Momentum Calculator for p = mv and Collisions
This momentum calculator works out linear momentum from the formula p = mv and analyzes collisions between two objects. Enter any two of momentum, mass, and velocity to solve for the third, or switch to collision mode to find the velocities after an elastic or perfectly inelastic impact.
It is built for physics students, teachers, and anyone checking homework or experiment results. Momentum is a vector quantity, so direction matters — use negative velocities for objects moving the opposite way. Every result includes a step-by-step formula breakdown, unit conversions, and a comparison with real-world references.
How to Calculate Momentum
Pick a mode
Choose the Linear Momentum tab to work with a single object, or the Collision tab to analyze two objects colliding.
Choose what to solve for
In Linear Momentum mode, select Momentum, Mass, or Velocity. In Collision mode, pick Elastic or Perfectly Inelastic.
Enter values and units
Type the known values and pick their units from the dropdowns. In Collision mode, enter the mass and initial velocity for both objects, using negative velocity for the opposite direction.
Read the result
The answer appears instantly as you type. Open Unit Conversions to see it in every supported unit, and review the formula steps, comparison bars, and energy analysis below.
Features
Linear Momentum (p = mv)
Solve for momentum, mass, or velocity by entering the other two values, with results updating in real time as you type.
Multiple Unit Systems
Momentum in kg·m/s, N·s, g·cm/s, lb·ft/s, slug·ft/s; mass in kg, g, mg, lb, oz, ton, slug; velocity in m/s, km/h, mph, ft/s, knots.
Formula Breakdown
See the complete calculation written out with your actual input values and the highlighted final answer.
Unit Conversion Table
Expand one panel to view your result converted into every supported unit at once, with the current unit highlighted.
Real-World Comparison
Compare your momentum against references like a tennis ball serve, a person running, a bicycle, a car, and a train.
Collision Calculator
Solve two-object collisions and get the final velocity of each object after the impact.
Elastic & Inelastic Types
Elastic collisions conserve momentum and kinetic energy; perfectly inelastic collisions have the objects stick together with energy lost.
Conservation Check
Momentum before and after is shown side by side so you can confirm that total momentum is conserved.
Kinetic Energy Analysis
View kinetic energy before and after a collision, plus the exact energy lost and the loss percentage for inelastic impacts.
Before / After Bars
Visual bars show how momentum and kinetic energy change across the collision at a glance.
Frequently Asked Questions
What is the formula for momentum?
Momentum is the product of mass and velocity: p = mv. Multiply an object's mass by its velocity to get its momentum. Because velocity has direction, momentum is a vector quantity and shares that direction.
How do you calculate momentum?
Enter the mass and velocity in Linear Momentum mode and the calculator multiplies them to give momentum. You can also solve in reverse — choose Mass or Velocity to find that value from a known momentum and the other quantity.
What units is momentum measured in?
The SI unit of momentum is the kilogram metre per second (kg·m/s), which is equivalent to the newton-second (N·s). The calculator also supports g·cm/s, lb·ft/s, and slug·ft/s, and the conversion table shows your result in all of them.
Can momentum be negative?
Yes. Since momentum is a vector, a negative value simply means the object is moving in the opposite direction to your chosen positive reference. In collision mode, use a negative velocity for an object travelling the other way.
What does "momentum is conserved" mean?
Conservation of momentum means the total momentum of a closed system stays the same before and after an interaction. It holds for every collision type, which is why the collision tab shows the momentum before and after side by side for you to verify.
What is the difference between elastic and inelastic collisions?
In an elastic collision, both momentum and kinetic energy are conserved and the objects bounce apart. In a perfectly inelastic collision, the objects stick together and move as one — momentum is still conserved, but some kinetic energy is converted to heat, sound, or deformation.
How much energy is lost in a perfectly inelastic collision?
It depends on the masses and velocities involved. The calculator shows the kinetic energy before and after the impact along with the exact energy lost and its percentage. That lost energy becomes heat, sound, and deformation.
Why do collision results show m/s even when I enter km/h?
The collision calculator converts every input to SI units (kg and m/s) internally for accurate computation, so the final velocities are displayed in m/s. The formula display still echoes your original values and units for reference.
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