Momentum is mass in motion: an object’s mass multiplied by its velocity. It is the quantity conserved in collisions, the reason a slow truck is harder to stop than a fast bicycle, and, as impulse, the measure of how hard and how long a force pushes. SI uses kilogram meters per second or the identical newton-second, older physics texts use gram centimeters per second, and US engineering mixes pounds and feet. This converter handles seven momentum units and, for scale, shows how fast a 1,500 kg car would be moving with the same momentum.
How to use the momentum converter
- Enter the momentum or impulse in Value.
- Choose its unit in From and the one you need in To.
- Read the result and the factors in both directions on the tape, plus the equivalent speed of a typical car.
- The table lists the value in all supported units.
Momentum conversion formula
Momentum is defined as
so every unit is a mass unit times a velocity unit. Each is stored as kg·m/s and converted with
The US factors come from exact definitions: 1 lb·ft/s = 0.45359237 × 0.3048 = 0.138254954376 kg·m/s, and 1 lbf·s = 0.45359237 × 9.80665 = 4.4482216152605 kg·m/s. The CGS unit, 1 g·cm/s, is 10⁻⁵ kg·m/s.
Worked example: a car on a city street
A 1,500 kg car travels at 20 m/s (72 km/h, about 44.7 mph):
p = 1,500 kg × 20 m/s = 30,000 kg·m/s
In US units: 30,000 × 7.233014 = 216,990 lb·ft/s, or 30,000 ÷ 4.448222 = 6,744 lbf·s.
To stop the car in 3 seconds, the brakes must supply an average force of 30,000 ÷ 3 = 10,000 N (about 2,248 lbf), because impulse equals the change in momentum.
Momentum unit conversions
| From | To | Multiply by |
|---|---|---|
| kg·m/s | N·s | 1 (identical) |
| kg·m/s | lb·ft/s | 7.2330139 |
| lb·ft/s | kg·m/s | 0.138254954376 (exact) |
| lbf·s | kg·m/s | 4.4482216 |
| kg·m/s | lbf·s | 0.2248089 |
| g·cm/s | kg·m/s | 0.00001 (exact) |
| kg·km/h | kg·m/s | 0.2777778 |
| g·m/s | kg·m/s | 0.001 (exact) |
Momentum for comparison
| Object | Mass | Speed | Momentum |
|---|---|---|---|
| Pitched baseball | 0.145 kg | 40 m/s (90 mph) | 5.8 kg·m/s |
| Running person | 70 kg | 5 m/s | 350 kg·m/s |
| Car at 72 km/h | 1,500 kg | 20 m/s | 30,000 kg·m/s |
| Loaded semi-truck at highway speed | 36,000 kg | 25 m/s | 900,000 kg·m/s |
The truck and the car differ thirtyfold in momentum even though their speeds are similar, which is the physics behind long truck stopping distances.
Momentum versus kinetic energy
Both depend on mass and speed, but differently. Momentum grows in proportion to speed (p = mv), while kinetic energy grows with its square (KE = ½mv²). Doubling a car’s speed doubles its momentum and quadruples its kinetic energy. Momentum is a vector with a direction, conserved in every collision; kinetic energy is a scalar and is conserved only in perfectly elastic collisions.
Impulse and the newton-second
Impulse, J = F × Δt, is the change in momentum produced by a force acting over time. Its unit, the newton-second, is identical to kg·m/s, so impulse values convert exactly the same way. Model-rocket motors are classed by total impulse (a “C” motor delivers 5–10 N·s), and larger rocket engines are rated in lbf·s.
To calculate momentum from mass and velocity, use the momentum calculator. For force-and-time problems, see the impulse calculator and the impulse-momentum calculator.
Frequently asked questions
Is a newton-second the same as a kg·m/s?
Yes. A newton is 1 kg·m/s², so multiplying by a second gives kg·m/s. Physicists tend to write N·s for impulse (force times time) and kg·m/s for momentum (mass times velocity), but the quantities and units are identical.
How do I convert kg·m/s to lb·ft/s?
Multiply by about 7.233014. One lb·ft/s is 0.45359237 kg × 0.3048 m/s = 0.138254954376 kg·m/s exactly, and 1 divided by that is 7.233014.
What is the difference between lb·ft/s and lbf·s?
lb·ft/s uses the pound as a mass (pound-mass times feet per second). lbf·s uses the pound-force and a second, which makes it about 32.17 times larger: 1 lbf·s = 4.448 kg·m/s. Rocket engine total impulse is usually quoted in lbf·s.