What is the momentum formula and what units does it use?

Linear momentum is p = m·v, the product of mass and velocity. In SI it is mass in kilograms times velocity in metres per second, giving kg·m/s. Example: a 2 kg ball at 3 m/s has p = 2 × 3 = 6 kg·m/s. Momentum is a vector, so the sign of the velocity carries through — a ball moving at −3 m/s has p = −6 kg·m/s, pointing the other way. Watch your units: 72 km/h must become 20 m/s first.

What is impulse and how does the impulse-momentum theorem work?

Impulse is J = F·Δt, the force multiplied by the time it acts, measured in N·s. The impulse-momentum theorem says that impulse equals the change in momentum: J = Δp = m·(v₂ − v₁). Example: a 10 N force pushing for 2 s delivers J = 20 N·s, which changes the object's momentum by 20 kg·m/s. Because N·s and kg·m/s are the same unit, you can plug a momentum change straight in to find the force or the time.

How do I find the force from a change in momentum?

Rearrange the theorem to F = Δp / Δt. If a 0.15 kg baseball arrives at 40 m/s and leaves the bat at −50 m/s, the momentum change is 0.15 × (−50 − 40) = −13.5 kg·m/s. If the bat is in contact for 0.7 ms, the average force is −13.5 / 0.0007 ≈ −19,300 N. Use the force mode: type the Δp and the contact time and it returns the average force, sign and all.

How does a longer impact time make a crash safer?

From F = Δp / Δt, the same momentum change spread over more time means a smaller force. An airbag, a crumple zone or bending your knees on landing all stretch Δt. If a collision must shed 4500 kg·m/s of momentum, doing it in 0.05 s needs 90,000 N, but doing it in 0.3 s needs only 15,000 N — six times gentler. Put the Δp in and try two different times to see the force drop.

What is the difference between momentum and kinetic energy?

Both depend on mass and speed, but momentum p = m·v is linear in velocity and is a vector, while kinetic energy KE = ½·m·v² is quadratic and a scalar. Double the speed and momentum doubles but energy quadruples. A truck and a bullet can share the same momentum yet carry wildly different energy. For energy questions use the kinetic energy calculator; for collision and impulse questions, momentum is the right quantity.

Is momentum always conserved?

In an isolated system with no external force, total momentum is conserved: the vector sum before a collision equals the sum after. That is why recoil works — a rifle kicks back with momentum equal and opposite to the bullet's. This tool solves p = m·v for one object; to check conservation, compute each object's momentum separately and add them as vectors (mind the signs), confirming the totals match before and after.

Solve a momentum homework problem in any direction

Your worksheet gives a 1500 kg car and a momentum of 30,000 kg·m/s and asks for its speed. Switch to "Velocity (from p, m)", type the two knowns, and read 20 m/s with the v = p / m step shown. Next question flips it and gives the speed, asking for momentum — same panel, "Momentum (from m, v)" mode. One tool covers every rearrangement so you check forward and reverse answers without re-deriving the formula each time.

Compute the average force in a collision

A 0.15 kg baseball changes velocity from +40 m/s to −50 m/s during a 0.7 ms bat contact. The momentum change is −13.5 kg·m/s. Use the impulse panel's "Force (from Δp, Δt)" mode, enter Δp and the contact time, and it returns an average force near −19,300 N — the kind of number that shows why bats and helmets are built the way they are.

Show why airbags and crumple zones reduce injury

Teaching the impulse-momentum theorem, you want students to feel that F = Δp / Δt. Fix a momentum change of 4500 kg·m/s and let them try Δt = 0.05 s versus 0.3 s. The force drops from 90,000 N to 15,000 N right in front of them. Share the URL with each value pre-loaded so the class opens straight to the comparison.

Convert km/h car speeds before plugging into momentum

Real traffic problems quote speed in km/h. Set the velocity unit to km/h, type 72, and the tool converts to 20 m/s internally before multiplying by mass. No more forgetting the ÷3.6 step and getting an answer off by a factor of 3.6 — the conversion is baked into every mode, momentum and impulse alike.

Check a recoil or conservation-of-momentum result

A 4 kg rifle fires a 0.01 kg bullet at 600 m/s. Compute the bullet's momentum here (6 kg·m/s), then switch to "Velocity (from p, m)", enter −6 kg·m/s and the 4 kg rifle mass, and read the recoil speed of −1.5 m/s. Two quick passes confirm the before-and-after momentum totals cancel, exactly as conservation predicts.

