Enter the system mass and the system velocity into the calculator to determine the System Momentum. 

System Momentum Calculator

Enter any 2 values to calculate the missing variable

System Momentum Formula

Use this calculator when an entire system can be modeled as one combined mass moving with one velocity.

p_s = m_s \cdot v_s
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 
p_s = m_s \cdot v_s
Mass 
m_s = \frac{p_s}{v_s}
Velocity 
v_s = \frac{p_s}{m_s}

When This Calculator Is Appropriate

  • Use it for a single object or a combined system moving together at one velocity.
  • If different parts of the system move at different velocities, total momentum must be added by parts.
p_{system} = \sum_{i=1}^{n} m_i v_i

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

For clean comparisons, keep all inputs in one consistent unit system before interpreting the result.

Quick Example

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

p_s = 9 \cdot 5 = 45 \ \text{kg}\cdot\text{m/s}

Common Mistakes

  • Ignoring direction and treating opposite velocities as the same.
  • Using total mass with a single velocity when the parts are actually moving differently.
  • 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.