Momentum Calculator

Free Online Momentum Calculator (p = mv)

This momentum calculator instantly solves for linear momentum, mass, or velocity using the fundamental formula p = m × v — Momentum equals Mass times Velocity. Enter any two known values — mass and velocity, momentum and velocity, or momentum and mass — in any common unit, and the calculator converts everything automatically, works through the full step-by-step solution, and plots your numbers on a labeled Momentum-Mass-Velocity triangle diagram so the entire calculation is visible at a glance.

Whether you're a physics student solving a momentum word problem, analyzing a collision, or just curious how much momentum a moving car or thrown ball carries, this tool handles kilograms, grams, pounds, and slugs for mass, m/s, km/h, mph, and ft/s for velocity, and kg·m/s, g·cm/s, lb·ft/s, or slug·ft/s for momentum — and always shows its complete working, not just the final number.

What Is Momentum? (Definition and Formula)

Momentum (specifically linear momentum) is a measure of the 'quantity of motion' an object has — it depends on both how much mass the object has and how fast it's moving. A heavy truck moving slowly and a light car moving fast can have similar momentum, since momentum scales directly with both mass and velocity. Momentum is a vector quantity, meaning it has both magnitude and direction, matching the direction of the object's velocity.

The formula for linear momentum is one of the cornerstone equations of classical mechanics:

• Momentum (p) = Mass (m) × Velocity (v)
• The SI unit of momentum is kilogram-meters per second (kg·m/s).
• Example: a 1000 kg car moving at 20 m/s has momentum = 1000 × 20 = 20,000 kg·m/s

Why Momentum Matters in Physics

Momentum is central to one of the most powerful principles in physics: the law of conservation of momentum, which states that the total momentum of a closed system remains constant unless acted on by an external force. This principle is what allows physicists and engineers to predict the outcome of collisions, explosions, and recoil events — from billiard balls colliding on a table to rockets launching into space — without needing to know every internal force involved.

How to Find Mass from Momentum and Velocity

If you already know an object's momentum and velocity, you can rearrange the momentum formula to solve for mass instead.

• Mass (m) = Momentum (p) ÷ Velocity (v)
• Example: an object has 15,000 kg·m/s of momentum while moving at 25 m/s → Mass = 15,000 ÷ 25 = 600 kg
• This rearrangement comes directly from dividing both sides of p = m × v by v.

How to Find Velocity from Momentum and Mass

If you know an object's momentum and mass, you can find its velocity by rearranging the formula once more.

• Velocity (v) = Momentum (p) ÷ Mass (m)
• Example: a 50 kg object has 500 kg·m/s of momentum → Velocity = 500 ÷ 50 = 10 m/s
• This rearrangement comes from dividing both sides of p = m × v by m.

The Momentum–Mass–Velocity Triangle

Just like the Speed-Distance-Time and Force-Mass-Acceleration triangles, the momentum formula has its own 'magic triangle' for remembering all three rearranged forms. Momentum sits at the top, with Mass and Velocity on the bottom row. Cover the quantity you're solving for with your finger, and what's left shows you the formula: covering p leaves m next to v (m × v); covering m leaves p over v (p ÷ v); covering v leaves p over m (p ÷ m). This calculator's diagram builds exactly this triangle using your real numbers, plus a moving-block sketch with the momentum vector drawn thicker to represent its magnitude.

Common Momentum, Mass, and Velocity Units

Momentum, mass, and velocity can each be expressed in several different unit systems depending on whether you're working in SI (metric), CGS, or imperial units. This calculator supports the most common ones used in physics classes and engineering.

• Momentum: kilogram-meters per second (kg·m/s), gram-centimeters per second (g·cm/s), pound-feet per second (lb·ft/s), slug-feet per second (slug·ft/s)
• Mass: kilograms (kg), grams (g), pounds (lb), slugs
• Velocity: meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), feet per second (ft/s)
• 1 kg·m/s = 100,000 g·cm/s ≈ 7.233 lb·ft/s ≈ 0.2248 slug·ft/s

How to Use This Momentum Calculator

Choose what you want to find — Momentum, Mass, or Velocity — from the dropdown. Then fill in the two values you already know, picking whichever unit matches your problem (kilograms, grams, pounds, or slugs for mass; m/s, km/h, mph, or ft/s for velocity; kg·m/s, g·cm/s, lb·ft/s, or slug·ft/s for momentum). The calculator instantly converts everything to a common base unit, applies p = m × v, and shows the result in your chosen unit — plus automatically converted into kg·m/s, g·cm/s, and lb·ft/s for quick reference.

