Introduction
Momentum is a key idea in physics that tells you how hard it is to stop a moving object. 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). 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. You also get a step-by-step solution that shows exactly how the answer was found, which is great for homework or double-checking your work. Try one of the built-in examples, like a speeding bullet or a freight train, to see how momentum changes with different masses and speeds.
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, decimal precision, and result notation.
Calculation Mode (Tabs): Pick what you want to solve for by clicking one of the three tabs at the top. Choose "Calculate Momentum" if you know mass and velocity, "Calculate Mass" if you know momentum and velocity, or "Calculate Velocity" if you know momentum and mass.
Mass: Type in the mass of the object. Use the dropdown menu next to the field to pick a unit such as kilograms (kg), grams (g), pounds (lb), ounces (oz), metric tons, or even atomic mass units (u).
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 a unit like meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), feet per second (ft/s), knots, or Mach.
Momentum: If you are solving for mass or velocity, type in the known momentum value. Use the dropdown to choose a unit such as kg·m/s, N·s (newton-seconds), kN·s, dyn·s, lb·ft/s, lbf·s, or slug·ft/s.
Decimal Precision: Select how many decimal places you want in your answer. Choose "Auto" to let the calculator decide, or pick a specific number from 3 to 9 digits.
Result Notation: Choose how you want your answer displayed. "Standard" shows a regular number, "Scientific" uses powers of ten (like 2.0e4), and "Engineering" uses exponents that are multiples of three.
Auto-Calculate: Check this box if you want the result to update right away each time you change an input. Uncheck it if you prefer to click the "Calculate" button yourself.
Results: After you calculate, the answer appears in the Results section along with a direction arrow showing positive or negative momentum. You can also use the "Alternative Units" dropdown to quickly convert your result into a different unit, or click "Copy Result" to copy it to your clipboard.
Step-by-Step Solution: Click "Show/Hide" under the results to see every step the calculator took, including unit conversions and the final formula used to reach your answer.
Quick Examples: Click any example card, such as Bullet, Car Crash, Baseball, Freight Train, Electron, or Satellite, to auto-fill the inputs with real-world values and instantly see the momentum result.
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). Because velocity has a direction, momentum is a vector, meaning it also has a direction. 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. The key idea is that impulse equals the change in momentum (J = Δp). 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.
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. This rule holds true for every type of collision.
There are two main types of collisions:
- Elastic collisions: Both momentum and kinetic energy are conserved. 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. Kinetic energy is not conserved; some of it turns into heat, sound, or deformation. 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. 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. 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). For everyday objects like a thrown ball, this wavelength is unimaginably small, far too tiny to detect. But for particles like electrons, the de Broglie wavelength is large enough to matter and is a cornerstone of quantum mechanics.