The Velocity Formula, Explained with Examples
By Shihab Mia June 20, 2026 6 min read
Quick answer
Average velocity = displacement divided by time, written as v = displacement / time. Displacement is the straight-line change in position, including direction, so velocity (unlike speed) can be negative. Under constant acceleration you can also use v = u + a x t or v squared = u squared + 2 x a x s, where u is the starting velocity, a is acceleration, t is time, and s is displacement.
What is velocity?
Velocity is the rate at which an object's position changes, expressed as a vector, meaning it has both a size and a direction. A car driving 60 km/h north has a different velocity from a car driving 60 km/h south, even though their speeds are identical. Ignore the direction and you are left with speed, the size of the velocity.
The word that matters most in the definition is displacement. Displacement is the straight-line distance from the start point to the end point, together with the direction of travel. It is not the same as total distance travelled. If you walk 5 m east and then 5 m back west, your distance is 10 m but your displacement is zero, so your average velocity over that walk is zero too, according to the Physics Classroom's lesson on speed and velocity.
The average velocity formula
The most common way to calculate velocity is the average velocity over an interval of time:
Average velocity
v = displacement / time, or in symbols, v = (final position minus initial position) / (time elapsed).
The standard SI unit is metres per second (m/s), but you will also see kilometres per hour (km/h), miles per hour (mph), and other distance-over-time units. As long as the top of the fraction is a length and the bottom is a duration, you have a valid velocity unit. The same displacement-over-time idea underlies the average rate of change you may have met in algebra, and you can convert between speed units instantly with the speed converter.
It helps to know a few common conversions so your answers land in the units a question expects. To go from metres per second to kilometres per hour, multiply by 3.6, so 5 m/s becomes 18 km/h. To convert the other way, divide by 3.6. For miles per hour, 1 m/s is roughly 2.24 mph. Here are the conversions you will reach for most often.
Quick velocity unit conversions
| From | To | Multiply by |
|---|---|---|
| m/s | km/h | 3.6 |
| km/h | m/s | 0.2778 |
| m/s | mph | 2.237 |
| mph | m/s | 0.447 |
| km/h | mph | 0.6214 |
Instantaneous velocity vs average velocity
Instantaneous velocity is the velocity of an object at one single moment, while average velocity is the displacement over an entire time interval; the two are equal only when velocity stays constant throughout that interval. On a position-versus-time graph, average velocity is the slope of the straight line connecting the start and end points, while instantaneous velocity is the slope of the line touching the curve at just one point, a relationship OpenStax's University Physics covers in more mathematical detail.
A speedometer is the everyday example: it reports something close to instantaneous speed at that instant, not the average over your whole trip. If you drive 100 km in 2 hours with a stop for lunch, your average velocity for the trip is 50 km/h in your direction of travel, even though your instantaneous speed was 0 km/h during lunch and well above 50 km/h on the open road.
Velocity under constant acceleration
When an object speeds up or slows down at a steady rate, three linked equations let you find velocity without needing calculus. Each one is useful when a problem gives you a different mix of known values.
Velocity equations for constant acceleration
| Equation | What it finds | Use it when you know |
|---|---|---|
| v = u + a x t | Final velocity | Starting velocity, acceleration, time |
| v squared = u squared + 2 x a x s | Final velocity | Starting velocity, acceleration, displacement (no time) |
| v(avg) = (u + v) / 2 | Average velocity | Starting and final velocity (constant acceleration only) |
Watch the sign of the acceleration in all three equations. If an object is slowing down, its acceleration points opposite to its motion, so you plug in a negative value for a. A ball thrown straight up with a starting velocity of 20 m/s feels gravity pulling it down at 9.80665 m/s squared, the standard value defined by NIST. Using v = u + a x t with a as negative 9.8, the ball reaches zero velocity after roughly 2 seconds, the moment it stops rising and begins to fall. Choosing a consistent positive direction at the start of a problem and sticking with it is the surest way to keep these signs straight.
Velocity vs speed: the key difference
Speed is a scalar built from total distance, while velocity is a vector built from displacement, so velocity can be negative and speed cannot. Here is a side-by-side comparison of the two.
Velocity compared with speed
| Feature | Speed | Velocity |
|---|---|---|
| Type of quantity | Scalar (size only) | Vector (size and direction) |
| Based on | Total distance travelled | Displacement |
| Can it be negative? | No, always zero or positive | Yes, direction can make it negative |
| Example value | 60 km/h | 60 km/h heading north |
| Zero when | Object is at rest | Start and end positions are the same |
Because of these differences, average speed and average velocity are not always equal. On a round trip back to where you started, your average speed can be high while your average velocity is exactly zero, because displacement is zero. For the scalar version of this formula, see the speed formula guide.
