Momentum Formula: How to Calculate p = mv

The momentum formula is p = mv: multiply an object’s mass by its velocity. Enter mass in kilograms and velocity in metres per second to calculate momentum in kilogram-metres per second; the sign shows the direction of motion.

Formula

Momentum = mass × velocity, written p = mv.

• p is momentum, measured in kilogram-metres per second (kg·m/s) in SI units.
• m is mass, measured in kilograms (kg).
• v is velocity, measured in metres per second (m/s). Velocity includes direction, unlike speed.

Momentum is a vector: its direction is the same as the object’s velocity. The calculator accepts a signed velocity along one chosen axis, so a negative value represents motion in the opposite direction. The formula applies to an object’s translational momentum at ordinary speeds; relativistic physics uses a different expression when speeds approach the speed of light.

Worked Example

Using the calculator’s default values, a 10 kg object moves at 5 m/s:

1. Write the relationship: p = mv.
2. Substitute the values: p = 10 kg × 5 m/s.
3. Multiply: p = 50 kg·m/s.

The result is 50.00 kg·m/s, shown to two decimal places. The units follow from the multiplication: kg multiplied by m/s gives kg·m/s.

What Momentum Means

Momentum describes how much motion an object has in a particular direction. For the same velocity, a more massive object has proportionally more momentum. For the same mass, increasing velocity also increases momentum in direct proportion. For example, doubling the mass while holding velocity fixed doubles momentum; doubling velocity while holding mass fixed does the same.

Momentum is not the same as kinetic energy. Momentum depends on velocity and mass as mv, while classical kinetic energy is ½mv². Their units differ: momentum uses kg·m/s, and kinetic energy uses joules. An object can have zero momentum if it is at rest in the chosen reference frame, even though it still has mass.

When to Use the Formula

Use p = mv when you know an object’s mass and velocity and need its momentum. It is useful in introductory mechanics, collision analysis, and descriptions of motion. In a collision, the momentum of an individual object can change, but the total momentum of a suitably defined isolated system is conserved: its total momentum before an interaction equals its total momentum afterward.

For motion in more than one direction, treat momentum as a vector. Calculate components along perpendicular axes rather than multiplying mass by a directionless speed. If an object has velocity components v_x and v_y, then its momentum components are p_x = mv_x and p_y = mv_y. Combine the components if you need the momentum’s magnitude and direction.

Units, Direction, and Conversions

Keep mass and velocity units consistent. The calculator uses kg and m/s, producing kg·m/s. In US customary units, mass may be expressed in slugs and velocity in feet per second, giving slug·ft/s. Do not multiply weight in pounds-force by velocity and treat the result as mass-based momentum: pounds-force measure force, not mass. Convert to mass units first.

• Convert grams to kilograms by dividing by 1,000.
• Convert kilometres per hour to metres per second by dividing by 3.6.
• Convert miles per hour to metres per second by multiplying by about 0.44704.
• For an object moving left while right is defined as positive, enter a negative velocity; the calculated momentum will also be negative.

For instance, 72 km/h is 20 m/s. A 1,000 kg vehicle at that velocity has momentum 20,000 kg·m/s in the direction it travels. The chosen direction convention determines whether the number is positive or negative.

Common Mistakes and Limits

A frequent error is substituting speed when the question requires a direction-aware result. Speed gives only a nonnegative magnitude; velocity carries direction. If only the magnitude of momentum is requested, use the magnitude of velocity and report the momentum magnitude as |p| = m|v|. If direction matters, preserve the sign or state the vector direction.

Another common issue is mixing units—for example, entering mass in grams as though it were kilograms, or using km/h directly with a result expected in kg·m/s. Convert first, and round only the final answer when practical. The calculator’s two-decimal display is a presentation choice; it does not imply the measurements themselves are precise to that level.

The basic equation assumes mass is known and treats the object as a whole. For a system containing multiple objects, calculate each object’s momentum with its own mass and velocity, then add the momenta as vectors. Momentum can also change when a net external force acts over time; the impulse-momentum relationship connects the change in momentum to the net force acting during an interval.

Frequently Asked Questions

What is the momentum formula?
For ordinary classical mechanics, momentum is mass multiplied by velocity: p = mv.

What is the SI unit of momentum?
The SI unit is the kilogram-metre per second (kg·m/s). It is equivalent in dimensions to a newton-second (N·s).

Can momentum be negative?
Yes. In one-dimensional calculations, a negative value indicates motion opposite to the direction chosen as positive. Momentum’s magnitude itself is not negative.

How do you calculate momentum from speed?
Multiply mass by speed to find the magnitude of momentum: |p| = m × speed. To include direction, use velocity instead and assign its appropriate sign or vector components.

Is momentum the same as force?
No. Momentum is mass times velocity, measured in kg·m/s. Force describes how momentum changes over time; in Newtonian mechanics, net force equals the rate of change of momentum.

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in m | Mass | kg | 10 | 0
in v | Velocity | m/s | 5 | 
out p | Momentum | kg·m/s | m * v | 2