Speed Calculator

Speed is distance divided by time. A sprinter who covers 100 meters in 20 seconds is moving at 5 m/s, and that single relationship rearranges to answer the other two questions people actually ask: how far you will get, and how long it will take. This calculator handles all three, and it will take miles and hours in and give meters per second back if that is what you need.

Two of the three values are always enough. Give it distance and time and it returns speed; give it speed and time and it returns distance; give it speed and distance and it returns the time. The steps below the result show the substitution, so you can check the arithmetic rather than trust it.

What speed is

Speed is the rate at which an object covers distance, measured in the SI system in meters per second (m/s). Kilometers per hour, miles per hour, feet per second and knots are all the same idea with different lengths and different clocks on the top and bottom of the fraction.

Which unit to use is a question of scale rather than correctness. A garden snail moves at roughly 0.013 m/s, which is a number nobody can picture, but 47 meters per hour is immediately clear. A rifle bullet travels at about 800 m/s; quoting it in millimeters per hour would be technically true and useless. Pick the unit that puts the number somewhere between about 0.1 and 1000, and the arithmetic stays readable.

Speed and velocity are different quantities

Speed is a scalar and velocity is a vector: speed has size only, velocity has size and direction. The distinction changes the answer as well as the wording.

Drive one lap of a 4 km circuit in 2 minutes and your average speed is 4 km in 120 seconds, or 33.3 m/s. Your average velocity is zero, because you finished exactly where you started and displacement, not distance, is what velocity divides by. Anything that goes round in a circle at a steady rate — a satellite, a wheel rim, a runner on a track — has constant speed and continuously changing velocity. That change is an acceleration, which is why an orbit needs no engine but does need gravity.

This calculator works in speed. If you need direction as well, work out the straight-line displacement first with the Distance Calculator and divide that by the time instead.

Average speed is not the average of your speeds

Average speed is total distance divided by total time, and it is almost never the arithmetic mean of the speeds you travelled at. This is the single most common error in speed problems.

Drive 60 km to a town at 30 km/h and the same 60 km home at 60 km/h. The instinct is to say 45 km/h. The outbound leg took 2 hours and the return took 1, so you covered 120 km in 3 hours: the average speed is 40 km/h, not 45. The slow leg dominates because you spend longer doing it.

For two legs of equal distance the correct answer is the harmonic mean:

which gives (2 × 30 × 60) / 90 = 40. Traffic engineers use this constantly: a commute that is half at 100 km/h and half at 20 km/h averages 33.3 km/h, not 60. If instead you spend equal time at each speed, the plain average is right, which is why the two cases have to be told apart before any arithmetic starts.

Three worked examples

Finding speed. A runner covers 400 meters in 52 seconds. Speed = 400 / 52 = 7.6923 m/s. Multiply by 3.6 to read it as 27.69 km/h, or divide by 0.44704 to get 17.21 mph.

Finding distance. A boat holds 12 knots for 3 hours 30 minutes. Distance = 12 × 3.5 = 42 nautical miles, which is 77.78 km. Knots and nautical miles pair up neatly like this, which is exactly why sailors still use them.

Finding time. A drive of 250 miles at an average 55 mph takes 250 / 55 = 4.5455 hours, or 4 hours 32 minutes 44 seconds. Note the word average: 55 mph on the cruise control is not 55 mph over the trip once fuel stops and roadworks are counted, so pad any real journey estimate.

Converting between units of speed

Multiply by 3.6 to turn meters per second into kilometers per hour, and divide by 3.6 to go back. That factor is just 3600 seconds in an hour divided by 1000 meters in a kilometer.

For imperial and metric, one mile is exactly 1609.344 meters, so 1 mph is exactly 0.44704 m/s and exactly 1.609344 km/h. A 60 mph limit is 96.56 km/h, and a 100 km/h limit is 62.14 mph. The knot is a nautical mile per hour, and a nautical mile is exactly 1852 meters, one minute of latitude, which makes 1 knot equal to 1.852 km/h or 0.514444 m/s.

Read a row as the unit on the left expressed in the unit at the top: 1 knot is 1.150779 mph. The converter on this page covers the wider list, including centimeters per hour, miles per second and the speed of light, and the general-purpose Conversion Calculator handles length and time separately if you need them apart.

How fast is that

Numbers mean more next to something familiar. Walking pace is about 1.4 m/s and the speed of sound at sea level is 343 m/s, so a jet at Mach 1 is moving roughly 245 times faster than you walk.

The bottom row is a defined constant rather than a measurement. The meter is defined so that light travels exactly 299,792,458 meters per second in vacuum, which is why that figure has no uncertainty attached. Sunlight takes 499 seconds to reach us, a little over eight minutes and nineteen seconds.

Using this calculator

Pick the tab for the value you want — Find Speed, Find Distance or Find Time — and the calculator replaces that field with a question mark and asks for the other two. Time is entered as hours, minutes and seconds in three boxes, so 1 hour 20 seconds goes in as 1 and 20 without any decimal conversion. Leave a box empty and it counts as zero.

The unit menus are independent of each other. Entering a distance in kilometers, a time in minutes and asking for the answer in knots is fine; the conversion happens internally in meters and seconds. Results are given to fourteen significant figures with trailing zeros removed, and the side panel repeats the answer in the five units people usually want alongside it. For running and cycling, where the useful figure is minutes per mile rather than miles per hour, the Pace Calculator inverts the same equation.