Momentum & Impulse Calculator

Classical Mechanics: Conservation of Linear Momentum

Momentum represents the quantity of motion an object possesses, proportional to both its mass and its velocity vector.

The Law of Conservation of Momentum

In any closed, isolated physical system with no net external forces, total vector momentum before any collision or explosion is strictly conserved:_1 v_1i + m_2 v_2i = m_1 v_1f + m_2 v_2f

Types of Collisions

• Elastic Collisions: Both total linear momentum and total kinetic energy are conserved (e.g., subatomic particle scattering, billiard balls).

• Inelastic Collisions: Total linear momentum is conserved, but kinetic energy is partially converted into heat, sound, and structural deformation (e.g., automotive vehicle collisions).

• Perfectly Inelastic Collisions: The colliding bodies stick together and move with a single unified final velocity.

How to Use This Calculator

Enter your Variable to Solve For — choose from Momentum (p = m × v), Mass (m = p / v), Velocity (v = p / m), Mass (m) (e.g. 1000), Mass Unit — choose from Kilograms (kg), Grams (g), Pounds Mass (lb), Velocity (v) (e.g. 20), Velocity Unit — choose from Meters per Second (m/s), Kilometers per Hour (km/h), Miles per Hour (mph), Impact / Collision Duration (milliseconds, for Impulse) (e.g. 100 ms), and Momentum (p) [When solving for m or v] (e.g. 20000). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Classical linear momentum (p) and impulse (J) physics equations: Momentum: p = m × v-Momentum Theorem: J = Δ p = F_avg × Δ t Impact Force: F_avg = (Δ p) / (Δ t) = (m (v_f - v_i)) / (Δ t) with Kinetic Energy: KE = (p^2) / (2m) = (1) / (2) m v^2 unit of momentum: 1 kg·m/s = 1 N·s = 0.068522 slug·ft/s

Worked Example

For example, a 1,000 kg automobile traveling at 20 m/s (44.7 mph): . Its kinetic energy is 200.0 kJ. If it crashes into a barrier and stops in 100 milliseconds (0.10 s), the average impact force experienced is .

Understanding Your Result

Scientific calculations require careful attention to significant figures and units. Your result is only as precise as your least precise input — expressing the result with more significant figures than the inputs implies false precision. For laboratory or regulatory work, verify which measurement standard applies (SI, ASTM, ISO) and whether temperature, pressure, or concentration conditions affect the formula. Cross-reference results against published reference values for your specific material or compound.