Momentum Calculator
Momentum measures how much motion an object carries, found by multiplying its mass by its velocity. Solve for momentum, mass or velocity, switch between metric and imperial units, add a second axis to get the magnitude and direction of a 2D vector, and read the kinetic energy alongside it.
Formula
Worked example
A 1500 kg car moving at 20 m/s has momentum p = m × v = 1500 × 20 = 30,000 kg·m/s in the direction of travel. Working backward, a 30,000 kg·m/s momentum at 20 m/s implies a mass of 30,000 ÷ 20 = 1500 kg.
What momentum means
Linear momentum is a measure of the quantity of motion an object has, defined as the product of its mass and its velocity, p = m·v. Because velocity is a vector, momentum is a vector too: it points in the same direction the object moves, and its sign depends on the axis you choose as positive. A heavy object moving slowly can have the same momentum as a light object moving quickly, since only the product of mass and velocity matters. In SI units, mass is in kilograms and velocity in metres per second, so momentum is expressed in kilogram-metres per second (kg·m/s), which is equivalent to newton-seconds. This calculator also reports the imperial equivalent in pound-feet per second for US engineering work.
Reverse solving and 2D vectors
Because p = m·v ties three quantities together, knowing any two gives the third. Set the solve mode to mass to compute m = p ÷ v, or to velocity to compute v = p ÷ m, which is handy when you measure a momentum (for example from an impulse) and want the speed it produces. For motion that is not along a single line, turn on the second axis: the calculator treats your first velocity as the x component and the new value as the y component, finds the momentum on each axis, then combines them with the Pythagorean theorem to get the magnitude and reports the direction as an angle from the x axis. You can mix units freely, choosing kilograms, grams, tonnes, pounds or ounces for mass and metres per second, kilometres per hour, miles per hour or feet per second for velocity; everything is converted to SI internally before the maths.
Why momentum is useful
Momentum matters because it is conserved: in a closed system with no external forces, the total momentum before an interaction equals the total momentum after it. This conservation law is what lets physicists predict the outcome of collisions, explosions, and rocket propulsion without knowing the messy details of the forces involved. Momentum also connects directly to force through impulse: the change in an object’s momentum equals the force applied multiplied by the time it acts, Δp = F·t. This is why airbags and crumple zones extend the stopping time of a crash, reducing the force on occupants while the same total change in momentum still occurs. The kinetic energy shown alongside (KE = ½·m·v²) grows with the square of speed, so it climbs far faster than momentum as an object speeds up.
Example momentum values
| Object | Mass (kg) | Velocity (m/s) | Momentum (kg·m/s) |
|---|---|---|---|
| Baseball pitch | 0.145 | 40 | 5.8 |
| Sprinting human | 70 | 10 | 700 |
| Family car | 1500 | 20 | 30000 |
| Loaded truck | 30000 | 25 | 750000 |
Momentum equals mass times velocity, so small fast objects can rival large slow ones.
Frequently asked questions
What is the formula for momentum?
Linear momentum is p = m·v, the mass of the object multiplied by its velocity. With mass in kilograms and velocity in metres per second, the result is in kilogram-metres per second (kg·m/s). This calculator also shows the imperial equivalent in pound-feet per second.
Can this calculator find mass or velocity from momentum?
Yes. Change the "Solve for" option to mass to compute m = p ÷ v, or to velocity to compute v = p ÷ m. You supply the momentum and the one quantity you know, and the calculator returns the missing one along with the show-your-work steps.
How do I find the momentum of an object moving in two directions?
Turn on the second axis. Enter the velocity along x and along y; the calculator computes the momentum on each axis, combines them with the Pythagorean theorem to get the magnitude, and reports the direction as an angle measured from the x axis.
Is momentum a vector or a scalar?
Momentum is a vector. It has both magnitude and direction, pointing the same way the object moves. A negative momentum simply means the object is moving in the direction you chose as negative along your axis.
How is momentum different from kinetic energy?
Momentum (m·v) scales linearly with velocity and is a vector, while kinetic energy (½·m·v²) scales with the square of velocity and is a scalar. Momentum is conserved in all collisions; kinetic energy is only conserved in elastic ones. This calculator shows both.