Momentum Calculator — p = m × v · Solve Momentum, Mass & Velocityp = m×v · Impulse = FΔt · Conservation of Momentum · kg·m/s · N·s
Use this free Momentum Calculator to instantly solve any unknown variable in the fundamental linear momentum equation of classical mechanics: p = m × v — where p is linear momentum in kg·m/s (or N·s), m is the mass of the object in kilograms (kg), and v is the velocity in metres per second (m/s). Enter any two known values to automatically solve the third — computing: momentum (p = m × v) in kg·m/s · mass (m = p / v) in kilograms · velocity (v = p / m) in m/s, km/h, or mph — alongside related calculations for impulse (J = F × Δt = Δp) · change in momentum (Δp = m × Δv) · conservation of momentum in collisions (p₁ + p₂ = p₁' + p₂').
The p = mv momentum formula is one of the most important equations in Newtonian mechanics and classical physics, applied extensively across: A-Level, GCSE, AP Physics, IB Physics, JEE, and NEET momentum and collision problems, elastic and inelastic collision analysis — conservation of momentum and kinetic energy, Newton's Second Law in momentum form (F = Δp/Δt), rocket propulsion and jet thrust calculations, vehicle crash and impact force analysis, sports biomechanics — ball impact momentum and player collision analysis, and particle physics — relativistic momentum (p = γmv). Understanding linear momentum as a vector quantity (magnitude and direction)— and its relationship to impulse, force, and the law of conservation of momentum — is foundational to all of classical mechanics, collision dynamics, and applied physics. Trusted by physics students, mechanical engineers, sports scientists, and aerospace researchers.
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Momentum Calculator — The Quantity That Governs Collisions and Impulse Problems
Momentum is mass times velocity — a 0.15 kg baseball at 40 m/s carries 6 kg·m/s of momentum; a 90,000 kg loaded truck at 30 m/s carries 2,700,000 kg·m/s. The difference in these magnitudes is why vehicle mass regulations and speed limits have enormous safety implications — stopping momentum requires force applied over time, and more momentum means either more force, more time, or both. The momentum calculator computes linear momentum and the impulse (force × time) required to change it, connecting abstract physics to practical safety engineering.
Conservation of momentum governs all collision analysis. In a perfectly elastic collision, both momentum and kinetic energy are conserved. In a perfectly inelastic collision (objects stick together), momentum is conserved but kinetic energy is lost to deformation and heat. A 1,200 kg car at 15 m/s colliding with a stationary 1,000 kg car and sticking together produces a combined mass of 2,200 kg moving at 8.18 m/s — conservation of momentum, but significant kinetic energy lost to the collision. The calculator handles both collision types with all post-collision state variables.
Angular momentum — the rotational equivalent of linear momentum — governs spinning objects and is conserved when no external torque acts. A figure skater pulling their arms in reduces their moment of inertia, which increases their angular velocity to conserve angular momentum. Gyroscopes maintain orientation due to angular momentum conservation. The calculator covers both linear and angular momentum, with the angular case requiring moment of inertia inputs appropriate for the object's geometry.