Math & Science
Velocity Calculator
Speed, distance or time — with the answer given in five units at once.
Velocity Calculator
About the Velocity Calculator
Speed is distance divided by time. This calculator applies that and then rearranges it, so you can solve for distance or time just as easily by leaving the unknown blank.
Every answer arrives in five units at once — metres per second, kilometres per hour, miles per hour, feet per second and knots. That saves a second conversion step, and it makes results easy to sanity-check against something you already know.
Inputs accept whatever units you have. Distance in miles with a time in minutes works fine; everything is converted internally to metres and seconds before the arithmetic happens.
How to use the Velocity Calculator
- Choose which variable to solve for.
- Enter the other two with their units — they can be mixed.
- Select Calculate.
- Every common speed unit is shown at once.
- This gives average speed over the whole distance, not instantaneous speed.
The three forms of one equation
v = d ÷ t (speed from distance and time)
d = v × t (distance from speed and time)
t = d ÷ v (time from distance and speed)
Worked example
You cycle 42 kilometres in 1 hour 45 minutes. What was your average speed?
Convert the time to hours: 1 h 45 min = 1.75 hours.
v = 42 ÷ 1.75 = 24 km/h
24 km/h — 6.67 m/s — 14.9 mph
Note the word average. You almost certainly went faster downhill and slower uphill; this is the single steady speed that would have covered the same ground in the same time.
Converting speed units
| From | To | Multiply by |
|---|---|---|
| m/s | km/h | 3.6 |
| km/h | m/s | ÷ 3.6 |
| mph | km/h | 1.609344 |
| km/h | mph | 0.621371 |
| m/s | mph | 2.23694 |
| m/s | ft/s | 3.28084 |
| knots | km/h | 1.852 |
| knots | mph | 1.15078 |
The m/s to km/h factor of 3.6 is exact, not rounded. There are 3,600 seconds in an hour and 1,000 metres in a kilometre, so the ratio is exactly 3,600 ÷ 1,000. Likewise a mile is defined as exactly 1,609.344 metres.
Speed and velocity are not synonyms
In everyday use the words are interchangeable. In physics they are not.
- Speed is a scalar — a size with no direction. 30 km/h.
- Velocity is a vector — a size and a direction. 30 km/h due north.
The distinction has real consequences. Run one lap of a 400 m track in 60 seconds and your average speed is 6.67 m/s, but your average velocity is zero — you finished exactly where you started, so your displacement was nothing. Speed uses distance travelled; velocity uses displacement.
This calculator works with magnitudes, which is what almost every practical question needs. For direction-sensitive problems you need vector components.
What a knot is
One knot is one nautical mile per hour, and a nautical mile is exactly 1,852 metres — roughly one minute of latitude along a meridian. That connection to the Earth's own geometry is why ships and aircraft still use it: a degree of latitude is 60 nautical miles anywhere on the globe, which makes chart navigation straightforward.
The name comes from the old method of measuring speed by paying out a knotted rope behind a ship and counting knots against a sand timer.
Useful reference speeds
| m/s | km/h | mph | |
|---|---|---|---|
| Walking | 1.4 | 5 | 3.1 |
| Running (recreational) | 3.3 | 12 | 7.5 |
| Cycling | 5.6 | 20 | 12.4 |
| Urban speed limit | 13.4 | 48 | 30 |
| Motorway | 31.3 | 113 | 70 |
| Usain Bolt, peak | 12.4 | 44.7 | 27.8 |
| Airliner cruise | 250 | 900 | 559 |
| Speed of sound (sea level) | 343 | 1,235 | 767 |
To work out an arrival time from a distance and speed, the arrival time calculator adds breaks and departure times. For a change in speed over time, use the acceleration calculator.
Velocity equation: average, final and initial velocity formulas
| To find | Formula | Example |
|---|---|---|
| Average velocity | v = displacement ÷ time | 120 m ÷ 15 s = 8 m/s |
| Final velocity | v = u + at | 0 + 2 × 10 = 20 m/s |
| Initial velocity | u = v − at | 20 − 2 × 10 = 0 m/s |
| Final velocity (no time) | v = √(u² + 2as) | √(0 + 2 × 2 × 100) = 20 m/s |
| Linear velocity (spinning) | v = ω × r | 5 rad/s × 0.3 m = 1.5 m/s |
Here u is the starting velocity, a is acceleration, t is time, s is distance and ω is angular velocity. For problems with acceleration, the acceleration calculator helps.
