Momentum Calculator - Linear Momentum, Impulse, and Energy

A momentum calculator is a physics tool that turns mass and velocity into linear momentum p = m v, or force and time into impulse J = F delta t, and reports kinetic energy p squared over 2m. It also reverses the relation to solve for KE when the momentum and mass are already known.

• • Vehicle and crash analysis: check the linear momentum of a 1000 kg car at 100 km/h against a barrier force.
• • Sports and ball sports: find the momentum of a 0.145 kg baseball at 40 m/s or a soccer ball in flight.
• • Newton's second law problems: impulse mode converts a force over time into the change in momentum of a cart or rocket stage.
• • Rocket and propulsion work: size a thruster by equating force over burn time to delta v times propellant mass.

Mass, velocity, force, and time can each be entered in everyday units (kg, lb, mph, lbf, s); the page converts to SI before the formula runs. Results feed adjacent tools such as the conservation-of-momentum page or the angular momentum page.

When the same problem also asks what happens to each body after a 1D elastic or inelastic collision, the Conservation of Momentum Calculator takes the p = m v result for both objects and returns the final velocities.

The momentum calculator uses three different physical relations, each written from a different set of known variables. The mode selector picks which one runs; the other inputs stay visible so the user can switch modes without retyping.

• p: linear momentum in kg m/s, converted to the chosen output unit (kg m/s, g cm/s, slug ft/s, or N s).
• m: mass of the moving object, converted to kg from kg, g, lb, or slug.
• v: velocity along the chosen axis, converted to m/s from m/s, km/h, mph, or ft/s.
• F: net force along the line of motion, impulse mode only.
• delta t: duration of the force in seconds, impulse mode only.
• J: impulse in newton-seconds, equal to F times delta t and equal to delta p.

All three formulas come from Newton's second law written for momentum: F = dp/dt. Integrating that over a finite interval gives the impulse-momentum theorem J = F delta t = delta p. KE = p squared over 2m is always positive because the energy depends on v squared.

According to OpenStax University Physics, linear momentum of a particle is the product of its mass and its velocity, written p = m v, with the SI unit kg m/s.

According to Wikipedia, linear momentum is mass times velocity, the impulse is the time integral of force, and the impulse-momentum theorem states J = F delta t equals delta p.

When the object is rotating instead of translating, the Angular Momentum Calculator takes the same m and v inputs and adds a radius and an angle to return the rotational momentum L = m v r sin theta.

Four ideas explain why the same mass and velocity pair produces both a vector answer (momentum) and a positive scalar answer (kinetic energy), and why impulse is the bridge between force and momentum.

Momentum and energy both come from mass and velocity but are different physical quantities: two identical cars at the same speed share p and KE, yet KE scales with v squared while p scales with v, so doubling speed doubles p but quadruples KE.

To convert the same mass and velocity into the kinetic-energy form of the same problem, the Work, Energy, and Power Calculator computes W, KE, and P from the same v input plus a distance or time.

Pick the mode that matches the data you already have. The form keeps every variable visible, but the calculator only uses the ones that apply to the chosen mode.

1. 1 Choose the input mode: select mass-velocity for a p = m v problem, impulse for a J = F delta t problem, or momentum-energy to convert a known momentum into kinetic energy and velocity equivalent.
2. 2 Enter the mass: type the mass in kg, g, lb, or slug. The calculator converts the value to kg internally.
3. 3 Enter the velocity: type the velocity in m/s, km/h, mph, or ft/s. Negative values return negative momentum and are valid in mass-velocity mode.
4. 4 Switch to impulse mode for force and time: select impulse, enter the net force in N, kN, or lbf, and the duration in seconds. The page reports J, delta p, and the resulting velocity.
5. 5 Switch to momentum-energy for KE from p: select momentum-energy, enter the mass and the known momentum, and read off the kinetic energy and the velocity that matches the same m and p.
6. 6 Pick the output unit: choose kg m/s for physics, slug ft/s for US engineering, g cm/s for CGS, or N s to read the answer in the same unit as an impulse value.

A student verifying a momentum problem enters mass-velocity mode with m = 1000 kg and v = 100 km/h. The page returns 27777.8 kg m/s, 385,802 J, and 27.78 m/s of velocity per unit mass, matching the OpenStax example for a 1 tonne car at highway speed.

When the next step is to find the velocity at a later time or the distance covered during the same motion, the Kinematics Motion Calculator runs the full set of SUVAT relations on the same v and a inputs.

These benefits matter when the momentum value feeds another calculation, or when a quick sanity check is needed against a published physics figure.

• • Three input paths in one page: mass-velocity, impulse, and momentum-to-energy are all accepted.
• • Multi-unit inputs and outputs: kg, g, lb, slug; m/s, km/h, mph, ft/s; N, kN, lbf; kg m/s, g cm/s, slug ft/s, N s.
• • Sign-aware results: negative velocities and forces return negative momentum and impulse, so direction stays signed.
• • Auxiliary KE and velocity: KE = p squared over 2m and v = p / m are reported alongside p for one-shot homework checks.
• • Edge-case safe: zero mass, zero time, or unknown mode produce a validation error instead of NaN.

When the next step is to combine the momentum value with a force on the same mass, the Forces and Newton's Laws Calculator returns the acceleration, the net force, and the individual Newton's-law relations from the same m and F inputs.

The output depends on the inputs and on a small number of physics caveats that apply to all three formulas.

• • The page models single-object momentum and impulse. For two-body collisions, the conservation-of-momentum page covers the elastic and inelastic cases.
• • The momentum-to-energy mode uses KE = p squared over 2m, the classical, non-relativistic expression. For motion at a sizable fraction of the speed of light, the relativistic energy relation is required.
• • Impulse mode assumes the net force is along the line of motion. An orthogonal force changes the direction as well as the magnitude, which the 1D form does not capture.

For most textbook and engineering checks, the single-object momentum and impulse assumption is the right starting point. When it breaks down (a relativistic particle, a rotating body, a multi-body collision), the value becomes one step inside a larger problem solved with the appropriate adjacent tool.

According to Britannica, momentum is a vector quantity equal to the product of an object's mass and velocity, and the total momentum of an isolated system is conserved in every interaction.