Velocity, displacement or time, plus final velocity with acceleration.
Physics homework, lab reports and driving questions keep coming back to the same few motion equations, and this velocity calculator covers the three used most: average velocity from displacement and time, final velocity under constant acceleration with v = u + at, and displacement from velocity and time. You can enter values in metres, kilometres, miles or feet, and in seconds, minutes or hours. Results are given in metres per second and converted to other units, with the working shown.
How to Use the Velocity Calculator
Pick a mode:
- Velocity (v = d/t): enter the displacement and the time taken.
- Final velocity (v = u + at): enter the initial velocity, the acceleration in m/s² and the time. You also get the distance covered.
- Find displacement: enter the velocity and the time.
Choose a unit from the dropdown next to each box. The calculator converts everything to SI units (metres and seconds) before working out the answer.
Velocity Formulas
- Average velocity: v = d ÷ t, where d is displacement and t is time.
- Final velocity: v = u + at, where u is initial velocity, a is acceleration and t is time.
- Distance under constant acceleration: s = ut + ½at²
- Displacement: d = v × t
Velocity Examples
Average velocity of a 100 m sprint. The 100 m world record is 9.58 seconds. v = 100 ÷ 9.58 = 10.44 m/s, which is about 37.6 km/h or 23.4 mph.
Final velocity from rest. A car starts from rest (u = 0) and accelerates at 3 m/s² for 5 seconds. v = 0 + 3 × 5 = 15 m/s (54 km/h). Distance covered: s = 0 + ½ × 3 × 5² = 37.5 m.
Displacement. A train travels at a constant 25 m/s for 2 hours (7,200 s). d = 25 × 7,200 = 180,000 m = 180 km, about 111.8 miles.
Velocity vs Speed
Speed is how fast something moves. Velocity is speed in a stated direction, so it is a vector. If a runner completes one lap of a 400 m track in 80 seconds, their average speed is 5 m/s, but their average velocity is zero, because they finish where they started and their displacement is zero. In one-dimensional problems a negative velocity means movement in the opposite direction.
Units of Velocity
| Unit | Equals (m/s) |
| 1 km/h | 0.2778 m/s |
| 1 mph | 0.44704 m/s |
| 1 ft/s | 0.3048 m/s |
| 1 knot | 0.5144 m/s |
To change km/h into m/s, divide by 3.6. To change m/s into km/h, multiply by 3.6.
Mistakes in Motion Problems
- Mixing units. Using kilometres with seconds, or miles with minutes, gives wrong answers. The calculator converts for you.
- Using v = u + at when acceleration is not constant. The equation only works for constant acceleration.
- Confusing distance with displacement when an object changes direction.
Speed, Units and Travel Time
- For everyday trips, such as how long a drive will take at a given speed, use the speed distance time calculator.
- To convert a speed between units, use the speed converter.
- For more maths support with roots in physics formulas, the square root calculator may help.
Velocity FAQs
What is the SI unit of velocity?
Metres per second (m/s). The calculator always gives the answer in m/s first, then in other units.
Can velocity be negative?
Yes. In one dimension, a negative velocity means the object is moving in the opposite direction to the one you chose as positive.
What does “u” mean in v = u + at?
u is the initial velocity, the velocity at the start of the time period. v is the final velocity at the end of it.
How is average velocity different from instantaneous velocity?
Average velocity covers a whole journey (total displacement ÷ total time). Instantaneous velocity is the velocity at one moment, like a speedometer reading.
How we checked this page: each example was worked by hand in SI units and matches the calculator’s results, and the unit conversions use the exact international definitions.