A 100 m sprint
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d = 100 m, t = 9.58 sv = d/t = 100 / 9.58 = 10.44 m/s, which is 37.58 km/h or 23.35 mph. It is an average over the race: the sprinter is slower out of the blocks and faster later on.
Velocity Calculator
Velocity from distance and time, or final velocity from an acceleration, in any units.
Last updated
Want to solve these without the calculator?
The Coddy physics course teaches the method: you solve each problem in steps on an interactive board, and it tells you which step went wrong.
How to find velocity
Velocity is how fast something moves and in which direction. The simplest way to find it is to divide how far it went by how long it took: v = d/t. With d in metres and t in seconds, the answer is in metres per second. Usain Bolt's 100 m world record of 9.58 s works out at 100 / 9.58 = 10.44 m/s.
When you know an acceleration instead, use v = v₀ + at: the final velocity is the starting velocity v₀ plus the acceleration times the time. A stone dropped from rest falls with an acceleration of 9.81 m/s², so after 3 s it is moving at 0 + 9.81 · 3 = 29.43 m/s, about 106 km/h, if air resistance is ignored.
The calculator has a tab for each formula. Fill in the values you know, leave blank the one you want, and it solves for the velocity, the distance, the time, the initial velocity or the acceleration, whichever is missing. Kilometres, miles, hours, km/h and mph are converted to SI units first, and the answer is shown in the unit you pick and in every other speed unit.
What to notice
- Speed is how fast; velocity is how fast and which way. 20 m/s is a speed; 20 m/s north is a velocity.
- v = d/t gives an average. A car that covers 120 km in 2 hours averaged 60 km/h, even if it stopped at lights and went faster in between.
- For a velocity, d is the displacement, the straight-line change in position. Put in the length of the whole path instead and the answer is the average speed. A lap of a 400 m track in 50 s is an average speed of 8 m/s but an average velocity of 0, because you finish where you started.
- A velocity can be negative. The minus sign means it points the other way from the direction you chose as positive.
- v = v₀ + at only holds while the acceleration is constant, as in free fall or steady braking.
- 1 m/s is 3.6 km/h and about 2.24 mph.
How to calculate velocity
Pick the formula
Displacement and time known: v = d/t, the first tab. Initial velocity, acceleration and time known: v = v₀ + at, the second tab.
Put the values in SI units
Metres, seconds, m/s and m/s². 42.195 km is 42,195 m and 2 h is 7200 s; the calculator makes these conversions for you and shows them.
Divide, or multiply and add
v = d/t = 42,195 / 7200 = 5.86 m/s. Or v = v₀ + at = 0 + 9.81 · 3 = 29.43 m/s.
Read the answer in the unit you need
Multiply m/s by 3.6 for km/h, or divide by 0.44704 for mph. 5.86 m/s is 21.1 km/h.
Velocity formulas, rearranged
Each formula solved for each unknown, with one example worked through it.
| To find | Formula | Example | Answer |
|---|---|---|---|
| Velocity | v = d/t | 100 m in 9.58 s | 10.44 m/s |
| Distance | d = vt | 100 km/h for 3 h | 300 km |
| Time | t = d/v | 300 km at 100 km/h | 3 h |
| Final velocity | v = v₀ + at | From rest at 9.81 m/s² for 3 s | 29.43 m/s |
| Initial velocity | v₀ = v − at | 20 m/s after 5 s at 2 m/s² | 10 m/s |
| Acceleration | a = (v − v₀)/t | 0 to 100 km/h in 6.2 s | 4.48 m/s² |
Worked examples
A two hour marathon
plain
d = 42.195 km, t = 2 hConvert first: 42.195 km = 42,195 m and 2 h = 7200 s. Then v = 42,195 / 7200 = 5.86 m/s, which is 21.1 km/h or 13.1 mph.
A dropped stone after 3 s
plain
v₀ = 0 m/s, a = 9.81 m/s², t = 3 sv = v₀ + at = 0 + 9.81 · 3 = 29.43 m/s, about 106 km/h. Each second of falling adds 9.81 m/s, as long as air resistance stays small.
How long a trip takes
plain
d = 300 km, v = 100 km/hLeave the time blank and pick hours for it: t = d/v. In SI that is 300,000 m / 27.78 m/s = 10,800 s, which is 3 h.
Common mistakes
- Mixing units. 42.195 km divided by 2 h is 21.1 km/h, not 21.1 m/s. Convert both to metres and seconds, or keep km and h and read the answer in km/h.
- Reading an average as a top speed. v = d/t is the average over the whole trip; the fastest moment was faster than that.
- Using the whole path for a velocity. Over a full lap the displacement is 0, so the average velocity is 0, even though the average speed is not.
- Dropping the sign. If forward is positive, a velocity of −5 m/s means moving backwards at 5 m/s.
- Using v = v₀ + at when the acceleration changes. It holds only for a constant acceleration.
- Dividing the time by the distance. t/d gives seconds per metre, the inverse of a speed. Velocity is distance over time.
Velocity FAQ
How do you find velocity?
Divide the displacement by the time: v = d/t. If you know the starting velocity, the acceleration and the time instead, use v = v₀ + at. With values in metres and seconds, both give metres per second.
What is the formula for velocity?
Average velocity is v = d/t, displacement over time. Final velocity under a constant acceleration is v = v₀ + at. 100 m in 9.58 s is 10.44 m/s; 3 s of free fall from rest is 29.43 m/s.
What is the difference between speed and velocity?
Speed only says how fast; velocity also says which way. Average speed is the whole path length over the time, average velocity is the displacement over the time. On a straight one-way trip they match; on a round trip the average velocity is 0.
How do you find final velocity without time?
Use the kinematic equation v² = v₀² + 2as, where s is the displacement. A car at 20 m/s braking at 5 m/s² over 30 m ends at √(400 − 300) = 10 m/s. The tabs on this page need a time; the kinematics calculator solves this equation.
How do you convert m/s to km/h or mph?
Multiply by 3.6 for km/h, because 1 m/s is 3600 m an hour, 3.6 km. For mph, divide by 0.44704. 10 m/s is 36 km/h or 22.4 mph.
Can velocity be negative?
Yes. The sign shows the direction: once you choose which way is positive, a negative velocity means moving the opposite way. Speed is the size of the velocity and is never negative.
What is the unit of velocity?
The SI unit is the metre per second, m/s. km/h, mph, ft/s and knots are common too; the calculator converts between all of them and shows the answer in each.
