Momentum CalculatorCalculator
Calculate linear momentum (p = mv), kinetic energy, and simulate 1D elastic and inelastic collisions between two colliding bodies.
Two-Body Collision Parameters
Post-Collision State & Conservation
Momentum Calculator - Linear Momentum & Collision Simulator: Calculate linear momentum (p = mv) and simulate 1D elastic vs inelastic collisions with energy loss. Free, private, and runs 100% directly in your web browser.
How to Use the Momentum Calculator
Input Masses of Colliding Bodies
Enter mass m1 and mass m2 for both interacting objects in kilograms.
Set Initial Velocities (u1 & u2)
Enter approach velocities in m/s (use negative values for head-on collisions).
Select Collision Nature
Choose between Perfectly Inelastic (stick together) or Perfectly Elastic (billiard rebound).
Inspect Conserved Momentum & Energy
Verify post-collision velocities and examine kinetic energy dissipation.
Physics Principles & Mechanics Guide
Linear momentum (denoted by p) is a vector physical quantity defined as the product of an object's mass and its velocity: p = m · v. Commonly described in everyday vernacular as "inertia in motion," momentum measures how difficult it is to bring a moving body to rest. The SI unit of momentum is the kilogram-meter per second (kg·m/s) or Newton-second (N·s).
The law of conservation of linear momentum is one of the most fundamental conservation laws in the universe. It dictates that for any isolated system free from external net forces, total system momentum remains strictly constant before, during, and after any internal interaction or collision: Σ p_initial = Σ p_final.
In a Perfectly Elastic Collision, both linear momentum and mechanical kinetic energy are conserved. The colliding bodies rebound without permanent structural deformation or thermal energy dissipation (exemplified by ideal gas molecules or steel ball bearings).
In a Perfectly Inelastic Collision, the colliding objects lock together upon impact and travel with a shared common final velocity: v_final = (m1·u1 + m2·u2) / (m1 + m2). While momentum remains perfectly conserved, a substantial portion of the initial kinetic energy is permanently dissipated into heat, sound, and structural deformation.
Key Engineering Advantages
Accident Reconstruction
Models vehicle crashes to reconstruct pre-impact speeds and energy absorption.
Elastic & Inelastic Simulation
Simulates both billiard-style rebounds and sticky crumple collisions.
Energy Dissipation Tracking
Quantifies exact Joules of kinetic energy converted into heat or deformation.
Conservation Verification
Proves mathematical invariance of system momentum across reference frames.
Instant Bivariate Re-calculation
Changes mass or speed parameters with immediate live impact readouts.
Private Physics Engine
Vehicle dynamics and forensic crash models remain 100% private in your browser.
Frequently Asked Questions
Yes. In any closed, isolated system with no external net forces, total linear momentum is always strictly conserved, regardless of whether the collision is elastic, inelastic, or explosive.
In an elastic collision, kinetic energy is conserved (no energy lost to heat). In an inelastic collision, some kinetic energy is converted into heat, sound, and plastic deformation.
If two objects of equal mass (m1 = m2) collide elastically, they completely exchange their velocities: v1 = u2 and v2 = u1.
Because momentum is conserved, in an inelastic collision between a heavy SUV and a light compact car, the change in velocity (Δv) experienced by the light car is vastly greater, subjecting its occupants to far higher accelerations.
Newton originally formulated his second law as F = dp / dt (force is the rate of change of momentum). For constant mass, this simplifies to F = m(dv/dt) = ma.