What is momentum?
Momentum (p) is the product of an object's mass and velocity: p = mv. The SI unit is kilogram-metres per second (kg·m/s), which is numerically equal to a newton-second (N·s). Momentum is a vector quantity—it has both magnitude and direction. A heavier object or a faster object carries more momentum. The law of conservation of momentum states that in a closed system with no external forces the total momentum before and after a collision remains the same, making it one of the most powerful principles in physics.
How to use this calculator
Choose what you want to find—Momentum, Mass, or Velocity—with the toggle. Enter the two known values and click Calculate. The result card shows the answer, the applied formula, mass, velocity in m/s and km/h, and the kinetic energy derived from the momentum (KE = p² / 2m). When solving for momentum, a set of unit conversions (kg·m/s, g·cm/s, N·s, lb·ft/s, slug·ft/s) appears automatically. When solving for velocity, speed conversions (m/s, km/h, mph, ft/s) are displayed.
Rearranging the formula
From p = mv you can derive m = p / v (find mass) and v = p / m (find velocity). The calculator handles the rearrangement automatically—just pick the unknown and enter the other two values.
Practical applications
Vehicle safety engineers analyse momentum to design airbags and crumple zones that extend the stopping time and reduce force. Sports scientists calculate the momentum of a sprinter, a batted ball, or a tackling player. Astronomers use momentum conservation to model planetary flybys and spacecraft slingshot manoeuvres. Particle physicists rely on momentum measurements in accelerator experiments. In everyday life, momentum explains why a loaded lorry is harder to stop than a bicycle moving at the same speed.
Tips
Use consistent SI units (kg and m/s) for results in kg·m/s. A negative velocity indicates motion in the opposite direction—momentum is a vector. For collisions, apply conservation of momentum: m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′. This free calculator runs entirely in your browser with no sign-up, no download, and instant results on any device. Bookmark it for quick momentum calculations whenever you need them.