Introduction
Momentum is a key idea in physics that tells you how hard it is to stop a moving object.1 It depends on two things: how much mass an object has and how fast it is going. The formula is simple: momentum (p) equals mass (m) times velocity (v).2 A heavy truck moving slowly can have the same momentum as a light bullet moving very fast. Understanding momentum helps explain car crashes, sports collisions, rocket launches, and much more.
This momentum calculator lets you quickly solve for momentum, mass, or velocity using the formula p = m × v. Just pick what you want to find, enter the two known values, and the tool does the rest. It supports many units like kilograms, pounds, meters per second, miles per hour, and more, so you can work with whatever measurements you have. Results update as you type. Two more tabs cover impulse and one-dimensional collisions, and a 2D option handles motion in a flat plane.
How to use our Momentum Calculator
Enter any two of the three variables (mass, velocity, or momentum), and this calculator will solve for the missing value using the formula p = m × v. You can also choose your preferred units.
Tabs: The three tabs at the top are Momentum (p = mv), Impulse (J = FΔt) and 1D Collisions. In the Momentum tab, use the Solve For menu to pick Momentum, Mass or Velocity. The field you are solving for shows the answer instead of taking an input.
1D / 2D: Choose 2D to enter the velocity as an x-component and a y-component. In 2D the tab always solves for momentum.
Mass: Type in the mass of the object. Use the dropdown menu next to the field to pick a unit: kilograms (kg), grams (g), milligrams (mg), pounds (lb), slugs, or metric tonnes.
Velocity: Type in the speed of the object. A negative number means the object is moving in the opposite direction. Use the dropdown to select meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), feet per second (ft/s), or knots.
Momentum: If you are solving for mass or velocity, type in the known momentum value. Use the dropdown to choose kg·m/s, g·cm/s, slug·ft/s, or N·s (newton-seconds). When you solve for momentum, this dropdown sets the unit of the answer.
Impulse tab: Use Solve For to pick impulse, average force, or time interval, then enter the other two. Force can be in N, kN, MN, lbf, or dyn; time in seconds, milliseconds, microseconds, or minutes; and impulse in N·s, kg·m/s, lbf·s, or dyn·s. The results also show the change in momentum, which equals the impulse.
1D Collisions tab: Choose Elastic or Perfectly Inelastic, then enter the mass and starting velocity of each object. Use a positive velocity for motion to the right and a negative one for motion to the left. The Momentum Unit menu sets the unit for the momentum totals, and Reset brings back the starting values.
Calculate: Results update as you type or change a unit. You can also click the Calculate button in each tab.
Results: The Momentum tab shows momentum, mass, and velocity, plus the object's kinetic energy in joules and foot-pounds and its de Broglie wavelength. In 2D it also shows the x and y parts of the momentum, its total size, the speed, and the direction angle measured from the +x axis. The 1D Collisions tab shows each object's final velocity, the total momentum before and after, and a chart comparing kinetic energy before and after.
What Is Momentum?
Momentum is a measure of how much "motion" an object has. It depends on two things: how heavy the object is (its mass) and how fast it is moving (its velocity). The formula is simple:
p = m × v
Here, p stands for momentum, m is mass, and v is velocity. A heavy truck moving slowly can have the same momentum as a light baseball moving very fast. Momentum is measured in units like kg·m/s (kilogram-meters per second).2 Because velocity has a direction, momentum is a vector, meaning it also has a direction.2 A positive value might mean "moving to the right," while a negative value means "moving to the left." This directional nature is important when analyzing motion.
The Impulse-Momentum Connection
Impulse is the effect a force has on an object when that force acts over a period of time. The formula is:
J = F × Δt
Here, J is impulse, F is the average force applied, and Δt is the time the force acts.3 The key idea is that impulse equals the change in momentum (J = Δp).3 This is why a baseball catcher pulls their hand back when catching a ball. By increasing the time of contact, they reduce the force on their hand, even though the change in momentum stays the same. Airbags work the same way: the momentum change in a crash is the same with or without one, but the force is much smaller when it acts over a longer time.3
Conservation of Momentum in Collisions
One of the most important rules in physics is the law of conservation of momentum. It says that when two objects collide with no outside forces acting on them, their total momentum before the collision equals the total momentum after.4 This rule holds true for every type of collision.5
There are two main types of collisions:
- Elastic collisions: Both momentum and kinetic energy are conserved.5 The objects bounce off each other and no energy is lost to heat, sound, or deformation. Billiard balls are a close real-world example.
- Perfectly inelastic collisions: Momentum is still conserved, but the objects stick together after the collision.5 Kinetic energy is not conserved; some of it turns into heat, sound, or deformation.5 A car crash where the vehicles crumple together is a common example.
Momentum in Two Dimensions
In real life, objects don't always move along a single straight line. When motion happens on a flat surface, you need to break velocity into two parts: an x-component (horizontal) and a y-component (vertical). Momentum then also has two components: pₓ = m × vₓ and pᵧ = m × vᵧ.6 The total magnitude of momentum is found using the Pythagorean theorem: |p| = √(pₓ² + pᵧ²). The direction angle is calculated with the arctangent function.
Kinetic Energy and the de Broglie Wavelength
Kinetic energy is the energy an object has because of its motion, calculated as KE = ½mv².1 It is closely related to momentum: KE = p² / (2m). In collisions, comparing kinetic energy before and after tells you how much energy was lost or kept.
At a very tiny scale, every moving object also behaves like a wave. The de Broglie wavelength links momentum to this wave behavior using the formula λ = h / p, where h is Planck's constant (6.626 × 10⁻³⁴ J·s).7 For everyday objects like a thrown ball, this wavelength is unimaginably small, far too tiny to detect.7 But for particles like electrons, the de Broglie wavelength is large enough to matter and is a cornerstone of quantum mechanics.