Momentum Calculator

momentum = mass × velocity stopping force = mass × velocity ÷ stopping time

m

Mass in kilograms — the field also takes pounds, tonnes and grams, and converts them before the multiplication runs

v

Velocity in metres per second — the field also takes km/h, mph, ft/s and knots. Strictly this is the speed: momentum is a vector, and the page reports its magnitude only

p

Momentum in kg·m/s, the SI unit; the second output row gives the same quantity in lb·ft/s, where the pound is a pound of mass and not a pound of force

t

Stopping time in seconds, used only by the reference table's last column, which assumes 0.1 s — a round number for a crash, not a constant

Use this page when the question is about force rather than energy: what a barrier has to take, how much an airbag has to spread out, whether a recoil will knock you over. The reason momentum is the right quantity there is that force is the rate of change of momentum, so a given momentum change spread over a longer stopping time means a smaller force — which is the entire design principle of a crumple zone. Two habits make the answers more useful. First, remember that momentum has a direction even though this page prints only its size: a head-on collision and a rear-end shunt have different vector sums, and the page cannot tell them apart. Second, when comparing two vehicles, compare the momenta and the energies separately — a loaded lorry at walking pace matches a car at motorway speed on the first and is nowhere near it on the second.

1. A 3,300 lb car at 60 mph

   1. 3,300 lb = 1,496.855 kg (the mass field takes kilograms, so the pounds go in its unit dropdown)
   2. 60 mph = 26.8224 m/s
   3. Momentum: 1,496.855 × 26.8224 = 40,149.2 kg·m/s
   4. The same quantity in the other system: 40,149.2 ÷ 0.138254954376 = 290,400 lb·ft/s
   5. Stopping force in 0.1 s: 40,149.2 ÷ 0.1 = 401.5 kN, which is about 90,260 lbf

   This is the reference table's middle row, reached from the same car. Note that the imperial row comes out as the round number 290,400 — that is not a coincidence and it is worth reading the second step again: dividing by the pound-to-kilogram and foot-to-metre factors returns exactly 3,300 × 88, because a mass in pounds times a speed in feet per second is what lb·ft/s means by definition. The metric row is the one carrying the rounding.

2. A 6,600 lb lorry at 30 mph

   1. 6,600 lb = 2,993.710 kg, twice the car above
   2. 30 mph = 13.4112 m/s, half the speed above
   3. Momentum: 2,993.710 × 13.4112 = 40,149.2 kg·m/s — the same 290,400 lb·ft/s as the car
   4. Kinetic energy on the other page: 269,225 J against the car's 538,449 J
   5. Stopping force in 0.1 s: the same 401.5 kN

   The point of this example is what does not change. Double the mass, halve the speed, and the momentum is identical — so the force needed to stop it in the same time is identical too. The energy is not: the lorry carries 269 kJ against the car's 538 kJ, because energy follows mass times speed squared rather than mass times speed. Two pages, the same two inputs, and the answer to 'which one is worse' depends entirely on whether you are asking about the force on a barrier or the heat in the brakes.

3. A rifle bullet, 0.008 kg at 800 m/s

   1. Mass: 0.008 kg, the 8 g on the box
   2. Momentum: 0.008 × 800 = 6.4 kg·m/s
   3. In the other system: 6.4 ÷ 0.138254954376 = 46.3 lb·ft/s
   4. Compare a 70 kg runner at 3 m/s: 210 kg·m/s, about 33 times as much
   5. Kinetic energy of the same bullet: 2,560 J, against 315 J for the runner

   This one runs the two pages against each other and is the reason they are separate. The bullet has eight times the runner's energy — 2,560 J against 315 J — but only one thirty-third of the momentum. A bulletproof vest is a momentum problem and a heat problem at the same time, and it is solved with different materials for each: the aramid stops the momentum over a longer time, and the deformation spreads the energy. The recoil of the rifle, which is the same 6.4 kg·m/s going backwards, is why the shooter's shoulder moves and the rifle does not.

