Momentum calculator
Signed momentum, mass or velocity from p = m · v.
Fill in the fields and the result will appear here automatically.
Calculates a body’s momentum component on one chosen axis and solves p = mv for velocity or mass. Velocity and momentum may be negative: their sign gives direction, while positive mass preserves that sign. The accompanying kinetic energy remains non-negative. This is a classical single-body model, not a complete multidimensional collision or relativistic-momentum calculation.
How it works
Formula and logic
p = mv, v = p/m and m = p/v. With m > 0, p and v have matching signs. Eₖ = mv²/2 = pv/2 ≥ 0. For fixed mass, doubling speed doubles momentum magnitude and quadruples kinetic energy.
Example
3 kg at +4 m/s gives p = +12 kg·m/s and Eₖ = 24 J; at −4 m/s it gives p = −12 kg·m/s with the same 24 J. p = −18 kg·m/s and v = −9 m/s imply m = 2 kg.
Fields and units
- What to find — list option
- Mass — kg
- Velocity component — m/s
- Momentum component — kg·m/s
- Mass — kg
- Momentum component — kg·m/s
- Velocity component — m/s
How to use
- — Choose momentum, velocity or mass.
- — Enter a strictly positive mass in kg and signed velocity in m/s or momentum in kg·m/s on one axis.
- — To find mass, velocity must be non-zero and momentum must have the same non-zero sign.
- — Zero velocity gives zero momentum in the forward mode; p = v = 0 cannot determine mass.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: vector momentum p = mv OpenStax: conditions for conservation of system momentum
- Limitation
- One-axis components, constant positive mass and classical speeds; momentum conservation requires no external impulse on the system. Motion is along the chosen axis; if only one component of three-dimensional velocity is entered, the energy row does not give the body’s total kinetic energy.
FAQ
How does momentum differ from kinetic energy?
Momentum is a vector proportional to velocity; energy is a scalar proportional to speed squared. Opposite momenta can cancel while the corresponding kinetic energies add.
Why does momentum matter in collisions?
Total vector momentum is conserved for a chosen system with no external impulse. An individual body’s momentum can change, and an inelastic collision can transfer kinetic energy into deformation and heat.
What does zero velocity mean?
For a positive mass it gives p = 0 and Eₖ = 0 in the chosen frame. In the inverse mode, p = v = 0 fits any positive mass.
Is the direction of momentum included?
Yes, on one axis: keep a common positive direction for p and v. Two- or three-dimensional motion requires components that this form does not request.
How does momentum relate to stopping force?
Momentum change equals the time integral of net external force. Momentum alone does not determine stopping force or distance without a time, force model and other conditions.