Momentum Calculator: p = mv, With Units and Steps
Find momentum, mass or signed velocity, or calculate impulse from a change in velocity. Choose input units and see the conversion to SI, equation and substitution. The tool handles one-dimensional classical motion with positive mass.
Enter your values or load an example to see the answer and worked steps. Calculations run in your browser.
Momentum includes direction
For a fixed choice of positive direction, p = mv. A 2 kg object moving at +3 m/s has momentum +6 kg·m/s; at −3 m/s its momentum is −6 kg·m/s. Speed alone is insufficient when objects travel in opposite directions.
Solve for the missing quantity
Rearrange to m = p/v or v = p/m. A positive mass requires momentum and velocity to have the same sign. If both p and v are zero, infinitely many positive masses are possible, so the calculator reports that the mass cannot be uniquely determined.
Impulse is a change in momentum
For constant mass, J = m(vᶠ − vᵢ). Changing a 2 kg object from +3 to −2 m/s gives J = −10 N·s. Over 0.5 seconds, the average net force is −20 N. This is an average over the interval, not a peak collision force.
Conservation applies to a system
Total momentum is conserved when the net external impulse on the chosen system is zero. For two objects along one line, add their signed momenta before and after the interaction. This calculator evaluates individual momentum or impulse terms; it does not infer an unknown collision model.
Check units and model limits
The result uses kilograms, metres and seconds. Pounds are treated as a unit of mass, not pounds-force. For speeds at or above 10% of the speed of light, use a relativistic calculation instead of this classical tool.
References
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Frequently Asked Questions
Can momentum be negative?
Yes. Its sign indicates direction relative to the positive axis you chose. Mass stays positive.
Why cannot zero momentum and velocity determine mass?
The equation 0 = m × 0 is true for any positive mass, so those two values do not identify one mass.
What is the difference between impulse and force?
Impulse is change in momentum, measured in N·s. Dividing by the time interval gives average net force in N.
Does this solve a two-dimensional collision?
No. It handles one-dimensional classical momentum and constant-mass impulse. More complex collisions require vector components and additional assumptions.
Continue in the app
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