Momentum Calculator
Solve p = mv for momentum, mass or velocity, and work out impulse from a force acting over time — with the rearranged formula shown each way.
p = m·v (impulse: J = F·t)
Momentum (kg·m/s)
Formula used for this direction
p = m·v
Your values
m = 1,200 kg, v = 27 m/s
Why Momentum Matters
Momentum is the quantity that is conserved in collisions. Whatever two objects do to each other when they meet — bounce, crumple, stick together — the total momentum before equals the total after, provided no outside force intervenes. That makes p = m·v one of the most useful equations in physics despite its simplicity.
Its companion is impulse: J = F·t, the change in momentum produced by a force acting over a time. Rearranged as F = Δp ÷ t, it explains every piece of crash-safety engineering ever built. You cannot change how much momentum a moving body has to lose, but you can change how long it takes to lose it, and the force falls in exact proportion.
Worked example — the lorry and the bullet
An 8,000 kg lorry creeping at 5 mph (2.235 m/s):
p = 8000 × 2.235 = 17,880 kg·m/s
A 4 gram bullet at 900 m/s: p = 0.004 × 900 = 3.6 kg·m/s. The lorry carries about 4,970 times the momentum of the bullet, despite moving 403 times more slowly.
A second example — stopping a car. A 1,200 kg car at 27 m/s carries 32,400 kg·m/s. Shedding all of it over 5.4 seconds of braking needs a force of 6,000 N; an impulse of 6,000 N applied for 5.4 s delivers 32,400 N·s, which matches. Halve the stopping time and you double the force.
Working backwards: a momentum of 32,400 kg·m/s in a 1,200 kg car implies a speed of 27 m/s.
Momentum versus energy, shown numerically
Take that same car and double its speed from 27 to 54 m/s. Momentum rises from 32,400 to 64,800 kg·m/s — exactly double. Kinetic energy rises from 437,400 to 1.750e+6 J — four times. That gap is why doubling your speed roughly quadruples your braking distance, not doubles it.
Keep going
- Momentum and kinetic energy both depend on mass and velocity but differently — momentum is linear in speed, energy is quadratic — which is why they behave so differently in collisions. Kinetic Energy Calculator
- A force acting over time changes momentum, and that product is impulse; the force calculator supplies the force side of that relationship. Force Calculator
Frequently Asked Questions
What is momentum?
Momentum is mass times velocity, p = m·v. It measures how hard something is to stop. A lorry at walking pace and a bullet in flight can carry comparable momentum despite wildly different speeds, because momentum weighs mass and velocity equally.
What is the difference between momentum and kinetic energy?
Momentum is linear in velocity (m·v) while kinetic energy is quadratic (½m·v²). Double the speed and momentum doubles but energy quadruples. That difference is why momentum is conserved in every collision while kinetic energy is only conserved in perfectly elastic ones — the extra energy goes into deformation, heat and sound.
What is impulse?
Impulse is force multiplied by the time it acts, J = F·t, and it equals the change in momentum. This is why airbags work: they do not reduce the momentum you must shed, they stretch the time over which you shed it, which cuts the force proportionally.
Can momentum be negative?
Yes, because velocity can be. The sign records direction. In a head-on collision the two objects carry opposite-signed momenta, and adding them gives a smaller total than either alone — which is exactly what makes head-on impacts so destructive in energy terms.
What units is momentum measured in?
Kilogram-metres per second, kg·m/s. It has no special named unit, unlike force (newton) or energy (joule). Equivalently it is newton-seconds, N·s, which is the same thing viewed as an impulse.
Related Calculators
- Force Calculator — Forces & Rotation
- Torque Calculator — Forces & Rotation
- Acceleration Calculator — Motion & Kinematics
- Velocity Calculator — Motion & Kinematics