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Momentum Calculator (p = mv)

Linear momentum from mass and velocity, with the kinetic energy of the same motion and the force to stop it in a second.

Inputs

Momentum
24 kg·m/s

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What each Momentum input means

Mass
The moving object's mass in kilograms.
Velocity
Its velocity in m/s. A negative value means the opposite direction, which matters when adding the momenta of two objects.

Momentum formula

p = m × v (kg × m/s) · impulse = F × Δt = Δp, so the average force to stop it in time t is p ÷ t · KE = ½mv² = p² ÷ 2m

p⃗=mv⃗,F⃗net=Δp⃗Δt\vec{p} = m\vec{v}, \qquad \vec{F}_{\text{net}} = \frac{\Delta\vec{p}}{\Delta t}

Momentum is mass times velocity — the quantity of motion an object carries, with the direction of the velocity. Newton wrote his second law in terms of it: force is the rate of change of momentum, which means a given force acting for a given time changes momentum by force × time, the impulse, whatever the object. That is why momentum is the number in collisions: a 3 kg ball at 8 m/s and a 24 kg ball at 1 m/s carry the same 24 kg·m/s and need the same impulse to stop, though their kinetic energies differ by a factor of eight. In a closed system the total momentum is conserved through any collision or explosion, elastic or not. The page gives p, the kinetic energy of the same motion for contrast, and the average force that would bring it to rest in one second.

Momentum worked example

3 kg moving at 8 m/s: p = 3 × 8 = 24 kg·m/s, carrying ½ × 3 × 64 = 96 J of kinetic energy. Stopping it in one second takes an average force of 24 N; in a tenth of a second, 240 N. A 1,500 kg car at 20 m/s has 30,000 kg·m/s — the same as a 30,000 kg truck creeping at 1 m/s.

More Momentum examples

A 145 g baseball at 40 m/s: p = 0.145 × 40 = 5.8 kg·m/s. A catcher's mitt that stops it in 0.01 s takes an average force of 580 N; letting the glove give, so the stop takes 0.05 s, cuts that to 116 N.

A 1,500 kg car at 20 m/s (72 km/h): p = 30,000 kg·m/s. Stopped in 0.1 s by a crash it takes an average 300,000 N; stretched to 1 s by crumple zones and braking, 30,000 N.

Where the Momentum calculator can give the wrong answer

  • Momentum is a vector. A negative velocity gives negative momentum, and two objects' momenta add with their signs — a head-on collision of equal momenta totals zero.
  • Momentum and kinetic energy are different things. Doubling the velocity doubles the momentum but quadruples the energy; halving a collision's speed halves the impulse needed and quarters the damage.
  • The 'force to stop in 1 s' line is an average over that second; a crash that stops a car in 0.1 s multiplies it by ten, which is what crumple zones and airbags stretch out.
  • p = mv is Newtonian and fine for everyday speeds; near the speed of light the relativistic momentum γmv is larger.
  • Units: kilograms and metres per second. kg·m/s is the same as N·s, the unit of impulse.

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Momentum FAQ

Multiply mass in kilograms by velocity in metres per second. A 0.145 kg baseball at 40 m/s has 5.8 kg·m/s. Enter both above; the page also shows the kinetic energy and the stopping force.

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