Introduction
Momentum is one of the most important ideas in physics. It tells you how hard it is to stop a moving object. 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 fast. This is because both mass and speed matter when you calculate how much "push" a moving object carries.
This momentum calculator lets you solve for any of the three values in the equation — momentum, mass, or velocity — when you know the other two. Just pick the variable you want to find, enter your numbers, and choose your units. The tool handles all unit conversions for you, so you can mix kilograms with miles per hour or grams with feet per second without doing extra math. It also shows a step-by-step solution so you can see exactly how the answer was found. Whether you're a student working through a homework problem, a teacher building a lesson, or just curious about the momentum of everyday objects like cars, baseballs, or bullets, this calculator gives you a fast and accurate answer every time.
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. Choose your calculation mode using the tabs at the top, and the result will appear instantly with a step-by-step solution.
Calculation Mode: Select the tab that matches what you want to find. 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: Enter the mass of the object as a positive number. Use the dropdown menu next to the field to pick your unit, such as kilograms (kg), grams (g), pounds (lb), ounces (oz), metric tons, or even atomic mass units (u).
Velocity: Enter how fast the object is moving. A negative number means the object moves in the opposite direction. Pick your unit from the dropdown, including meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), feet per second (ft/s), knots, or Mach. If you need to determine velocity from other variables first, our acceleration calculator can help you find speed from acceleration and time.
Momentum: When solving for mass or velocity, enter the known momentum value here. Select your momentum unit from the dropdown, such as kg·m/s, Newton-seconds (N·s), or pound-feet per second (lb·ft/s).
Decimal Precision: Choose how many decimal places you want in your answer. Leave it set to "Auto" and the calculator will pick a clean, readable format for you.
Result Notation: Pick how the answer is displayed. "Standard" shows a regular number, "Scientific" uses powers of ten like 2.0e4, and "Engineering" uses exponents that are multiples of three. For help converting between standard and scientific notation, try our scientific notation calculator.
Auto-calculate on input change: Keep this box checked if you want the result to update right away each time you change a number or unit. Uncheck it if you prefer to click the "Calculate" button yourself.
Quick Examples: Click any example card — such as a bullet, car, baseball, freight train, electron, or satellite — to load real-world values into the calculator and see the momentum result right away.
What Is Momentum?
Momentum is a key idea in physics that describes how hard it is to stop a moving object. Every object that has mass and is moving has momentum. The heavier an object is and the faster it moves, the more momentum it has. A slow-moving freight train and a speeding bullet can both have large momentum, but for different reasons — one is very heavy, and the other is very fast.
The Momentum Formula
Momentum is calculated using a simple equation:
p = m × v
In this formula, p stands for momentum, m stands for mass, and v stands for velocity. The standard unit for momentum is kg·m/s (kilogram-meters per second). You can rearrange this formula to find any of the three values if you know the other two:
- To find mass: m = p ÷ v
- To find velocity: v = p ÷ m
This equation is closely related to Newton's second law of motion. Since force equals the rate of change of momentum, you can use our force calculator to explore how force, mass, and acceleration connect to momentum.
Momentum Is a Vector
Momentum is a vector quantity, which means it has both a size (magnitude) and a direction. A car moving east at 60 km/h has a different momentum than the same car moving west at 60 km/h. The direction of an object's momentum is always the same as the direction of its velocity. This is why the calculator shows an arrow pointing left or right — a negative value means the object is moving in the opposite direction. When analyzing motion in two dimensions, our projectile motion calculator can help you break velocity into components, which is useful for finding momentum along each axis.
Why Momentum Matters
Momentum is important because of the law of conservation of momentum. This law states that in a closed system with no outside forces, the total momentum before an event (like a collision) equals the total momentum after it. Scientists and engineers use this law to study car crashes, rocket propulsion, sports collisions, and the motion of particles at the atomic level.
Real-World Examples of Momentum
Momentum shows up everywhere in daily life and in science:
- A 9mm bullet (8 grams at 380 m/s) has about 3.04 kg·m/s of momentum. It is light but extremely fast.
- A car (1,500 kg at 60 km/h) has about 25,000 kg·m/s of momentum. It is much heavier, so even at a modest speed its momentum is very large.
- A freight train (10,000 metric tons at 80 km/h) has an enormous momentum of about 222,000,000 kg·m/s, which is why trains take such a long distance to stop.
- An electron orbiting an atom has incredibly tiny momentum because its mass is only about 9.1 × 10⁻³¹ kg, even though it moves at millions of meters per second.
For objects in free fall — such as a skydiver or a dropped ball — you can use our free fall calculator to find the velocity just before impact, and then plug that value into this momentum calculator to determine the object's momentum at that instant.
Momentum vs. Kinetic Energy
Momentum and kinetic energy both describe moving objects, but they are not the same thing. Kinetic energy depends on the square of velocity (KE = ½mv²), while momentum depends on velocity directly (p = mv). This means that doubling an object's speed will double its momentum but quadruple its kinetic energy. Another key difference is that momentum is a vector (it has direction), while kinetic energy is a scalar (it does not). To explore the energy side of motion, try our kinetic energy calculator. You can also compare kinetic energy with stored energy using the potential energy calculator.
Impulse and Changing Momentum
To change an object's momentum, you need to apply a force over a period of time. This is called impulse, and it equals the change in momentum: J = F × t = Δp. This is why airbags work — they increase the time over which a force acts during a crash, which reduces the peak force on a person even though the total change in momentum stays the same. Our impulse calculator lets you compute impulse directly from force and time, and our force calculator can help you determine the force required to produce a given change in momentum. For situations involving rotational motion rather than linear motion, the torque calculator is the rotational equivalent of these concepts. You may also find the displacement calculator useful when analyzing how far an object travels while its momentum changes.