Relative velocity
Relative velocity is how fast and in what direction one object appears to move as seen from another moving object, found with v(AB) = v(A) minus v(B). If two cars travel the same direction at 40 m/s and 25 m/s, the faster car pulls away from the slower one at 40 minus 25 = 15 m/s. If they travel toward each other instead, treating one direction as negative, their closing velocity adds up rather than subtracts.
Relative velocity matters whenever motion is described from a moving viewpoint, such as overtaking on a motorway, aircraft accounting for wind, or two runners closing a gap on a track. The same subtraction rule applies no matter which direction each object is heading, as long as you keep the signs consistent with the positive direction you chose at the start.
Worked examples
A cyclist travels 150 metres east in 30 seconds along a straight road. Find the average velocity.
- Identify the displacement: 150 metres east.
- Identify the time elapsed: 30 seconds.
- Apply the formula: v = displacement / time = 150 / 30.
- Divide: 150 divided by 30 equals 5.
- State the answer with direction: the average velocity is 5 m/s east.
Worked example: constant acceleration
A car starts at 10 m/s and accelerates at 2 m/s squared for 4 seconds. Find its final velocity using v = u + a x t: multiply acceleration by time (2 x 4 = 8), then add the starting velocity (10 + 8 = 18). The final velocity is 18 m/s.
Worked example: no time given
A skateboarder starts at 2 m/s and accelerates at 1.5 m/s squared over a displacement of 10 m, with no time value given. Use v squared = u squared + 2 x a x s: v squared = 2 squared + 2 x 1.5 x 10 = 4 + 30 = 34, so v is the square root of 34, about 5.8 m/s. You can check a calculation like this instantly with the velocity calculator.
Common mistakes to avoid
- Confusing distance with displacement. Average velocity uses displacement, the straight-line change in position, not the total path length.
- Dropping the direction. A velocity answer without a direction is incomplete; it has become a speed.
- Mixing units. Keep distance and time in matching units before dividing, for example metres with seconds, or convert first with a speed converter.
- Using v = u + a x t when acceleration is not constant. That equation, and the other two constant-acceleration equations, only hold for steady (uniform) acceleration.
- Forgetting that velocity can be negative. A negative sign simply means motion in the opposite direction to the one you chose as positive.
- Treating a speedometer reading as average velocity. A speedometer shows instantaneous speed at that moment, not the average over a trip.
Frequently asked questions
What is the velocity formula?
The average velocity formula is v = displacement / time, meaning velocity equals the change in position divided by the time taken. For motion with constant acceleration you can also use v = u + a x t or v squared = u squared + 2 x a x s, where u is the starting velocity, a is acceleration, t is time, and s is displacement.
What is the difference between velocity and speed?
Speed is a scalar that measures only how fast something moves, using total distance. Velocity is a vector that includes direction and uses displacement. Two objects can share the same speed but have different velocities if they move in different directions.
How do you calculate average velocity?
Divide the displacement by the time elapsed. First find the change in position from start to end, including its direction, then divide by how long the motion took. For example, 150 metres east in 30 seconds gives an average velocity of 5 m/s east.
Can velocity be negative?
Yes. A negative velocity simply means the object is moving in the direction you defined as negative. The sign indicates direction, not a mistake. Speed, by contrast, is never negative because it ignores direction entirely.
What is instantaneous velocity?
Instantaneous velocity is an object's velocity at one specific moment, rather than averaged over an interval. On a position-time graph it is the slope of the tangent line at that point. A car speedometer reads something close to instantaneous speed, the size of the instantaneous velocity, at each moment.
What is relative velocity?
Relative velocity is how fast and in which direction one object appears to move as seen from another moving object, calculated as v(AB) = v(A) minus v(B). If a car at 40 m/s overtakes a car at 25 m/s travelling the same way, its relative velocity compared to the slower car is 15 m/s.
What are the units of velocity?
The SI unit of velocity is metres per second (m/s). Other common units include kilometres per hour (km/h) and miles per hour (mph). Any unit of distance divided by a unit of time is a valid velocity unit, as long as direction is stated.
Is velocity the same as acceleration?
No. Velocity is how fast position changes, while acceleration is how fast velocity changes. If velocity is steady, acceleration is zero. Acceleration is measured in metres per second squared, whereas velocity is measured in metres per second; see the [acceleration formula guide](/blog/acceleration-formula-explained/) for the full breakdown.