Momentum Calculator
Quickly find the linear momentum of any moving object by entering its mass and velocity. Use it in physics problems, collision analysis, or when applying Newton's second law.
About this calculator
Linear momentum is a measure of how much motion an object carries. It is defined by the formula p = mass × velocity, where mass is in kilograms and velocity is in metres per second, giving momentum in kg·m/s. Momentum is a vector quantity, meaning it has both magnitude and direction. The concept is central to Newton's second law, which states that the net force on an object equals the rate of change of its momentum. In a closed system with no external forces, total momentum is conserved — a principle used to analyse collisions and explosions. Heavier objects and faster objects both carry greater momentum, which is why a slow-moving truck can be harder to stop than a fast-moving bicycle.
How to use
Suppose a 1,200 kg car is travelling at 15 m/s. Enter mass = 1200 kg and velocity = 15 m/s. The calculator applies p = mass × velocity: p = 1200 × 15 = 18,000 kg·m/s. Now try a 0.145 kg baseball thrown at 40 m/s: p = 0.145 × 40 = 5.8 kg·m/s. Despite being far lighter, the baseball's momentum tells you exactly how much force is needed over a given time to bring it to rest.
Frequently asked questions
What is the difference between momentum and kinetic energy?
Momentum (p = mv) measures the quantity of motion and is a vector with direction, while kinetic energy (KE = ½mv²) measures the energy of motion and is a scalar. Both depend on mass and velocity, but kinetic energy grows with the square of velocity whereas momentum grows linearly. In a perfectly elastic collision both are conserved, but in an inelastic collision only momentum is conserved. This distinction is crucial when analysing crashes, sports impacts, and rocket propulsion.
Why is momentum always conserved in a closed system?
Newton's third law states that every action has an equal and opposite reaction. When two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction, so the changes in their momenta cancel out exactly. As long as no external net force acts on the system, the total momentum before and after any event remains constant. This conservation law underpins everything from billiard ball collisions to spacecraft trajectory corrections.
How do you calculate momentum when an object changes direction?
Because momentum is a vector, direction matters. Assign a positive direction (e.g. rightward = positive) and a negative sign to motion in the opposite direction. For example, a 2 kg ball moving left at 5 m/s has momentum −10 kg·m/s. When calculating changes in momentum after a bounce or collision, subtract the initial vector momentum from the final vector momentum. The result gives the impulse applied to the object, which equals force multiplied by contact time.