Solve for velocity, distance, or time using v = d / t. Change any value to recalculate instantly, with unit conversion and a step-by-step walkthrough.
Velocity
10m/s
WalkingCarJetBullet
That is about 1.3× cyclist speed (8 m/s).
How is this calculated?
v = d / t
1. Distance in SI: 100 m = 100 m
2. Time in SI: 10 s = 10 s
3. Velocity = distance ÷ time = 10 m/s
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About the Velocity Calculator
Velocity is the rate at which an object changes position, and unlike speed it is a vector quantity carrying both magnitude and direction. That distinction is not pedantic. A car driving a complete lap of a circuit at 200 km/h has a substantial speed throughout but an average velocity of exactly zero, because it finished where it started and displacement is the numerator in the velocity equation. Velocity underpins essentially all of classical mechanics: it appears in momentum, in kinetic energy, in the definition of acceleration as its own rate of change, and in every equation of motion used to predict where something will be. Physics distinguishes average velocity, which describes an entire journey as a single ratio, from instantaneous velocity, which is the value at one precise moment and is what a speedometer approximates. Understanding when each applies is what separates a correct answer from a plausible-looking one in kinematics problems.
Mathematical Formula & Logic
Velocity relates displacement to the time taken to cover it.
1. Average velocity:
v = Δs / Δt = (s_final − s_initial) / (t_final − t_initial)
Where s is displacement (a vector), not distance travelled (a scalar).
2. Instantaneous velocity:
v = ds/dt
The limit of average velocity as the time interval approaches zero.
3. Final velocity under constant acceleration:
v = u + a·t
Where u is initial velocity, a is acceleration, and t is elapsed time.
4. Velocity from displacement without knowing time:
v² = u² + 2·a·s
5. Average velocity under constant acceleration:
v_avg = (u + v) / 2
This shortcut is valid ONLY when acceleration is constant.
6. SI unit:
metres per second (m/s)
1 m/s = 3.6 km/h = 2.23694 mph
Step-by-Step Example
A train accelerates uniformly from rest, reaching 30 m/s after 20 seconds, then travels a further 1,200 m at that constant speed:
Phase 1 — the acceleration phase
1. Initial velocity u = 0 m/s, final velocity v = 30 m/s, time t = 20 s.
2. Acceleration a = (v − u) / t = (30 − 0) / 20 = 1.5 m/s²
3. Average velocity in this phase = (u + v) / 2 = (0 + 30) / 2 = 15 m/s
4. Displacement in this phase = v_avg × t = 15 × 20 = 300 m
Phase 2 — the constant-velocity phase
5. Distance = 1,200 m at a constant 30 m/s
6. Time = 1,200 / 30 = 40 s
The journey as a whole
7. Total displacement = 300 + 1,200 = 1,500 m
8. Total time = 20 + 40 = 60 s
9. Average velocity for the whole journey = 1,500 / 60 = 25 m/s
Note that 25 m/s is not the average of 15 and 30, because the two phases lasted different lengths of time. Average velocity is always total displacement divided by total time, never the mean of the individual phase velocities. Converting the result: 25 m/s × 3.6 = 90 km/h.
Reference Data & Values
quantity
metres per_second
km per_hour
mph
Walking pace
1.4
5.0
3.1
Sprinter (world class)
10.4
37.4
23.3
Urban car
14.0
50.4
31.3
Motorway car
31.0
111.6
69.3
Bullet train
83.0
298.8
185.7
Jet airliner (cruise)
250.0
900.0
559.2
Speed of sound (20°C air)
343.0
1,234.8
767.3
Speed of light (vacuum)
299,792,458
1.079e9
6.706e8
Frequently Asked Questions
Speed is a scalar describing only how fast something moves, while velocity is a vector describing how fast and in which direction. The practical consequence is that they use different numerators: speed divides total distance travelled by time, whereas velocity divides displacement, meaning the straight-line change in position, by time. A runner completing one lap of a 400 m track in 50 seconds has an average speed of 8 m/s but an average velocity of zero, because the finish point coincides with the start and the displacement is nil.
Yes, and circular motion is the standard example. A satellite in a perfectly circular orbit or a car travelling a roundabout at a steady 30 km/h has an unchanging speed, but its direction of travel changes continuously, and since direction is part of velocity, the velocity is changing at every instant. A changing velocity means the object is accelerating even though it is not speeding up or slowing down. That acceleration points toward the centre of the circle and is what keeps the object on its curved path.
Instantaneous velocity is the velocity at one specific moment, defined formally as the derivative of displacement with respect to time, ds/dt. Average velocity compresses an entire journey into a single ratio of total displacement to total time and can hide enormous variation within it. A car that covers 100 km in one hour has an average velocity of 100 km/h whether it held that speed throughout or alternated between standstill and 200 km/h. A speedometer displays a close approximation of instantaneous speed.
To convert metres per second to kilometres per hour, multiply by 3.6, since there are 3,600 seconds in an hour and 1,000 metres in a kilometre. To go the other way, divide by 3.6. For miles per hour, multiply metres per second by 2.23694, or multiply kilometres per hour by 0.621371. A useful mental anchor is that 10 m/s is exactly 36 km/h and roughly 22.4 mph, which makes rough conversions quick without a calculator.
Because each speed was held for a different length of time, so a plain mean gives equal weight to phases that contributed unequally to the journey. Average velocity is always total displacement divided by total time. If you drive 60 km at 60 km/h, taking one hour, then 60 km at 120 km/h, taking half an hour, the average is 120 km over 1.5 hours, or 80 km/h — not the 90 km/h that averaging the two speeds would suggest. The slower phase occupied more time and therefore dominates.
Yes. A negative velocity simply means the object is moving in the direction opposite to whichever way you defined as positive when setting up the problem. If you take east as positive, a car travelling west at 20 m/s has a velocity of −20 m/s while its speed remains 20 m/s, since speed is a magnitude and cannot be negative. The sign carries directional information, which is precisely what makes velocity a vector and why signs must be tracked consistently through a calculation.