Pipe velocity calculator: flow speed in a pipe
Water in a pipe moves at a speed set by the flow rate and the pipe's size.
Velocity = flow rate (Q) ÷ pipe cross-section area (A)
A = π × (inside diameter ÷ 2)²
A flow of 0.002 m³/s (2 L/s) through a pipe 50 mm across: A = 3.1416 × 0.025² = 0.00196 m². Velocity = 0.002 ÷ 0.00196 = 1.02 m/s. Many plumbing guides keep water speed in household pipes below about 2–3 m/s to limit noise and wear.
Angular velocity formula
ω = angle turned ÷ time = v ÷ r
A wheel turning one full turn (2π radians) a second has an angular velocity of 6.28 rad/s. Its rim, 0.3 m from the centre, moves at v = ωr = 1.88 m/s. That second form, v = ωr, is also the linear velocity formula for circular motion.
Velocity time graph
On a velocity time graph, the slope is the acceleration and the area under the line is the distance travelled. A car speeding up from 0 to 20 m/s over 10 s draws a straight line with slope 2 m/s². The area under it, a triangle, is ½ × 10 × 20 = 100 m.
Relative velocity and terminal velocity
- Relative velocity formula: vAB = vA − vB. Two cars heading the same way at 70 and 60 mph close at 10 mph; heading towards each other, at 130 mph.
- Terminal velocity formula: vt = √(2mg ÷ (ρACd)). It is the speed where air drag equals weight. A skydiver falling belly-down reaches roughly 55 m/s (about 120 mph).
Other ways to use this calculator
Speed, distance and time, plus related velocity questions.
- Average velocity calculator — enter displacement and time.
- Final and initial velocity calculator — use v = u + at from the formula table above.
- Pipe and duct flow velocity calculator — divide the flow rate by the cross-section area.
- Angular to linear velocity — v = ω × r.
- Speed calculator — distance time speed: speed = distance ÷ time.
- MPH to km/h — multiply by 1.609; mph to kmh in reverse divides.
- Average speed formula and average velocity formula — total distance (or displacement) ÷ total time.
- Final velocity formula and initial velocity formula — v = u + at and u = v − at.
Frequently asked questions
Speed equals distance divided by time: v = d ÷ t. Cycling 42 km in 1 hour 45 minutes gives 42 ÷ 1.75 = 24 km/h. Convert the time to a single unit first — 1 h 45 min is 1.75 hours, not 1.45. Rearranged, the same equation gives distance as v × t and time as d ÷ v, so any two values produce the third.
Multiply by 3.6. A speed of 15 m/s is 15 × 3.6 = 54 km/h. Going the other way, divide by 3.6. The factor is exact rather than approximate: there are 3,600 seconds in an hour and 1,000 metres in a kilometre, so the conversion is exactly 3,600 ÷ 1,000. This calculator shows both units alongside each other automatically.
Speed is a scalar — just a magnitude, like 30 km/h. Velocity is a vector, carrying a direction as well: 30 km/h due north. The difference matters in practice. Running one lap of a 400 m track in 60 seconds gives an average speed of 6.67 m/s but an average velocity of zero, because you finish where you started and your displacement is nothing.
A knot is one nautical mile per hour, and a nautical mile is exactly 1,852 metres — about one minute of latitude. That is why ships and aircraft use it: one degree of latitude is 60 nautical miles anywhere on Earth, which simplifies chart navigation. One knot is 1.852 km/h or 1.151 mph. The name comes from counting knots on a rope paid out behind a ship.
v = u + at, where u is the starting velocity, a is acceleration and t is time. Starting from rest and accelerating at 2 m/s² for 10 seconds gives a final velocity of 20 m/s.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — SI speed units and exact conversion factors
- NIST — International and US survey units — the exact definition of the international mile and foot
- Speed — Encyclopaedia Britannica — the scalar/vector distinction between speed and velocity