Scroll down for the complete step-by-step solution, which mirrors exactly how you'd solve it by hand: the formula first, then your real values substituted in with unit conversion shown explicitly, then the arithmetic worked through to the final answer.

Worked Examples

Finding momentum: a 1000 kg car moving at 20 m/s → Momentum = 1000 × 20 = 20,000 kg·m/s.

Finding momentum for a small fast object: a 0.16 kg cricket ball bowled at 40 m/s → Momentum = 0.16 × 40 = 6.4 kg·m/s.

Finding momentum for a runner: a 70 kg sprinter at 10 m/s → Momentum = 70 × 10 = 700 kg·m/s.

Finding mass: an object with 15,000 kg·m/s of momentum moving at 25 m/s → Mass = 15,000 ÷ 25 = 600 kg.

Finding velocity: a 50 kg object with 500 kg·m/s of momentum → Velocity = 500 ÷ 50 = 10 m/s.

Momentum in Collisions: Elastic vs. Inelastic

Momentum calculations are especially important when analyzing collisions between two or more objects. In any collision — whether cars crashing, billiard balls striking each other, or subatomic particles interacting — the total momentum of the system before the collision equals the total momentum after the collision, as long as no external forces act on the system. In an elastic collision, kinetic energy is also conserved (objects bounce apart cleanly), while in an inelastic collision, some kinetic energy converts to heat, sound, or deformation, though momentum is still conserved. This calculator computes the momentum of a single object; comparing multiple objects' momentum before and after a collision is how conservation of momentum problems are typically solved.

Real-World Applications of Momentum

The momentum formula and the conservation of momentum principle appear throughout science, sports, and engineering:

• Automotive safety — analyzing crash forces and designing crumple zones based on how momentum changes during impact.
• Sports science — measuring the momentum of a bat, ball, or athlete to understand impact force and technique.
• Rocketry — momentum conservation explains rocket propulsion, where expelled exhaust gas gives the rocket forward momentum.
• Ballistics — calculating bullet or projectile momentum for impact and penetration analysis.
• Particle physics — momentum conservation is fundamental to analyzing collisions in particle accelerators.

Impulse and Its Relationship to Momentum

Impulse is closely related to momentum: it's defined as the change in momentum of an object, and equals the net force applied multiplied by the time over which it acts (Impulse = F × Δt = Δp). This is why airbags, padded gloves, and crumple zones work — they extend the time over which a force acts during a collision, reducing the peak force for the same change in momentum. Impulse and momentum share the same units (kg·m/s or N·s, which are equivalent), and the impulse-momentum theorem is a direct extension of the p = m × v formula this calculator is built around.

Tips for Solving Momentum Word Problems

Most textbook and exam word problems involving momentum follow a predictable pattern, and a few habits make them far easier to solve correctly:

• Identify which two quantities are given and which one is being asked for — this tells you whether to use p = m × v, m = p ÷ v, or v = p ÷ m.
• Write down the units of every given value before doing any arithmetic, and convert everything to kilograms and m/s first if unsure.
• Remember momentum is a vector — direction matters in collision and conservation problems, even though this calculator focuses on magnitude.
• Sanity-check your final answer: a walking person has momentum in the tens to low hundreds of kg·m/s; a moving car is typically in the thousands to tens of thousands of kg·m/s.

Frequently Asked Questions

What is the formula for momentum? Momentum = Mass × Velocity (p = m × v). This is the fundamental equation of linear momentum in classical mechanics.

How do you calculate momentum in kg·m/s? Multiply the object's mass in kilograms by its velocity in meters per second. For example, a 5 kg object moving at 3 m/s has momentum = 5 × 3 = 15 kg·m/s.

What is the difference between momentum and force? Momentum measures the 'quantity of motion' an object has (mass × velocity); force is what changes momentum over time (F = Δp ÷ Δt).

Is momentum conserved in every collision? Total momentum is always conserved in a closed system with no external forces, whether the collision is elastic or inelastic — though kinetic energy is only conserved in elastic collisions.

Can this calculator solve for mass or velocity, not just momentum? Yes — switch the 'What do you want to find?' dropdown to Mass or Velocity, and the calculator rearranges the formula automatically and solves for whichever value you need.

What is the SI unit of momentum? The SI unit of momentum is kilogram-meters per second (kg·m/s), which is equivalent to newton-seconds (N·s).