Key takeaways
- Velocity is v = d ÷ t: distance divided by time, in metres per second.
- Time must be greater than zero — you can't divide by zero.
- Velocity includes direction; speed on its own does not.
- Multiply m/s by 3.6 to convert to km/h.
In this guide
What is velocity?
Velocity is distance travelled divided by the time taken. It tells you how quickly something is covering ground, whether that's a runner on a track or a car on a highway.
Why does velocity matter?
Velocity is the building block for almost every other motion formula — acceleration, momentum, and kinetic energy all start from it. Get a good velocity reading, and everything downstream follows.
A runner completing a 400 m lap in 50 seconds is moving at 8 m/s. Over the full 100 m sprint distance, top sprinters reach much higher speeds — a lap average always hides the faster and slower moments inside it.
The formula
| Symbol | What it means | Example |
|---|---|---|
| v | The velocity, in metres per second (m/s) | 8 m/s |
| d | The distance travelled, in metres (m) | 400 m |
| t | The time taken, in seconds (s) | 50 s |
How to calculate velocity step by step
- 1Measure the distance. Record the distance travelled in metres.
- 2Measure the time. Record how long it took, in seconds.
- 3Divide distance by time.
d ÷ tgives you the velocity. - 4Write the answer in m/s. That's metres covered every second.
Try the calculator below with your own distance and time to see the working step by step.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Using zero or negative time. Time must be a positive number greater than zero, since you can't divide by zero.
- Confusing velocity with acceleration. Velocity is how fast something moves; the acceleration calculator tells you how quickly that speed itself is changing.
- Reporting distance instead of velocity. 400 m is not a speed — dividing by time is what turns it into one.
Tips and tricks
- Working backwards from velocity to time? Divide distance by velocity:
t = d ÷ v. - For everyday trips measured in kilometres and hours instead of metres and seconds, the speed calculator uses the exact same idea.
- Once you know velocity, the kinetic energy calculator shows how much energy that motion carries.
Where you'll use it in real life
- Sport: timing systems calculate a runner's or swimmer's average velocity across a race.
- Traffic: speed cameras and traffic studies rely on the same distance-over-time idea.
- Physics problems: velocity is the starting point for almost every motion question in a physics class.
- Navigation: GPS devices estimate arrival times using your current velocity over the remaining distance.
Quick summary
To find velocity, divide the distance travelled in metres by the time taken in seconds. The result is in m/s, and multiplying by 3.6 converts it to the more familiar km/h. Use the calculator above to work through your own numbers.
Worked example
A runner covers the full 400 m of an athletics track in 50 seconds. What is their average velocity?
- 01v = d/t
- 02v = 400/50
- 03v = 8 m/s
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate velocity?
Divide the distance travelled in metres by the time taken in seconds: v = d ÷ t. The result is in m/s.
What's the difference between speed and velocity?
Speed is just how fast something moves. Velocity is the same idea but also includes direction, such as 10 m/s north.
Why can't time be zero in this formula?
Dividing by zero has no defined answer, and physically it would mean no time passed at all, so no velocity can be calculated.
How do I convert m/s to km/h?
Multiply the velocity in m/s by 3.6. For example, 10 m/s equals 36 km/h.
