Velocity Calculator
A car that travels 100 meters in 20 seconds has an average velocity of 5 meters per second. This velocity calculator gives you two of the most useful ways to find velocity in a single tool. In average mode you enter a displacement in meters and a time in seconds, and the calculator divides distance by time to return the average velocity over that interval. In final mode you enter an initial velocity, a constant acceleration, and an elapsed time, and it applies the kinematic equation v = u + a times t to return the final velocity at the end of that time. Every answer comes back in meters per second, the standard scientific unit, and is also converted into kilometers per hour and miles per hour so you can read the result in whichever units make sense for your problem. Whether you are checking a physics homework answer, working out how fast an object is moving after it accelerates, or converting a lab measurement into everyday units, the calculator handles the arithmetic and the unit conversions for you.
Quick answer
Average velocity equals displacement divided by time, so 100 meters in 20 seconds is 5 meters per second.
What this tells you
- •Average velocity equals displacement divided by time, so 100 meters in 20 seconds is 5 meters per second.
- •Final velocity under constant acceleration equals initial velocity plus acceleration times time, written v = u + a times t.
- •Velocity is a vector, so a negative displacement or a negative acceleration produces a signed result that shows direction as well as magnitude.
- •In average mode the time must be greater than zero, because dividing a distance by zero seconds is undefined.
- •The primary answer is in meters per second, the SI unit, and is rounded to four decimal places for display.
- •The tool also converts your result to kilometers per hour by multiplying by 3.6 and to miles per hour by multiplying by 2.23694.
How to Use
- 11. Choose a mode. Pick Average velocity if you know how far something moved and how long it took, or Final velocity if you know a starting speed, an acceleration, and a time.
- 22. In average mode, enter the displacement in meters and the time in seconds. Displacement can be negative if the object moved in the negative direction.
- 33. In final mode, enter the initial velocity in meters per second, the acceleration in meters per second squared, and the elapsed time in seconds. Use a negative acceleration for deceleration.
- 44. Press Calculate to read the velocity in meters per second as the primary result.
- 55. Check the secondary results underneath for the same velocity expressed in kilometers per hour and miles per hour.
How It Works
Formula
Average: v = d / t. Final: v = u + a * tAverage velocity is total displacement d divided by the total time t taken to cover it, giving the constant speed that would produce the same displacement over the same interval. Because it uses displacement rather than distance traveled, the result is a vector that carries a sign showing direction. Final velocity uses the first equation of motion for constant acceleration, v = u + a times t, where u is the initial velocity, a is the acceleration, and t is the elapsed time. When acceleration is positive the object speeds up, when it is negative the object slows down or reverses. In average mode the time must be positive because velocity is undefined for a zero-length or negative time interval. All results are rounded to four decimal places for display while the underlying value keeps full precision.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Average velocity of a sprinter
A displacement of 100 meters covered in 20 seconds gives 100 divided by 20, which is 5 meters per second. Multiplying by 3.6 gives 18 kilometers per hour, and multiplying by 2.23694 gives about 11.18 miles per hour.
Final velocity of a dropped object
An object dropped from rest has an initial velocity u of 0. After 3 seconds of falling at 9.8 meters per second squared, v = 0 plus 9.8 times 3, which is 29.4 meters per second downward.
A car accelerating from a rolling start
Starting at 10 meters per second and accelerating at 2 meters per second squared for 5 seconds gives v = 10 plus 2 times 5, which is 20 meters per second, or 72 kilometers per hour.
Braking to a slower speed
A vehicle moving at 30 meters per second that decelerates at 5 meters per second squared for 4 seconds reaches v = 30 plus negative 5 times 4, which is 10 meters per second. The negative acceleration models braking.
Velocity Unit Conversions
Common velocity values in meters per second and their equivalents in other units.
| m/s | km/h | mph | Everyday comparison |
|---|---|---|---|
| 1 | 3.6 | 2.24 | A brisk walk |
| 5 | 18 | 11.18 | A steady jog |
| 10 | 36 | 22.37 | A fast cyclist |
| 20 | 72 | 44.74 | City driving speed |
| 30 | 108 | 67.11 | Highway driving speed |
| 100 | 360 | 223.69 | A commercial aircraft on approach |
To convert meters per second to kilometers per hour multiply by 3.6, and to convert to miles per hour multiply by 2.23694.
Velocity versus speed, and why the sign matters
Speed and velocity are often used as if they mean the same thing, but in physics they are different. Speed is a scalar, a single positive number that tells you how fast something is moving with no regard to direction. Velocity is a vector, which means it carries both a magnitude and a direction. That is why this calculator can return a negative value. A velocity of negative 5 meters per second means the object is moving at 5 meters per second in the direction you have chosen to call negative.
Average velocity uses displacement, the straight-line change in position, rather than the total path length. If you walk 3 meters east and then 3 meters back west in 6 seconds, your total distance is 6 meters but your displacement is 0, so your average velocity is 0 even though your average speed was 1 meter per second. This distinction becomes important the moment an object changes direction during the interval you are measuring.
Final velocity in the second mode assumes acceleration stays constant for the whole time interval. Real vehicles and falling objects rarely accelerate at a perfectly steady rate because of friction, air resistance, and changing forces, so treat the v = u + a times t result as the ideal value for a constant-acceleration model. It is exact for the physics problems that specify constant acceleration and a close approximation for many real situations over short intervals.
Common mistakes
- Confusing distance with displacement. Average velocity uses displacement, the net change in position, so an object that returns to its start has zero displacement and zero average velocity regardless of how far it actually traveled.
- Entering time as zero in average mode. Dividing by zero seconds is undefined, so the calculator returns no result until you enter a positive time.
- Forgetting the sign of acceleration when braking. Deceleration is a negative acceleration, so enter a negative value in final mode to model slowing down or reversing.
- Mixing units before entering values. The calculator expects meters, seconds, and meters per second, so convert kilometers or hours to base units first or your answer will be off by a large factor.
- Reading the km/h or mph figure as the primary answer. The primary result is always in meters per second, and the other two rows are unit conversions of that same velocity.
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