Momentum Calculator: Formula and Worked Example

A momentum calculator finds an object’s linear momentum from its mass and velocity, returning a signed value that shows both how much motion it has and its direction. Enter mass in kilograms and velocity in metres per second to calculate momentum in kilogram-metres per second (kg·m/s).

Formula

Linear momentum is mass multiplied by velocity:

p = m × v

• p is momentum, measured in kilogram-metres per second (kg·m/s).
• m is mass, measured in kilograms (kg).
• v is velocity, measured in metres per second (m/s).

Velocity includes direction, so it is represented with a positive or negative sign in a one-dimensional calculation. The calculator’s first result, Momentum, preserves that sign. Momentum magnitude is the nonnegative size of the momentum, calculated as |p|. In three dimensions, momentum is a vector: p⃗ = m v⃗, and the mass multiplies each component of velocity.

Worked Example

Using the calculator’s default values, the mass is 2 kg and the velocity is 3 m/s.

1. Apply the formula: p = m × v.
2. Substitute the values: p = 2 kg × 3 m/s.
3. Calculate: p = 6 kg·m/s.

The momentum magnitude is |6| = 6 kg·m/s. Both displayed results are rounded to two decimal places, so the calculator shows 6.00 kg·m/s for each.

What Momentum Means

Momentum describes an object’s motion in a way that combines how much matter it has with how fast and in what direction it moves. A heavy object moving slowly can have the same momentum as a light object moving quickly. For example, a 1,000 kg vehicle moving at 10 m/s has momentum of 10,000 kg·m/s; a 2,000 kg vehicle at 5 m/s has the same momentum.

Momentum is not the same as kinetic energy. Momentum depends on velocity, including its direction, while kinetic energy is a scalar and depends on the square of speed. In classical mechanics, kinetic energy is ½mv². Two objects can therefore have equal momentum but different kinetic energies if their masses differ.

The calculator treats mass as a positive quantity and velocity as signed. A negative velocity means motion in the direction you have defined as negative; it does not mean negative mass or a negative speed. If you only know speed, enter it as a positive number and interpret the result as momentum magnitude.

Using the Calculator and Choosing Units

For a useful result, make sure the mass and velocity describe the same object at the same moment. Convert measurements before entering them: the calculator’s formula expects kilograms and metres per second.

• To convert grams to kilograms, divide by 1,000. For example, 500 g = 0.5 kg.
• To convert kilometres per hour to metres per second, divide by 3.6. For example, 72 km/h = 20 m/s.
• To convert pounds of mass to kilograms, multiply by approximately 0.45359237. Distinguish pounds of mass from pound-force, which is a force unit.
• To convert miles per hour to metres per second, multiply by approximately 0.44704.

In US customary units, momentum is often expressed as slug·ft/s or lb·s when using a consistent force-and-mass system. Do not multiply pounds of mass directly by feet per second and label the result slug·ft/s: convert the mass to slugs first, or convert all inputs to SI units. The SI result kg·m/s is equivalent in dimensions to newton-seconds (N·s), since 1 N = 1 kg·m/s².

Conservation and Real-World Limits

Momentum is especially useful when analysing interactions such as collisions, recoil, and objects pushing apart. In an isolated system, total momentum is conserved: the vector sum of the objects’ momenta before an interaction equals the vector sum afterward. “Isolated” means external forces have no net impulse over the period being considered. A collision can change each object’s momentum while leaving the system’s total momentum unchanged.

This calculator finds the momentum of one object at one instant. It cannot by itself predict the outcome of a collision. That typically requires the masses and velocities of all relevant objects, a chosen coordinate direction, and information about external forces or the nature of the interaction. In multiple dimensions, calculate components separately or use vector arithmetic rather than simply adding magnitudes.

The equation p = mv is the classical, non-relativistic definition. It is appropriate for ordinary objects moving far below the speed of light. At speeds close to light speed, relativistic momentum is p = γmv, where γ = 1/√(1 − v²/c²), and c is the speed of light. The basic calculator does not apply that correction.

Common Mistakes

• Mixing units: Multiplying kilograms by km/h does not produce kg·m/s. Convert velocity to m/s first.
• Using distance instead of velocity: Momentum needs velocity, not distance travelled. If you have distance and elapsed time, calculate velocity only when the motion can reasonably be represented by that average.
• Ignoring direction: In a one-dimensional problem, choose a positive direction and use negative velocity for motion the other way. Adding speed values alone can give the wrong total momentum.
• Confusing mass and weight: Mass is measured in kilograms; weight is a force measured in newtons. The formula uses mass.
• Rounding too early: Keep extra digits during unit conversions and round the final displayed result. The calculator shows two decimal places, which may not reflect the precision of the original measurements.

Frequently Asked Questions

What is the formula for momentum?
For classical linear motion, momentum equals mass multiplied by velocity: p = mv. Use kilograms and metres per second to obtain kg·m/s.

Can momentum be negative?
Yes. In a one-dimensional calculation, a negative result indicates motion in the direction defined as negative. The magnitude of momentum is always zero or positive.

How do I calculate momentum from mph or km/h?
Convert speed to metres per second first. Divide km/h by 3.6, or multiply mph by approximately 0.44704, then multiply by mass in kilograms.

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

What is the difference between momentum and impulse?
Impulse is the change in momentum. For a constant force, impulse equals force multiplied by the time it acts, and is measured in N·s, equivalent to kg·m/s.

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in m | Mass | kg | 2 | 0
in v | Velocity | m/s | 3 | 
out momentum | Momentum | kg·m/s | m * v | 2
out magnitude | Momentum magnitude | kg·m/s | abs(momentum) | 2