Momentum & Impulse Calculator — p = m·v and J = F·Δt

p = m·v and J = F·Δt = Δp — solve any one of momentum, mass, velocity, impulse, force or time, with kg·m/s, g, m/s and km/h units — browser-only

Runs locally
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Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Calculator

Solve for

Mass m

Velocity v

Momentum p

kg·m/s

Result

Momentum6 kg·m/s

Formula steps

p = m·v
p = 2 kg × 3 m/s
p = 6 kg·m/s

Velocity and momentum keep their sign: a negative value means motion in the opposite direction.

What this tool does

Free momentum and impulse calculator for physics homework, lab reports and engineering checks. The momentum panel uses p = m·v: enter any two of momentum, mass and velocity and it solves the third, so it works as a mass finder and a velocity finder too, not just a forward p = m·v plug-in. The impulse panel uses the impulse-momentum theorem J = F·Δt = Δp: enter force and time to get the impulse, or feed a momentum change Δp with the time to back out the average force, or the force to get the contact time. Momentum is treated as a vector, so a negative velocity means the object moves the other way and the momentum sign follows. Switch mass between kilograms and grams and velocity between metres per second and kilometres per hour; the math always runs in SI under the hood and converts at the edge. Every step of the formula is shown so you can copy the working into a write-up, and a one-click copy and a shareable URL reproduce the exact problem. 100% client-side, nothing is uploaded.

Tool details

Input: Files + Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Momentum & Impulse Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Solve a momentum homework problem in any direction
Your worksheet gives a 1500 kg car and a momentum of 30,000 kg·m/s and asks for its speed. Switch to "Velocity (from p, m)", type the two knowns, and read 20 m/s with the v = p / m step shown. Next question flips it and gives the speed, asking for momentum — same panel, "Momentum (from m, v)" mode. One tool covers every rearrangement so you check forward and reverse answers without re-deriving the formula each time.
Compute the average force in a collision
A 0.15 kg baseball changes velocity from +40 m/s to −50 m/s during a 0.7 ms bat contact. The momentum change is −13.5 kg·m/s. Use the impulse panel's "Force (from Δp, Δt)" mode, enter Δp and the contact time, and it returns an average force near −19,300 N — the kind of number that shows why bats and helmets are built the way they are.
Show why airbags and crumple zones reduce injury
Teaching the impulse-momentum theorem, you want students to feel that F = Δp / Δt. Fix a momentum change of 4500 kg·m/s and let them try Δt = 0.05 s versus 0.3 s. The force drops from 90,000 N to 15,000 N right in front of them. Share the URL with each value pre-loaded so the class opens straight to the comparison.
Convert km/h car speeds before plugging into momentum
Real traffic problems quote speed in km/h. Set the velocity unit to km/h, type 72, and the tool converts to 20 m/s internally before multiplying by mass. No more forgetting the ÷3.6 step and getting an answer off by a factor of 3.6 — the conversion is baked into every mode, momentum and impulse alike.
Check a recoil or conservation-of-momentum result
A 4 kg rifle fires a 0.01 kg bullet at 600 m/s. Compute the bullet's momentum here (6 kg·m/s), then switch to "Velocity (from p, m)", enter −6 kg·m/s and the 4 kg rifle mass, and read the recoil speed of −1.5 m/s. Two quick passes confirm the before-and-after momentum totals cancel, exactly as conservation predicts.

Common pitfalls

Treating momentum like kinetic energy. Momentum p = m·v is linear in speed and is a vector; energy KE = ½·m·v² is quadratic and a scalar. Squaring the velocity here, or dropping the sign, gives the wrong answer. Doubling the speed doubles momentum but quadruples energy — keep the two quantities separate.
Forgetting to convert km/h to m/s. A speed of 72 km/h is 20 m/s, not 72. Plugging the raw km/h value inflates the momentum by 3.6. Set the velocity unit to km/h and let the tool convert, or divide by 3.6 yourself before using m/s.
Dropping the sign on a momentum change. In a bounce, velocity reverses, so Δp = m·(v₂ − v₁) can be much larger than m·v alone. A ball arriving at +40 and leaving at −50 changes by −90 m/s worth of velocity, not −10. Carry the signs through or the impulse and force come out far too small.

Privacy

Every calculation — the p = m·v solve, the impulse-momentum theorem, the unit conversions and the formula steps — is plain JavaScript that runs in your browser tab. Nothing you type is uploaded and there is no logging of your numbers. The one caveat: the shareable URL encodes your inputs and mode in the query string, so a "share link" pasted into chat will record those values in the recipient server's access log. For anything sensitive, use the copy button and paste the text rather than sharing the URL.

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Momentum & Impulse Calculator — p = m·v and J = F·Δt

Result

Formula steps

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Momentum & Impulse Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Solve a momentum homework problem in any direction

Compute the average force in a collision

Show why airbags and crumple zones reduce injury

Convert km/h car speeds before plugging into momentum

Check a recoil or conservation-of-momentum result

Common pitfalls

Privacy

FAQ

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