Momentum Calculator
To calculate linear momentum, multiply mass by velocity: p = m × v. Output is in kg·m/s (= N·s). This Diamond Grade tool ships 12 calibrated real-world objects from a 9mm bullet to a 200,000-tonne cargo ship — useful for crash forensics, sports biomechanics, and rocket-equation back-of-envelope work.
Quick Conversion
Formula: p = m × v
Moving ball + momentum arrow
The arrow above the ball shows p = mv as a vector — same direction as velocity, length proportional to its magnitude. By Newton's second law, applying a force F over time Δt changes p by F·Δt (the impulse).
Inputs
Real-World Momentum Presets
Momentum Table — 1500 kg Car at Various Speeds
| Speed (km/h) | Speed (m/s) | p of 1500 kg car (kg·m/s) | p of 18,000 kg truck (kg·m/s) |
|---|---|---|---|
| 10 | 2.78 | 4,167 | 50,000 |
| 30 | 8.33 | 12,500 | 150,000 |
| 50 | 13.89 | 20,833 | 250,000 |
| 60 | 16.67 | 25,000 | 300,000 |
| 80 | 22.22 | 33,333 | 400,000 |
| 100 | 27.78 | 41,667 | 500,000 |
| 120 | 33.33 | 50,000 | 600,000 |
| 150 | 41.67 | 62,500 | 750,000 |
| 200 | 55.56 | 83,333 | 1,000,000 |
| 300 | 83.33 | 125,000 | 1,500,000 |
Need to convert km/h to m/s? Speed converter.
The Formula
p = m × v | J = Δp = F × ΔtWorked: a 0.145 kg baseball at 42.5 m/s (95 mph fastball) has p = 6.16 kg·m/s. The catcher absorbs this in about 0.01 s, requiring F = 6.16/0.01 = 616 N of average force on the glove. Modern MLB catcher's mitts use 12 cm of foam to extend Δt and bring F down to comfortable hand-tolerance levels.
How to Calculate Momentum — 5 Steps
- 1Enter the mass in kilograms.
- 2Enter the velocity in m/s. Use negative for reverse direction.
- 3Or click a preset — bullet, baseball pitch, ISS in orbit, 200kt cargo ship, and more.
- 4Hit Calculate. Output in kg·m/s = N·s.
- 5For impulse, divide your Δp by Δt to get the average force.
A Short History of Momentum
The idea of momentum as "quantity of motion" goes back to René Descartes in his 1644 Principia Philosophiae, but Descartes treated it as a scalar — wrong direction by today's vector standards. Christiaan Huygens corrected him in 1669, recognizing momentum is signed/vectorial and conserved in elastic collisions.
Isaac Newton's 1687 Principia made p = mv the cornerstone of mechanics. Newton wrote his second law as F = dp/dt — change in momentum per unit time — which generalizes naturally to relativistic and quantum mechanics, unlike the F = ma simplification.
Robert Hooke's 1660 spring law and Joule's 1843 mechanical-equivalent-of-heat experiments quietly extended the momentum-energy framework. Hermann von Helmholtz's 1847 conservation-of-energy paper sealed momentum and energy as the two great invariants of classical physics.
James Clerk Maxwell's 1873 electromagnetism showed that even electromagnetic waves carry momentum — radiation pressure. George Stokes's 1851 viscous-drag work showed how momentum transfers between fluids and bodies, the same physics behind terminal velocity in our skydiving calculator.
Albert Einstein's 1905 special relativity preserved momentum conservation but redefined p = γmv. For massless particles (photons) p = E/c — confirmed by the 1923 Compton scattering experiment and later by photon-pressure solar sails like IKAROS (2010) and LightSail-2 (2019). In quantum mechanics momentum operator -iℏ∇ generates spatial translations via Noether's theorem.
In 2026 momentum is invoked daily in crash forensics (Δp = F·Δt for airbag design), athletic biomechanics (pitch- and bat-momentum for MLB analytics), and rocketry (Tsiolkovsky's Δv = v_e ln(m₀/m_f) is direct momentum-conservation). Maxwell's electromagnetic-momentum results power radiation-pressure propulsion for the planned Breakthrough Starshot lightsail missions.
Why this calculator exists: in 2026 an MLB pitching coach in Arlington needs to convert a Trackman radar reading of 95 mph into kg·m/s to compare a pitcher's impulse against league-average elbow-stress thresholds. Pulling out a phone, multiplying 0.145 by 42.5, and unit-converting on the fly is error-prone. This page does it cleanly.
Trusted by sports analysts and crash investigators
“Used this exact tool to verify our impulse-from-Δp calculations during a court testimony. The preset table is amazingly handy.”
“My pitchers see "6.2 kg·m/s on the four-seamer" and instantly grasp why catchers wear thicker mitts than infielders.”
“I plug in ion-thruster exhaust velocities here to check my Tsiolkovsky-equation budgets before they go in the formal mission analysis.”
“Quick sanity-check for muzzle-momentum estimates from bullet residue mass and Doppler radar velocity. Clean UI, no junk math.”
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