How can I calculate linear momentum from mass and velocity?

Use p = mv. Here, *p* is linear momentum, *m* is mass, and *v* is velocity. Multiply the mass by the velocity—not by speed alone if the direction matters. Momentum is a vector in the same direction as velocity, so in a one-dimensional problem its sign carries direction information. [S1]

For the standard SI momentum unit, put mass in kilograms (kg) and velocity in meters per second (m/s); the result is kg·m/s. [S1] Before calculating, identify which direction your problem treats as positive. That convention gives meaning to a plus or minus sign.

Suppose, as an example, an object has a mass of 2 kg and moves at 3 m/s in the negative direction. These are illustrative values, not measurements. Write its velocity as −3 m/s, then substitute:

p = mv = (2 kg)(−3 m/s) = −6 kg·m/s

The magnitude is 6 kg·m/s, while the negative sign says the momentum points in the direction you defined as negative. Do not erase the sign just because a magnitude is positive: the signed answer is useful when comparing motion or combining one-dimensional momenta.

Convert the values to kilograms and meters per second before multiplying if you want momentum in kg·m/s. For instance, if a worksheet gives mass in grams, first express that mass in kilograms; if velocity is in another distance-per-time unit, convert it to m/s. Keep the velocity’s direction sign through the conversion.

A useful setup is to write the conversion and units on the page before doing the arithmetic:

p = (mass in kg) × (velocity in m/s)

Then check the units: kg multiplied by m/s gives kg·m/s. [S1] The source establishes this SI-unit setup; it does not supply conversion factors for every possible unit, so use the conversion information provided by your class or problem.

Check three things: you multiplied mass by velocity, the units match the units you intended, and the sign agrees with your chosen direction convention. If the mass is positive, the momentum’s sign should match the velocity’s sign because p = mv. [S1]

For a copyable solution, write:

Direction convention: + = [chosen direction] m = [mass in kg] v = [signed velocity in m/s] p = mv = ([mass] kg)([signed velocity] m/s) = [signed result] kg·m/s

For the example above, choosing the object’s travel direction as negative gives −6 kg·m/s. This method is for one-dimensional classical momentum calculations; it does not determine missing mass or velocity, or resolve a problem whose direction convention is unclear.