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Mass in motion

Momentum Calculator

Find linear momentum, mass, or velocity from the other two values. Mix units and use positive or negative signs to keep track of direction.

Calculate momentum, mass, or velocity

Use one object and one reference frame. Momentum and velocity may be signed; mass must be greater than zero.

Choose one positive axis direction. A negative velocity or momentum points the other way. Use a period for decimals; grouped values such as 1,000.50 are accepted.

Example: 2 kg × 3 m/s → 6 kg·m/s.

Momentum

Enter the two known values, then select Calculate.

≈ marks display rounding. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.

Three worked examples

Momentum

A 2 kg cart moving at 3 m/s

p = m × v

2 × 3 = 6 kg·m/s, also written as 6 N·s. Reversing the velocity to −3 m/s gives −6 kg·m/s, with the same magnitude.

Velocity

A 500 g object with −6 N·s momentum

v = p ÷ m

500 g = 0.5 kg. Then −6 ÷ 0.5 = −12 m/s, or −43.2 km/h. The minus sign means motion in the negative axis direction.

Mass

−10 kg·m/s at −2 m/s

m = p ÷ v

−10 ÷ −2 = 5 kg. The matching negative signs cancel. Momentum and velocity with opposite signs would imply a negative mass, outside this model.

Model, units, and rounding

This tool uses classical linear momentum, p = mv, for one object with positive mass moving along one axis in a chosen reference frame. A sign gives the direction on that axis. It does not resolve three-dimensional vectors, combine multiple objects, or solve collisions. See OpenStax — Linear momentum.

Unit conversions use exact definitions: 1 N·s = 1 kg·m/s; 1 g·cm/s = 0.00001 kg·m/s; 1 kg·km/h = 5/18 kg·m/s; 1 kg = 1,000 g; 1 lb = 0.45359237 kg; 1 ft = 0.3048 m; 1 mph = 0.44704 m/s; and 1 km/h = 5/18 m/s. Pounds here mean avoirdupois mass. References: NIST conversion factors and NIST exact pound definition, note 22.

When finding mass, momentum and velocity must be nonzero and have the same sign. Two zeros do not determine a unique mass. Just one zero is incompatible with a finite positive mass. With a supplied positive mass, zero momentum and zero velocity are valid.

Classical momentum is an approximation for speeds small compared with light speed. The calculator shows a caution when the speed magnitude reaches 10% of c; that threshold is a display convention, not a guarantee of accuracy below it. At or above c, the displayed arithmetic is not physically valid for a massive object. It never switches to a relativistic formula. See OpenStax — Relativistic momentum. The exact vacuum light speed used is c = 299,792,458 m/s, as defined in NIST's SI defining constants.

Active inputs accept at most 64 characters, 15 integer digits, and 10 decimal places. Expressions, scientific notation, and units inside numeric fields are not accepted. Hidden fields are disabled and ignored.

Arithmetic and unit conversions retain exact fractions. Only displayed values are rounded; halfway values round away from zero, and trailing zeros are omitted. ≈ identifies rounding. A tiny nonzero value can display as ≈ 0; its direction still comes from the unrounded value. Changing result units or maximum decimal places updates the result without adding a recent-calculation entry. Display precision does not establish measurement accuracy.

Common questions

Can momentum be negative?

Yes. A negative sign means momentum points opposite your chosen positive direction. The magnitude is its absolute value and cannot be negative. With positive mass, momentum and velocity always have matching signs.

Is N·s the same as kg·m/s?

Yes. A newton is kg·m/s², so multiplying by seconds gives kg·m/s. Impulse uses the same units and describes a change in momentum; a momentum value alone does not tell you the impulse of a collision.

Is momentum the same as kinetic energy?

No. Classical momentum is p = mv and includes direction. Classical translational kinetic energy is K = ½mv² and is a nonnegative scalar. Reversing velocity reverses momentum while leaving kinetic energy unchanged.

Can this calculate the result of a collision?

This calculator evaluates one object's momentum, mass, or velocity. A collision analysis needs the other objects and additional conditions, such as whether momentum is conserved for the chosen system and whether the collision is elastic.

Does zero momentum mean an object has no mass?

No. An object with positive mass has zero momentum when its velocity is zero in your reference frame. Zero momentum and zero velocity cannot reveal its mass because any positive mass would satisfy p = mv.