Momentum is a vector and this page prints a magnitude. There is no direction input, so a head-on collision and a rear-end shunt with the same speeds give the same number here, and the page cannot do the vector sum that the aftermath of a real crash needs. The lb·ft/s row uses the pound as a unit of mass, which is one of two conventions in circulation — the other is slug·ft/s, and the two differ by a factor of 32.174, so a figure quoted in lb·ft/s can be read as poundals by someone expecting lbf. The stopping force in the reference table assumes a tenth of a second; a rigid impact is nearer a hundredth and a car with a crumple zone and a belted occupant nearer a third, so the column is an order of magnitude, not a prediction. There is no conservation analysis: the page describes one object before or after an interaction, never both sides of a collision, so it cannot tell you the recoil speed of a coupled pair or how much of the momentum a wall absorbed. It is the classical expression, p = mv, which is exact at everyday speeds and understates momentum as the speed approaches that of light. Angular momentum is a separate quantity entirely and is not computed here, and neither is the impulse of a force that varies over time — this page only knows the average. Finally, mass is taken as constant: a rocket burning fuel, a lorry being loaded, or anything else whose mass changes mid-motion is outside what a single p = mv can describe.

How do I calculate momentum?

Multiply the mass by the velocity, in kilograms and metres per second. A 3,300 lb car at 60 mph is 1,496.855 kg × 26.8224 m/s = 40,149.2 kg·m/s. There is no square and no halving, so the arithmetic is one step — which is exactly why momentum is easier to reason about than energy and harder to be impressed by.

What is the impulse-momentum theorem?

It says the impulse delivered to an object — force times the time it acts — equals the change in its momentum: F × Δt = Δp. Rearranged, F = Δp ÷ Δt, which is the relation the reference table's last column uses. Stopping 40,149.2 kg·m/s in 0.1 s takes 401.5 kN; stretching the same stop over 0.3 s takes 133.8 kN, and that factor of three is the entire engineering case for crumple zones and airbags.

What are the units of momentum?

kg·m/s in SI, with no special name of its own — unlike energy, which gets the joule and the newton metre. The page also prints lb·ft/s, where the pound is a pound of mass; the alternative imperial convention is slug·ft/s, and the two differ by a factor of 32.174, so the same motion can be quoted as 290,400 or as 9,027 depending on which is meant.

How is momentum different from kinetic energy?

Momentum is mv and energy is ½mv², and the difference is what makes two pages necessary. Double the speed and the momentum doubles while the energy quadruples; double the mass and both double. A 6,600 lb lorry at 30 mph and a 3,300 lb car at 60 mph carry the same 290,400 lb·ft/s, and stopping either in a tenth of a second takes the same force — but the car carries twice the energy, so it puts twice the heat into the brakes.

Why is stopping force not a fixed number?

Because it depends on how long you allow for the stop, and nothing about the moving object decides that. F = Δp ÷ Δt, so the same momentum spread over a longer time is a smaller force. The reference table assumes 0.1 s for that reason and says so in its note; a rigid barrier against a rigid object is nearer 0.01 s and a belted occupant behind a crumple zone nearer 0.3 s, giving forces from ten times to a third of the tabulated figures.

Does the direction of motion matter?

For the real quantity, yes; for this page, no. Momentum is a vector, so the momentum of a car travelling north and one travelling south cancel when you add them, and that cancellation is what a collision analysis is actually computing. The page reports magnitudes only, with no direction input, so it is the right tool for one object in isolation — the force needed to stop it, the recoil it will produce — and the wrong tool for the vector sum over several objects.

• Linear Momentum and Force (College Physics 2e, §8.1) — p = mv as the definition of momentum, and Newton's second law written as force equals the rate of change of momentum — OpenStax
• NIST Guide to the SI — the kilogram metre per second as the coherent SI unit of momentum, and the exact factors for pounds (0.45359237 kg) and feet (0.3048 m) that the lb·ft/s row is built from — National Institute of Standards and Technology
• Momentum — the relation to impulse and to Newton's second law, and the distinction between momentum and kinetic energy that this page is built around — Wikipedia