What this calculator does
The velocity formula gives the rate and direction an object moves in, not just how fast. Velocity is a vector: it carries a sign or a compass direction alongside its size, which is what separates it from plain speed. This calculator covers the two most common ways to reach it, from a displacement and a time, or from an initial speed, an acceleration and a time.
Displacement is not the same thing as distance. If you walk 50 m east then 50 m back west, the distance covered is 100 m but the displacement, and therefore the average velocity over that trip, is zero. Keeping that distinction straight is the one thing people most often get wrong when they first meet the velocity equation.
The formula
The first mode divides displacement by time, v = d/t, giving the straight-line average velocity between a start and end point. The second mode uses v = u + a·t, adding the change built up by a constant acceleration over a time to an initial velocity. Both return a signed result: positive means the motion is in the direction taken as forward, negative means it is running the opposite way.
| Term | Meaning |
|---|---|
| v | Velocity: the quantity being solved for, in metres per second unless converted. |
| d | Displacement: straight-line change in position, with a sign for direction. |
| u | Initial velocity, used in the second mode alongside acceleration and time. |
| a | Acceleration: the constant rate of change of velocity, used in the second mode. |
| t | Time taken, in seconds. |
The inputs explained
| Field | What to enter |
|---|---|
| Calculate using | Choose which two quantities you already have: a displacement and a time, or an initial velocity with an acceleration and a time. |
| Displacement (+ forward, − backward) (m) | The straight-line change in position. Use a negative value for displacement in the opposite direction to whatever you are calling forward. |
| Time taken (s) | The time over which the displacement happened, or the time acceleration acted for. |
| Initial velocity (m/s) | The velocity at the start of the interval, before any acceleration is applied. |
| Acceleration (m/s²) | A constant acceleration. Use a negative value for deceleration or acceleration acting backward. |
When to use it
Working from a GPS trace or track log
A start point, an end point and an elapsed time give displacement directly, which is what the first mode expects rather than the total path length the device may have logged.
Working from a physics problem giving acceleration
Many textbook problems supply an initial speed, a constant acceleration and a time rather than a displacement, which is exactly what the second mode solves without needing to work out displacement first.
Checking the sign of a result
Setting a consistent forward direction before entering values means a negative answer reads immediately as motion the other way, rather than needing to be reasoned out afterward.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How average velocity changes with time at a fixed displacement
The same 400 m displacement, covered over a range of times.
| Time taken | Velocity | In km/h |
|---|---|---|
| 10 s | 40.000 m/s | 144.00 |
| 20 s | 20.000 m/s | 72.00 |
| 40 s | 10.000 m/s | 36.00 |
| 80 s | 5.000 m/s | 18.00 |
| 100 s | 4.000 m/s | 14.40 |
| 200 s | 2.000 m/s | 7.20 |
How velocity changes with acceleration at a fixed initial speed and time
Starting at 5 m/s, the velocity reached after 10 s at a range of accelerations.
| Acceleration | Velocity | Direction |
|---|---|---|
| -2 m/s² | -15.000 m/s | Negative (backward) |
| -1 m/s² | -5.000 m/s | Negative (backward) |
| 0 m/s² | 5.000 m/s | Positive (forward) |
| 1 m/s² | 15.000 m/s | Positive (forward) |
| 2 m/s² | 25.000 m/s | Positive (forward) |
| 4 m/s² | 45.000 m/s | Positive (forward) |
Questions
What is the difference between speed and velocity?
Speed is how fast something moves, with no direction attached; velocity is speed plus direction, expressed as a signed number along a line or as a vector in space. Two trips can have identical speed but opposite velocity if one runs forward and the other back.
Can average velocity be zero even if something moved the whole time?
Yes. If the start and end position are the same, displacement is zero and so is average velocity, no matter how much distance was actually covered getting there and back.
Why does this calculator ask for two different sets of inputs?
The velocity formula is written a few different ways depending on what is known. Displacement and time is the most direct route to an average velocity; initial velocity, acceleration and time is the standard route when a constant acceleration is involved instead.
What if I only know initial and final velocity, not acceleration?
That is one of the five SUVAT equations of motion rather than this calculator’s two modes. The SUVAT equations calculator solves for any of the five variables, including this case.
For journey-planning arithmetic based on distance and elapsed time rather than signed displacement, see the speed, distance and time calculator. For the full five-variable equations of motion, including this one as a special case, use the SUVAT equations calculator.