Momentum Calculator

Background.

This momentum calculator computes linear momentum p = m·v for any massive body, and will also rearrange the relation to solve for mass or velocity when you already know p. Momentum, the product of an object's mass and its velocity, is the single most useful book-keeping quantity in classical mechanics. Once you measure it for every object in a closed system, the total cannot change unless an external force acts — that is Newton's third law restated as conservation of momentum, and it is the principle that quietly governs car crashes, billiard breaks, rocket launches, recoiling rifles, neutron-star mergers and the deflection of a tennis ball off a racket. Force is the rate at which momentum changes; impulse is the accumulated change; energy is the squared cousin that gets dissipated as heat. Get momentum right and the rest of mechanics follows.

The calculator accepts mass in kilograms, grams or pounds and velocity in m/s, km/h or mph, converting everything internally to SI base units using exact NIST SP 811 factors before applying p = m·v. It also reports the kinetic energy KE = ½ m v² so you can see at a glance how the two quantities scale differently: doubling velocity doubles momentum but quadruples kinetic energy. That asymmetry is why a slow heavy truck and a fast light car can carry the same momentum yet deliver dramatically different damage in a collision, and why braking distance grows with the square of speed even though stopping force is linear in momentum.

Three solve modes are supported. In solve-for-momentum mode you supply mass and velocity and we return p, m, v and KE. In solve-for-mass mode you supply momentum and velocity and we invert m = p/v — useful for inferring the mass of a recoiling object from the measured momentum of what it ejected. In solve-for-velocity mode you supply momentum and mass and we return v = p/m — the standard trick when applying conservation of momentum to a one-dimensional collision.

Sign conventions matter: velocity (and therefore momentum) is a vector, so a negative entry means motion in the opposite direction along your chosen axis. For two-body collisions you can run the calculator once per object, add the signed momenta to get the system total, and check that the total is conserved before and after the event. The same workflow handles explosions, rocket stages, and Newton's-cradle ball strikes.

The intro to the page below the widget walks through a 1,000 kg car at 30 m/s — a deliberately classroom-friendly example — and the FAQ tackles the questions that come up most often when students first meet momentum: why it differs from force, how it relates to impulse, what conservation actually requires, the difference between elastic and inelastic collisions, and where relativistic corrections start to bite. Momentum is one of the few quantities physicists trust at every scale, from a 1 µg dust grain in low-earth orbit to a 10³⁰ kg neutron star. Use the calculator, then read the explainer if the result surprises you.

What is momentum calculator?

Linear momentum, written p, is the product of an object's mass m and its velocity v: p = m·v. It is a vector quantity — it has both a magnitude (kg·m/s) and a direction, the same direction as the velocity. Unlike kinetic energy, which is a scalar, momentum keeps track of direction, which is why it is the natural quantity to track through collisions and explosions where direction-of-motion changes matter. The defining feature of momentum is its conservation law: the total momentum of a closed system (no net external force) is constant in time. Newton himself stated his second law in terms of momentum rather than acceleration — F = dp/dt — and only the special case of constant mass collapses to the familiar F = m·a. Momentum is also what couples mass to gravitational and electromagnetic fields in modern physics, and the relativistic generalisation p = γm·v is one half of the four-momentum that conserves energy and momentum simultaneously under Lorentz transformations.

How to use this calculator.

1. 01Choose what you want to solve for: momentum (default), mass, or velocity.
2. 02Enter the mass of the object and pick its unit — kilograms, grams, or pounds.
3. 03Enter the velocity and pick its unit — m/s, km/h, or mph. Use a negative sign for motion in the opposite direction along your chosen axis.
4. 04If you are solving for mass or velocity, also enter the momentum in kg·m/s.
5. 05Read the primary result (momentum, mass, or velocity) and the derived kinetic energy in the output panel.
6. 06For two-body problems, run the calculator once per object and add the signed momenta to apply conservation.

The formula.

The core relation is p = m·v, where p is linear momentum in kg·m/s, m is mass in kilograms, and v is velocity in metres per second. p, v and the equation itself are vector statements — write p⃗ = m·v⃗ when direction matters. Rearranged, m = p/v and v = p/m, which is how the calculator handles its two inverse modes. The kinetic energy of the same body is KE = ½ m v², which can be rewritten in terms of momentum as KE = p²/(2m). That second form makes the momentum-energy link explicit: at fixed momentum, lighter bodies carry more kinetic energy; at fixed velocity, heavier bodies carry more of both, but kinetic energy scales linearly with mass and quadratically with speed, while momentum scales linearly with each. Newton's second law in its general form is F⃗ = dp⃗/dt, so impulse J⃗ = ∫F⃗ dt = Δp⃗ — applying a force over a time interval changes momentum by exactly the force-time integral. For a system of n particles the total momentum is the vector sum P⃗ = Σᵢ mᵢ v⃗ᵢ, and conservation says dP⃗/dt = F⃗_external, so P⃗ is constant whenever the external force is zero. Relativistically, p = γm·v with γ = 1/√(1 − v²/c²); the Newtonian expression is the v ≪ c limit and is accurate to better than 1% for v < 0.14c.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica. Book I, Definition II (quantitas motus, the quantity of motion) and Law II (mutationem motus proportionalem esse vi motrici impressae) — the original statement of F = dp/dt and the definition of momentum as the product of mass and velocity.
2. [2]Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (11th ed.), Chapter 9 'Center of Mass and Linear Momentum'. Wiley. The standard undergraduate treatment of p = m·v, impulse-momentum theorem, and conservation in 1D and 2D collisions.
3. [3]Thompson, A., & Taylor, B. N. (2008). NIST Special Publication 811: Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology. Tables B.6 and B.8 give the exact conversion factors used by this calculator (1 lb = 0.45359237 kg; 1 mph = 0.44704 m/s).
4. [4]Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Volume I, Chapter 10 'Conservation of Momentum'. Caltech / Addison-Wesley. Feynman's derivation of momentum conservation from Newton's third law and his treatment of recoil and rocket propulsion.
5. [5]Goldstein, H., Poole, C., & Safko, J. (2002). Classical Mechanics (3rd ed.), Chapter 1 'Survey of the Elementary Principles'. Addison-Wesley. Derives linear and angular momentum conservation from Noether's theorem and the translational symmetry of the Lagrangian — the modern, symmetry-based justification of why momentum is the right conserved quantity.