Calculate momentum, mass, or velocity from any two values with kg/lb and m/s, ft/s, or mph unit conversions for physics calculations.

Classical, one-axis momentum. Use total mass and center-of-mass velocity; positive and negative values follow your chosen axis. lb means pound-mass.

System Momentum Formula

For classical one-axis momentum, use total mass and center-of-mass velocity: p = M × Vcm. This also applies when components move differently, provided Vcm is their mass-weighted average velocity. Use signed components in one chosen inertial frame.

pₛ = mₛ × vₛ
Symbol Meaning Common Unit Practical Note
ps System momentum kg·m/s Direction matters; use sign when needed.
ms Total system mass kg Add masses only if they are part of the same modeled system.
vs System velocity m/s Use a negative value for motion opposite your chosen positive direction.

Rearranged Equations

If you know any two values, solve for the third with the matching form below.

Find Equation
Momentum
pₛ = mₛ × vₛ
Mass
mₛ = (pₛ) / (vₛ)
Velocity
vₛ = (pₛ) / (mₛ)

When This Calculator Is Appropriate

  • Use it for a single object, a system moving together, or a system with known center-of-mass velocity.
  • If different parts of the system move at different velocities, total momentum must be added by parts.
psystem = Σᵢ₌₁ⁿ mᵢ vᵢ

How to Calculate System Momentum

  1. Determine the total mass of the system.
  2. Determine the system velocity in a consistent unit set.
  3. Multiply mass by velocity.
  4. Report the result with units and direction/sign if applicable.

Unit Guide

Mass Unit Velocity Unit Momentum Unit
kg m/s kg·m/s
lb ft/s lb·ft/s
lb mph lb·mph

The calculator converts input units before applying p = M × Vcm, then divides by the selected output-unit factor. lb is pound-mass: 1 lb = 0.45359237 kg. Velocity and momentum may be signed; system mass must be positive. Zero velocity gives zero momentum, but zero momentum and zero velocity cannot determine mass.

Quick Example

A 9 kg system moving at 5 m/s has:

pₛ = 9 × 5 = 45 kg × m / s

Common Mistakes

  • Ignoring direction and treating opposite velocities as the same.
  • Using total mass with one component’s velocity instead of the system’s center-of-mass velocity.
  • Mixing SI and imperial units without conversion.
  • Forgetting that if velocity is zero, momentum is zero.

Helpful Notes

Situation What to Do
Object speeds up Momentum increases if mass stays constant.
Object changes direction Momentum sign changes with the chosen axis.
Two objects move in opposite directions Net system momentum may partially or fully cancel.
System moves together after combining Use total mass and the shared final velocity.