Momentum Calculator
Mass with a direction attached: p = m·v, the ledger physics keeps in signs rather than sizes — and the one quantity a closed system can never lose.
Momentum Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One dimension — direction is a sign, not an angle
- Point masses; no rotation or angular momentum
In short: A 1,200 kg car at 14 m/s carries p = 1,200 × 14 = 16,800 kg·m/s of momentum, signed + for rightward travel. The same car at 28 m/s carries 33,600 — double, LINEARLY: momentum has no square tax (energy quadruples where momentum only doubles, and the pair card computes both so you can watch them diverge). Head one car at +14 against one at −14 and the total is 16,800 + (−16,800) = 0 — not because the crash erased anything, but because momentum adds signs, not sizes, and the two ledgers were mirror images. That sign discipline is why conservation of momentum survives every collision energy accounting can be cheated by.
Formula
p = m·v · Σp is conserved when no external force acts · KE = p²/2m (the conversion law)
Momentum is the quantity that changes only when an external force acts — internal forces (a crash, an explosion) shuffle it between objects but never touch the total. The sign convention on this page is one-dimensional: plus is a direction, minus is the same size travelling the other way.
Worked Example
- Enter mass and the SIGNED velocity — choose a positive direction and keep it.
- Read p in kg·m/s; the sign is which way the ledger leans.
- Read the pair card: the same motion's energy, and both at double speed.
- For collisions, add momenta with signs before believing any crash narrative.
Defaults: 16,800 kg·m/s at +14 m/s; at 28, 33,600 (2×) while the same step sends energy to 4×. A head-on pair at ±14 sums to exactly 0 — the sign ledger at work.
Strengths & Limits Of This Model
Where this engine is strong
- Sign ledger kept explicit, not stripped
- Energy pairing card shows linear vs square live
Where it stops
- No 2-D vectors or collision solver
- No friction bookkeeping after the instant
Practical Use Cases
Crash analysis
signs first, sizes second
Rocketry
recoil bookkeeping in one dimension
Teaching
conservation without a single exception
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Momentum Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why keep the sign?
Because momentum is a VECTOR in a one-dimensional coat: +16,800 and −16,800 are opposite claims on the ledger and their sum is genuinely zero. Drop the signs and head-on collisions look like double the trouble instead of perfect cancellation — the oldest error in crash journalism.
Momentum or energy — which breaks the crash?
Different informants. Momentum says what the wreck's combined motion must be (conserved exactly); energy says how much got absorbed as deformation (only kinetic energy can change if heat is allowed). The pair card shows both growing differently at 2v — 2× versus 4× — which is why double-speed crashes are worse than double-mass ones.
What does 'conserved' actually promise?
That with no EXTERNAL force, Σp before = Σp after, no matter how violent the middle. Skaters pushing apart, bullets leaving rifles, planets swinging — the total signs-plus-sizes never move. Friction with the ground or a wall's push is an external force and ends the promise.
How is energy different if both use mass times speed?
The exponent, and everything downstream: p = mv is linear, KE = ½mv² is squared. There is an exact bridge — KE = p²/2m — and the pair card walks it live: the same motion read twice, once per ledger.
Why kg·m/s as a unit?
Because the unit IS the definition: mass times velocity. Its alternate name, the newton-second, leaks the plot — momentum is what force accumulates over time, which is exactly the impulse page's law and the reason the two pages share a border.
Can momentum be zero while energy is not?
Yes — and the head-on pair proves it: +p and −p sum to zero while BOTH cars carry positive kinetic energy. Zero total momentum with nonzero energy is the signature of objects moving apart; the two ledgers answer different questions.
What about 2-D and 3-D?
Each dimension keeps its own sign ledger, and the total is a vector sum — this page is the 1-D spine of that idea. Angled collisions decompose into one of these per axis; the discipline learned here is the one that scales.
Why does a cannon recoil?
The explosion is INTERNAL: it can shuffle momentum between ball and cannon but cannot touch the total, which was zero at rest. Forward ledger plus backward ledger must still read zero — so the cannon takes a backward share sized by the mass ratio. The universe keeps double-entry books.