By Zencalcy Editorial TeamLast reviewed About us
A ballistic pendulum captures a projectile in a hanging block and measures how high the block swings. Momentum conservation gives the speed just after impact, and energy conservation converts the rise into that speed, which recovers the muzzle velocity.
Muzzle speed from a ballistic pendulum rise.
v_after = √(2gh) v_muzzle = (m + M)/m · v_after
This assumes a perfectly inelastic impact and that the block's rise is small enough to ignore the change in pendulum geometry.
| Symbol | Meaning |
|---|---|
| m | Projectile mass, in kilograms. |
| M | Pendulum block mass, in kilograms. |
| h | Rise of the block, in metres. |
| v_muzzle | Projectile speed before impact, in metres per second. |
The block leaves the impact at about 1.40 m/s, so the bullet's muzzle velocity is about 702 m/s.
Continue with the Polar Moment of Inertia Calculator, Projectile Motion Calculator, or the Projectile Range Calculator — or browse more kinematics tools and all physics calculators.
The impact is inelastic, so kinetic energy is lost. Momentum is conserved through the impact and energy is conserved during the swing.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026