Velocity Calculator
Solve for final velocity, initial velocity, acceleration, time or distance travelled — in m/s, km/h, mph or ft/s — with the rearranged formula shown every time.
v = u + a·t (average velocity: v = d ÷ t)
Final velocity
Formula used for this direction
v = u + a·t
Your values
u = 0 m/s, a = 2.7 m/s², t = 10
Velocity, Step by Step
Velocity is displacement per unit time, with a direction attached. The constant-acceleration relationship v = u + a·t connects it to acceleration: whatever velocity you started with, add the acceleration multiplied by how long it acted.
Because that is one equation in four quantities, any three of them give the fourth. This calculator exposes all of those directions, plus the displacement form d = u·t + ½·a·t², which is what you need when the question is about distance covered rather than speed reached.
Worked example — a cyclist pulling away
A cyclist starts from rest and accelerates at 3 m/s² for 8 seconds.
v = 0 + 3 × 8 = 24 m/s
Over the same 8 seconds the distance covered is d = 0 × 8 + ½ × 3 × 8² = 96 m, so the average velocity was 12 m/s — exactly half the final velocity, which is what constant acceleration from rest always gives.
A second example at motorway scale. 70 mph is 31.29 m/s, or 112.7 km/h. Those three numbers describe the identical motion — only the unit differs, which is why unit conversion belongs inside the calculator rather than as a separate step you do by hand first.
Common mistake
Averaging the start and end speeds to get average velocity. That works only under constant acceleration. For a journey that speeds up, cruises, then stops, you must divide total displacement by total time — and if the trip returns to its starting point, the average velocity is zero no matter how fast you went.
Keep going
- If a velocity changed over a known time, the rate of that change is the acceleration; the acceleration calculator solves for it directly. Acceleration Calculator
- A mass moving at the velocity you just found carries kinetic energy proportional to the square of it, so doubling speed quadruples energy; the kinetic energy calculator shows that. Kinetic Energy Calculator
Frequently Asked Questions
What is the difference between speed and velocity?
Speed is how fast something moves; velocity is how fast it moves in a stated direction. Velocity is a vector, so it can be negative — a ball thrown upward at 12 m/s has velocity −12 m/s on the way back down, even though its speed is 12 m/s both times. Every formula on this page works with velocity, which is why negative answers are meaningful rather than errors.
What is the formula for final velocity?
v = u + a·t. Start from the initial velocity u and add however much velocity the acceleration delivers over time t. If you know distance rather than time, use v² = u² + 2·a·d instead, which avoids needing t at all.
What is average velocity?
Total displacement divided by total time: v_avg = d ÷ t. It is not generally the average of your starting and ending speeds — that shortcut only works when acceleration is constant. Over a journey with stops and varying speed, average velocity can even be zero if you end where you started.
Why can velocity be negative but speed cannot?
Because velocity carries a direction and speed does not. Negative simply means 'in the opposite direction to the one I called positive'. Speed is the magnitude of velocity, so it discards the sign and is never negative.
How do I convert between m/s, km/h and mph?
A mile per hour is exactly 0.44704 m/s and a kilometre per hour is exactly 1/3.6 m/s, both defined rather than measured. So 100 km/h is about 27.78 m/s and 60 mph is exactly 26.8224 m/s. This calculator converts automatically — pick the unit you actually have.
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