Momentum is a vector quantity defined as mass times velocity. It measures the motion content of an object and is conserved in isolated systems.

Which units does the calculator support?

SI units (kg, m/s) and Imperial inputs (lbm, ft/s). Imperial inputs are internally converted to SI; momentum may be shown in kg·m/s and slug·ft/s for clarity.

When should I use relativistic momentum?

Use relativistic momentum when speeds are a significant fraction of the speed of light (v ≳ 0.1c). The calculator warns if you exceed the physical limit v < c.

Can the tool handle inelastic collisions?

Yes. Choose Two-body collision and pick Perfectly inelastic (stick) or specify a coefficient of restitution (0 ≤ e ≤ 1) for partially inelastic impacts.

Is impulse equal to momentum?

Impulse equals the change in momentum. Bringing an object to rest from velocity v requires an impulse equal in magnitude to its initial momentum (in SI, N·s = kg·m/s).

Does the sign of velocity matter?

Yes. Direction matters. Negative velocity indicates the opposite reference direction, and momentum carries the same sign.

What assumptions are used for collisions?

1D, straight-line motion with instantaneous collision; external forces are negligible during impact; restitution e parameterizes elasticity (e=1 elastic, e=0 perfectly inelastic).

Momentum Calculator

Q: Can the tool handle inelastic collisions?

Yes. Choose Two-body collision and pick Perfectly inelastic (stick) or specify a coefficient of restitution (0 ≤ e ≤ 1) for partially inelastic impacts.

Q: Is impulse equal to momentum?

Impulse equals the change in momentum. Bringing an object to rest from velocity v requires an impulse equal in magnitude to its initial momentum (in SI, N·s = kg·m/s).

Q: Does the sign of velocity matter?

Yes. Direction matters. Negative velocity indicates the opposite reference direction, and momentum carries the same sign.

Q: What assumptions are used for collisions?

1D, straight-line motion with instantaneous collision; external forces are negligible during impact; restitution e parameterizes elasticity (e=1 elastic, e=0 perfectly inelastic).

Compute linear momentum with professional accuracy. This tool supports classical p = m·v, relativistic momentum for high speeds, and 1D two‑body collisions (elastic and inelastic). Built for students, instructors, and engineers who need reliable results quickly.

Calculation mode

Single object Two-body collision Relativistic

Choose the type of calculation to reveal the relevant inputs.

Unit system

SI (kg, m/s) Imperial (lbm, ft/s)

Imperial inputs are converted internally to SI. Results can display both where helpful.

Mass

Enter mass, not weight. In Imperial, use lbm (pounds mass); the calculator converts to slugs/kg as needed.

Velocity

m/s

Signs indicate direction (e.g., left vs right). Negative velocity gives negative momentum.

Results

Authoritative Data Source and Methodology

Primary reference: OpenStax, College Physics, Chapter 8: Momentum and Collisions (latest edition, 2021 update). DOI: 10.24982/4.9781947172012. OpenStax College Physics

Physical constant: Speed of light in vacuum, c = 299,792,458 m/s (exact, SI). Source: NIST CODATA (2022).

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Classical momentum: p = m \times v

Relativistic momentum: p = \gamma m v,\quad \gamma = \frac{1}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}

1D two-body collision (coefficient of restitution e): \begin{aligned} v_1 &= \frac{m_1 u_1 + m_2 u_2 - m_2 e (u_1 - u_2)}{m_1 + m_2} \\ v_2 &= \frac{m_1 u_1 + m_2 u_2 + m_1 e (u_1 - u_2)}{m_1 + m_2} \end{aligned}

Perfectly inelastic (stick together): v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2}

Glossary of Variables

m, m₁, m₂ — mass (kg in SI; lbm input is converted; 1 slug = 32.174 lbm).
v, u₁, u₂ — velocity (m/s in SI; ft/s in Imperial). Sign indicates direction.
p — linear momentum (kg·m/s = N·s). Also shown as slug·ft/s when Imperial inputs are used.
e — coefficient of restitution (0 ≤ e ≤ 1). e = 1 elastic, e = 0 perfectly inelastic.
γ — Lorentz factor for relativistic speeds, γ = 1 / sqrt(1 - (v/c)²).
c — speed of light in vacuum, exactly 299,792,458 m/s.

Come Funziona: Un Esempio Passo‑Passo

Scenario: A 2 kg cart moves at 3 m/s on a frictionless track. What is its momentum?

Select mode: Single object.
Units: SI (kg, m/s).
Inputs: m = 2 kg, v = 3 m/s.
Apply the formula p = m × v → p = 2 × 3 = 6 kg·m/s. In SI, N·s is equivalent, so p = 6 N·s.

Frequently Asked Questions (FAQ)

Is kg·m/s the same as N·s?

Yes. 1 N = 1 kg·m/s², so momentum in kg·m/s is dimensionally identical to impulse in N·s.

How do signs work in collisions?

Pick a positive direction (e.g., right). Provide u₁ and u₂ with signs based on that convention. The formulas then return v₁ and v₂ with correct signs.

What are common pitfalls with Imperial units?

Do not mix weight (lbf) with mass (lbm). The calculator converts lbm to slugs internally using g_c = 32.174 lbm·ft/(lbf·s²).

When should I set e between 0 and 1?

Use e between 0 and 1 for partially inelastic impacts where some kinetic energy is lost but bodies do not stick.

Does the tool check v < c?

Yes. In relativistic mode, the input is validated so that |v| < c (or < 100% of c).

Can I compute kinetic energy as well?

For single-object cases, the tool also displays kinetic energy using K = 1/2 m v² (classical), helping sanity‑check results.

Tool developed by Ugo Candido.
Content verified by CalcDomain Physics Editorial Team.
Last reviewed for accuracy on: September 15, 2025.