Velocity CalculatorAverage velocity · v = Δd ÷ Δt
Velocity is displacement divided by time: v = Δd ÷ Δt. Enter how far an object moved and how long it took to get its velocity in m/s, km/h or mph. You can also find final velocity from acceleration (v = u + at), or solve for the displacement or time. Every answer comes with the working shown.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Enter your values
Choose what to solve for, then type any values. Units convert automatically.
Step-by-step working
What is velocity?
Velocity is the rate of change of an object’s position: displacement divided by the time taken, in a specified direction. Its SI unit is metres per second (m/s).
Because velocity is a vector, it has both a magnitude (how fast) and a direction (which way). Two cars driving at 60 km/h in opposite directions have the same speed but opposite velocities. When velocity changes, whether in size or direction, the object is accelerating.
Quick answers
How do you calculate velocity with distance and time?
Divide the displacement by the time: v = d ÷ t. A cyclist who ends up 3 km east of her start after 10 minutes has an average velocity of 3,000 m ÷ 600 s = 5 m/s east. If the route doubles back, use the straight-line distance between start and finish, not the odometer reading.
What is the formula for average velocity?
Average velocity = total displacement ÷ total time. When acceleration is constant there’s a shortcut: vavg = (u + v) ÷ 2. The shortcut fails for stop-start traffic, so stick with displacement over time there.
How do I find velocity with acceleration and time?
Use v = u + at. Starting from 4 m/s and accelerating at 2 m/s² for 6 s gives 4 + 12 = 16 m/s. Switch to the Final velocity tab above, or open the dedicated final velocity calculator if you know the distance instead of the time.
How do you convert velocity from m/s to km/h and mph?
Multiply m/s by 3.6 for km/h and by 2.237 for mph. So 25 m/s is 90 km/h, or about 55.9 mph. The results panel shows all three automatically.
Velocity formula
Use the first formula for average velocity over any trip. Use the second and third only when acceleration is constant.
| Symbol | Meaning | SI unit |
|---|---|---|
| v | Velocity (final or average) | m/s |
| Δd | Displacement: change in position, with direction | m |
| Δt | Time interval | s |
| u | Initial velocity | m/s |
| a | Constant acceleration | m/s² |
| t | Elapsed time | s |
How to calculate velocity
- Pick a direction as positive. Velocity is a vector, so decide which way counts as positive (for example east or up).
- Find the displacement. Subtract the start position from the end position: Δd = xfinal − xinitial.
- Measure the time interval and convert everything to SI units (metres and seconds).
- Divide displacement by time. The sign of the answer tells you the direction of motion.
Worked example: Usain Bolt’s 100 m world record
In Berlin in 2009 Usain Bolt ran 100 m in 9.58 s. What was his average velocity?
v = 100 m ÷ 9.58 s
v = 10.44 m/s ≈ 37.58 km/h ≈ 23.35 mph
That is an average. Bolt started from rest, so his top speed was higher still: split timing put it at about 12.4 m/s (around 44.7 km/h) between 60 m and 80 m. This is exactly why average and instantaneous velocity differ. The calculator above loads this example by default.
Velocity vs speed: what’s the difference?
Speed is a scalar: it tells you only how fast something moves. Velocity is a vector: it tells you how fast and in which direction. If you run one full 400 m lap in 80 s, your average speed is 400 ÷ 80 = 5 m/s. Your average velocity, though, is zero, because you finish where you started and your displacement is zero. For a single straight-line trip in one direction, the two numbers are the same. For speed alone, use the speed calculator.
| Speed | Velocity | |
|---|---|---|
| Type | Scalar (size only) | Vector (size + direction) |
| Based on | Total distance travelled | Displacement (start → end) |
| Can be negative? | No | Yes: the sign shows direction |
| Lap of a track | Distance ÷ time | 0, since you end where you started |
| SI unit | m/s | m/s |
Typical velocities for reference
Use these benchmarks to sanity-check an answer. If your result for a person walking comes out at 40 m/s, a unit has slipped somewhere.
| Moving object | m/s | km/h | mph |
|---|---|---|---|
| Walking pace | 1.4 | 5 | 3.1 |
| Recreational cyclist | 6 | 21.6 | 13.4 |
| Usain Bolt (100 m average) | 10.44 | 37.6 | 23.4 |
| Car on a highway | 30.6 | 110 | 68.4 |
| Cheetah sprint (peak) | ≈ 29 | ≈ 104 | ≈ 65 |
| Cruising airliner | ≈ 250 | ≈ 900 | ≈ 560 |
| Speed of sound (20 °C air) | 343 | 1,235 | 767 |
Common mistakes to avoid
- Using distance instead of displacement. Velocity needs the straight-line change in position, not the length of the path you took.
- Mixing units. Kilometres divided by minutes is not m/s. Convert first, or let the unit selectors do it for you.
- Averaging two speeds with a plain mean. 60 km/h out and 40 km/h back over the same distance averages 48 km/h, not 50, because you spend longer at the slower speed.
- Ignoring the sign. A negative velocity is not an error. It means the motion runs opposite to the direction you chose as positive.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Velocity Calculator: frequently asked questions
Average velocity is displacement divided by time: v = Δd ÷ Δt. With constant acceleration, final velocity is v = u + at, where u is the initial velocity, a the acceleration and t the time.
The SI unit of velocity is metres per second (m/s). Common alternatives are km/h (divide m/s by 0.27778, or multiply by 3.6) and mph (multiply m/s by 2.23694).
Subtract the starting position from the final position to get the displacement, then divide by the total time taken. For 100 m in 9.58 s, v = 100 ÷ 9.58 = 10.44 m/s.
Yes. A negative velocity means the object moves in the direction you defined as negative. Speed, by contrast, can never be negative.
No. Speed is how fast an object moves; velocity is how fast and in what direction. They have the same size only for straight-line motion in a single direction.
Multiply by 3.6. For example, 10 m/s × 3.6 = 36 km/h. To go from km/h to m/s, divide by 3.6.
Average velocity is total displacement over total time. Instantaneous velocity is the velocity at a single moment: the slope of the position–time graph at that point, or what a speedometer would show.
Use v = u + at. A car starting from rest (u = 0) and accelerating at 3 m/s² for 5 s reaches v = 0 + 3 × 5 = 15 m/s.
Velocity is the gradient of a displacement–time graph: rise (Δd) over run (Δt). A steeper line means a higher velocity, and a horizontal line means the object is at rest.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 3, Motion Along a Straight Line
- HyperPhysics, Georgia State University — Velocity and motion equations
- NIST — SI Units — metre and second definitions
- World Athletics — Records — 100 m world record, 9.58 s (Berlin 2009)
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.