Momentum Calculator
Momentum of one object, plus elastic and inelastic two-body collisions.
What is Momentum?
Momentum is mass times velocity, written p = mv, and it is the quantity that is always conserved in a collision. Two collisions look very different in terms of kinetic energy — an elastic collision keeps it all, an inelastic one loses some to heat and deformation — but both conserve total momentum, which is why momentum is the reliable tool for collision problems.
How it works
For a single object, p = mv. For a two-body collision the solver applies conservation of momentum to both objects, and in the elastic case additionally imposes conservation of kinetic energy, which fixes both final velocities. The inelastic case gives them a shared final velocity. Both modes report momentum before and after, and the energy lost, so the difference between the two kinds of collision is visible rather than asserted.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What is the difference between elastic and inelastic collisions?
In an elastic collision both momentum and kinetic energy are conserved — billiard balls are close. In a perfectly inelastic collision the objects stick together and move off as one, conserving momentum but losing kinetic energy to heat and deformation.
Does a negative velocity mean anything?
It means the object is moving in the opposite direction from the one you called positive. Sign matters for momentum, which is a vector — two objects moving towards each other have momenta of opposite sign.
Why is kinetic energy lost but momentum not?
Momentum conservation follows from Newton's third law, which has no exceptions. Kinetic energy can be converted into other forms — sound, heat, bent metal — and in an inelastic collision that is exactly what happens.