Momentum Calculator

Find Momentum From Mass and Velocity

Momentum Formula

Formula

\[ p = m \cdot v \]

Where:

\(p\) — momentum (kg·m/s)
\(m\) — mass of the object (kg)
\(v\) — velocity of the object (m/s)

Momentum is the product of an object's mass and its velocity. The two equations below let you rearrange the same relationship to solve for mass or velocity when momentum is known:

\[ m = \frac{p}{v} \qquad v = \frac{p}{m} \]

Momentum – Calculation Example

Example: a cart with a mass of 10 kg rolls along a track at 5 m/s. Find its momentum.

\[ p = m \cdot v = 10 \times 5 = 50 \ \text{kg·m/s} \]

Result: the momentum of the cart is 50 kg·m/s.

The same calculation works in reverse: if a 10 kg object has a momentum of 50 kg·m/s, its velocity is \( 50 / 10 = 5 \) m/s, and if it moves at 5 m/s with a momentum of 50 kg·m/s, its mass is \( 50 / 5 = 10 \) kg.

How to Use the Calculator

Open the “I want to calculate” dropdown and choose whether you need Momentum (p), Mass (m), or Velocity (v). The calculator hides the field for the value you are solving for.
Enter the Mass (m) and select kg or g as the unit in the dropdown next to the input.
Enter the Velocity (v) and select m/s or km/h as the unit.
If you are solving for mass or velocity, enter the known Momentum (p) in kg·m/s instead of the missing field.
Read the result under Result. Momentum is given in kg·m/s, mass in kg, and velocity in m/s.

What Is Momentum?

Momentum (also called linear momentum) is a measure of the quantity of motion an object has. It combines two things that matter in a collision: how much stuff is moving (mass) and how fast it is moving (velocity). A loaded truck creeping at 5 km/h and a rifle bullet at 900 m/s can carry comparable momentum, even though their masses and speeds differ enormously.

Momentum is a vector quantity: it has both a magnitude and a direction, and the direction is the same as the object's velocity. In one-dimensional problems the sign of the result tells you the direction — a negative momentum means the object moves in the negative direction of your chosen axis. This calculator works with the magnitude, so enter speeds as positive numbers unless your problem defines a direction.

Momentum matters because it is conserved. In an isolated system — one with no external forces acting — the total momentum before an event equals the total momentum after it. This conservation law is what makes collision analysis possible: you can predict how objects rebound after a crash, how rockets gain speed by expelling exhaust, or how a recoil works, all by tracking momentum. It follows directly from Newton's second law, since force equals the rate of change of momentum, \( F = \Delta p / \Delta t \).

When interpreting your result, remember that momentum alone doesn't tell the whole story of a collision. Two objects with the same momentum can deliver very different forces on impact, because the force depends on how quickly the momentum changes — a principle you can explore with our Stopping Distance Calculator. For rotating objects, the analogous quantity is angular momentum; see our Angular Momentum Calculator.

Units and Conversions

The SI unit of momentum is the kilogram-meter per second (kg·m/s), which is what this calculator returns. If you enter mass in grams, the calculator converts it to kilograms (1 kg = 1000 g), and if you enter velocity in km/h, it converts it to m/s (divide by 3.6) before applying the formula. For example, 1 kg at 36 km/h has a momentum of \( 1 \times (36/3.6) = 10 \) kg·m/s, not 36.

Assumptions and Limitations

Classical speeds only. The formula \( p = mv \) is valid at everyday speeds. Near the speed of light, relativistic effects increase momentum, and this calculator does not account for them.
Constant mass. The object's mass is assumed not to change during the motion. Systems like rockets, which lose mass as they burn fuel, need a variable-mass treatment.
Point-mass, straight-line motion. The calculator treats the object as a single mass moving along a line. Rotating bodies have additional rotational motion described by angular momentum.
Direction is not tracked. Enter the speed (magnitude of velocity). If your problem involves opposite directions, assign signs manually — for example, head-on collisions where one object's momentum is negative.
Zero values. Solving for mass requires a non-zero velocity, and solving for velocity requires a non-zero mass; the calculator warns you if the divisor is zero. An object at rest (\( v = 0 \)) simply has zero momentum.

Practical Tips

Keep units consistent before doing math by hand: convert grams to kilograms and km/h to m/s first, exactly as the calculator does automatically.
In collision problems, calculate the momentum of each object separately, assign signs by direction, then add them to get the total momentum of the system.
Momentum pairs naturally with kinetic energy: momentum depends on \( v \), while kinetic energy depends on \( v^2 \). Doubling the speed doubles momentum but quadruples kinetic energy.
For motion problems involving gravity, combine this tool with the Free Fall Calculator to find velocities before computing momentum.

Frequently Asked Questions

How do I calculate momentum step by step without a calculator?

First convert mass to kilograms (divide grams by 1000) and speed to m/s (divide km/h by 3.6). Then simply multiply: momentum = mass × velocity. For example, a 500 g ball moving at 72 km/h: mass is 0.5 kg, speed is 20 m/s, so \( p = 0.5 \times 20 = 10 \) kg·m/s. Keep a note of the direction if the problem involves more than one moving object.

What is a typical momentum of everyday objects?

A 70 kg person walking at 1.5 m/s has about 105 kg·m/s of momentum. A 1500 kg car driving at 90 km/h (25 m/s) carries roughly 37,500 kg·m/s. A 10 g bullet at 400 m/s has only 4 kg·m/s — small mass, high speed. These comparisons show why heavy, slow objects and light, fast objects can be similarly hard to stop.

How do I convert momentum to other units like g·cm/s or N·s?

To go from kg·m/s to g·cm/s, multiply by 100,000 (1 kg·m/s = 10⁵ g·cm/s), since 1 kg = 1000 g and 1 m = 100 cm. One kg·m/s is also equal to 1 newton-second (N·s), the unit of impulse, because impulse equals change in momentum. In imperial units, 1 kg·m/s ≈ 7.23 slug·ft/s or about 2.2 lb·s.

What is the difference between momentum and kinetic energy?

Momentum is \( mv \) and is a vector (it has direction); kinetic energy is \( \tfrac{1}{2}mv^2 \) and is a scalar. Momentum is conserved in every isolated collision, while kinetic energy is only conserved in perfectly elastic ones. Doubling speed doubles momentum but quadruples kinetic energy. That's why a slow truck and a fast bullet can have equal momentum yet very different impact energy.

Can momentum be negative, and how do I handle direction?

Yes. Because momentum is a vector, its sign shows direction along your chosen axis: positive means one way, negative means the other. This calculator works with magnitudes, so in head-on collision problems assign signs yourself — for example +40 and −30 kg·m/s — then add them to find total system momentum. The direction of momentum always matches the direction of velocity.

How do I find velocity after a collision using momentum?

Use conservation of momentum: total momentum before equals total momentum after. Calculate each object's momentum separately, assign signs for direction, and add them. If the objects stick together, divide the total momentum by the combined mass to get their common velocity: \( v = p_{total} / m_{total} \). This works for both elastic and inelastic collisions; only kinetic energy conservation depends on the collision type.

When does the formula p = mv stop working?

At speeds approaching the speed of light, relativistic effects inflate momentum, and you'd need \( p = \gamma mv \) instead. At everyday speeds — even a jet aircraft — the classical formula is accurate to many decimal places. Also note this calculator assumes constant mass, so it doesn't describe rockets shedding fuel, and it ignores rotation, which is covered by angular momentum.