What Is Momentum? How to Calculate It
Our Momentum Calculator helps you calculate the linear momentum of an object — or solve for its mass or velocity when momentum is known. Simply choose a unit system (metric or imperial), select what to solve for, enter two of the three values, and get your answer instantly.
The Momentum Formula
Linear momentum is the product of an object's mass and its velocity:
p = m × v
Where:
- p — momentum of the object
- m — mass of the object
- v — velocity of the object
Because mass is a scalar and velocity is a vector, momentum is also a vector quantity — it has both magnitude and direction.
Units of Momentum
| System | Mass unit | Velocity unit | Momentum unit |
|---|---|---|---|
| SI (Metric) | kilogram (kg) | metre per second (m/s) | kg·m/s = N·s |
| Imperial (US) | pound (lb) | foot per second (ft/s) | lb·ft/s |
Unit conversion: 1 kg·m/s = 7.233 lb·ft/s | 1 lb·ft/s ≈ 0.1383 kg·m/s
How to Use This Momentum Calculator
- Select unit system — choose Metric (SI) or Imperial (US).
- Select what to solve for — Momentum, Mass, or Velocity.
- Enter the two known values — the third is calculated automatically.
- Click Calculate — results appear instantly with the formula used.
Momentum Examples
Example 1 — Jogging person:
A person with a mass of 65 kg jogging at 2 m/s has a momentum of:
p = 65 kg × 2 m/s = 130 N·s (130 kg·m/s)
Example 2 — Dump truck:
An empty dump truck weighing 12 t (12 000 kg) travelling at 35 mph (≈ 15.6 m/s) has a momentum of:
p = 12 000 kg × 15.6 m/s = 187 200 kg·m/s ≈ 187.2 kN·s
Example 3 — Charging elephant:
An elephant weighing 5 000 kg charging at 35 km/h (≈ 9.72 m/s) has a momentum of:
p = 5 000 kg × 9.72 m/s = 48 600 kg·m/s ≈ 48.6 kN·s
Inverse Calculations
The momentum formula can be rearranged to find any unknown:
- Find mass: m = p ÷ v
- Find velocity: v = p ÷ m
Example — Finding velocity: If a baseball with a mass of 0.145 kg has a momentum of 5.8 kg·m/s, its velocity is:
v = 5.8 ÷ 0.145 = 40 m/s (≈ 144 km/h)
Why Is Momentum Important?
Momentum is fundamental in classical mechanics because of the law of conservation of momentum: in a closed system with no external forces, the total momentum is conserved. This principle governs collisions, rocket propulsion, and countless everyday phenomena.
Momentum is also directly related to Newton's Second Law of Motion in its more general form:
F = Δp / Δt
The net force on an object equals the rate of change of its momentum. When Δt is constant, this reduces to the familiar F = m·a.
Frequently Asked Questions
Q: What is the SI unit of momentum?
A: The SI unit is kg·m/s, which is equivalent to N·s (Newton-second).
Q: Is momentum a scalar or vector?
A: Momentum is a vector quantity — it has both magnitude and direction, identical to the direction of velocity.
Q: Can momentum be negative?
A: Yes. A negative momentum means the object is moving in the negative direction of the chosen coordinate axis.
Q: What is the difference between momentum and kinetic energy?
A: Momentum (p = mv) is a vector; kinetic energy (KE = ½mv²) is a scalar. They are both related to motion but capture different aspects — momentum is conserved in all collisions, kinetic energy only in perfectly elastic ones.