
Find out how much motion a moving object carries, and so how hard it is to stop. That amount is its momentum. It is the mass times the velocity (speed in a given direction): p = m × v. A loaded truck and a bicycle at the same speed have very different momentum. That's why the truck is so much harder to stop. Momentum points the same way the object moves, so it can be negative.
To change an object's momentum, a force has to push on it for some time. The average force times that time is called the impulse. It equals the change in momentum: Δp = F × Δt. Here Δ (the Greek letter delta) means "change in". This calculator fills in whichever value you're missing, in metric (SI) or US units.
Where it's used
Why this math matters outside the classroom:
- Hockey pucks. A 0.16 kg hockey puck sliding at 30 m/s has a momentum of 0.16 × 30 = 4.8 kg·m/s.
- Airbags. Airbags lengthen the time a passenger takes to stop, so the same change in momentum comes with a smaller force.
- Impulse. A 500 N push held for 0.2 s delivers 100 N·s of impulse, enough to get a 50 kg sled moving at 2 m/s.
- Recoil and rockets. Students explain recoil and rocket thrust by momentum conservation: what goes forward is balanced by what goes back.
Grade level and standards: Grades 9–10; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose whether to solve for momentum, mass, velocity or an impulse.
- In impulse mode, pick whether you want the impulse, the average force or the contact time.
- Enter the values you know, with their units. Use negative numbers for motion in the opposite direction.
- Choose the unit for the answer. You'll also see the result in the other units for momentum, mass, speed, force or time.
What the inputs mean
- Velocity (v)
- Negative for motion in the opposite direction; momentum takes the same sign.
- Momentum (p)
- 1 kg·m/s is the same as 1 N·s. 1 lb·ft/s is 0.138255 kg·m/s and 1 lbf·s is 4.448222 N·s.
- Impulse (Δp)
- Impulse equals the change in momentum, so a ball that arrives at +10 kg·m/s and leaves at −8 kg·m/s received an impulse of −18 N·s.
- Contact time (Δt)
- Contact times are often very short. A bat touches a ball for around a thousandth of a second, so you can enter milliseconds.
Formula and method
p = m × v m = p ÷ v v = p ÷ m J = Δp = F × Δt
p is momentum, m is mass and v is velocity. J is the impulse, F is the average force and Δt is how long the force acts. Δp is the change in momentum. With mass in kilograms and velocity in meters per second, momentum comes out in kg·m/s. The calculator converts your inputs to those units first. Then it converts the answer back to the unit you choose.
The impulse rule is Newton's second law, written for momentum. The average net force (the total push once all forces are added up) times the time it acts gives the change in momentum. Spread the same change over a longer time, and the force gets smaller. That's the idea behind airbags and crumple zones in cars.
Worked example
A 1,500 kg car travels at 20 m/s. What is its momentum? Separately, a 600 N average force acts for 50 ms. What impulse does it deliver?
- Momentum: p = 1,500 × 20 = 30,000 kg·m/s.
- Impulse: first change the time to seconds, 50 ms × 0.001 = 0.05 s.
- J = 600 × 0.05 = 30 N·s.
Result: The car carries 30,000 kg·m/s of momentum (about 216,990.4 lb·ft/s). The 600 N push for 50 ms changes an object's momentum by 30 N·s.
Understanding the result
In a collision with no outside force, momentum is conserved. That means the total before the crash equals the total after. Comparing two objects' momentum tells you which one will win out in a collision.
A large impulse can come from a big force for a short time, or a small force for a long time. To lower the peak force in a collision, make the contact time longer.
Assumptions and limitations
- Motion is along a single straight line, and you pick which way counts as positive.
- In impulse mode, F is the average net force over the contact time.
- The mass stays the same, and speeds are far below the speed of light.
- Spinning objects also carry angular momentum (momentum from turning), which isn't included.
- Impulse mode uses an average force. The peak force during an impact can be much higher.
- Speeds close to the speed of light (relativistic speeds) need a different, relativistic momentum formula.
Frequently asked questions
What is the unit of momentum?
In metric (SI) units, it's the kilogram meter per second (kg·m/s). That's exactly the same as the newton second (N·s). US units include the pound foot per second and the pound-force second.
Is impulse the same as momentum?
Impulse is a change in momentum, so it uses the same units. Momentum describes how an object is moving right now. Impulse describes how much a force changed that motion over a period of time.
Can momentum be negative?
Yes. Momentum points the same way as the velocity. So an object moving in the negative direction has negative momentum. Its size (mass times speed) is never negative.
How does momentum differ from kinetic energy?
Momentum is m × v, and it has a direction. Kinetic energy (the energy of motion) is ½ × m × v², and it has no direction. Doubling the speed doubles the momentum, but it makes the kinetic energy four times as big.
How this calculator is checked
Method: Classical linear momentum p = mv and the impulse–momentum theorem J = FΔt = Δp. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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