Momentum combines mass and velocity into one quantity, and it is what stays conserved when objects collide — not speed, which is easy to conflate with it.
How it works
Momentum, and a perfectly inelastic collision
p = m v · v_final = (m₁v₁ + m₂v₂) / (m₁ + m₂)
The collision formula is for a perfectly inelastic collision — two objects that stick together on impact — where total momentum before equals total momentum after.
Why momentum, not speed, decides a collision
A heavy truck moving slowly can carry the same momentum as a light car moving fast. What determines the outcome of a collision between them is the momentum each brings, not which one “seems” to be moving faster — a fact intuition gets wrong precisely because it tends to focus on speed alone. This calculator’s collision mode makes the arithmetic explicit: enter both objects’ mass and velocity, and it computes the combined velocity they move at together afterward.
How to use this calculator
- For a single object’s momentum, use the simple mode with mass and velocity.
- For a collision, switch to the collision mode and enter both objects’ mass and velocity — use a negative velocity for something moving in the opposite direction.
- Read the combined velocity, or the individual momentum.
Frequently asked questions
What does a negative velocity mean in the collision mode?
Motion in the opposite direction to whatever you have treated as positive. Two objects with equal and opposite momenta — same mass, equal and opposite velocities — cancel out entirely, and the combined result after a collision is zero: they stop dead.
What’s the difference between momentum and kinetic energy?
Momentum (mv) is conserved in every collision, elastic or not. Kinetic energy (½mv²) is only conserved in a perfectly elastic collision — in the perfectly inelastic collisions this calculator models, some kinetic energy is lost (usually to heat and deformation) even though momentum is not.
Why “perfectly inelastic” specifically?
Because it is the simplest case to compute exactly — the two objects move together afterward at one shared velocity, so there is only one unknown to solve for. Real collisions are often somewhere between perfectly elastic and perfectly inelastic, which needs more information than mass and velocity alone.
Can momentum be more useful than speed for predicting a collision’s outcome?
Often, yes — because momentum accounts for mass as well as speed, it is the quantity that is actually conserved, and predicting a collision’s outcome from speed alone, ignoring mass, will generally give the wrong answer.
Why is momentum a vector, and does this calculator handle direction properly?
Momentum has both size and direction, which is why velocity (not just speed) appears in the formula. This calculator handles one dimension — objects moving along the same line — with direction represented by the sign of the velocity, positive or negative.
