Speed Distance Time Calculator

Background.

How long does 250 km take at 90 km/h? Divide one by the other and you get 2.7778. That is hours as a decimal, not hours and minutes: the 0.7778 is a fraction of an hour, so the drive takes about 2 hours 47 minutes, not 2 hours 78 minutes and not 2 hours 7. Most mistakes with speed, distance and time are of this kind. The physics is one line; the errors live in the units and in what the word average means.

That line is distance = speed × time. Rearranged, speed is distance ÷ time and time is distance ÷ speed, so any two of the three settle the third. You choose which one to solve for and enter the other two in whatever units you have: metres, kilometres or miles; seconds, minutes or hours; m/s, km/h or mph. Every value is converted to metres and seconds before the division or multiplication happens, so miles can sit beside minutes with an answer requested in km/h. The conversion factors are definitions, not measurements. A mile has been exactly 1,609.344 m since 1959, when the international yard was fixed at 0.9144 m, and an hour is 3,600 s. The speed also comes back in metres per second whichever unit you chose, because that is the form physics formulas expect.

The speed you get is an average over the whole interval. Cover 100 km in two hours and the answer is 50 km/h whether you held a steady cruise or sprinted between traffic lights; nothing in the arithmetic knows what happened in between. For planning an arrival time that is exactly the figure you want, provided the time you feed in is the time that actually elapsed, stops and queues included. For a race split or a training run it is the average pace the watch would show at the finish. Where the in-between matters, such as the distance a car covers while it is still accelerating, the average alone is not enough, and the questions below show what to do instead.

What is speed distance time calculator?

Speed is the distance something covers per unit of time. Over any stretch of a journey, average speed is the total distance divided by the total time taken, which is the definition used here. The figure on a speedometer is instantaneous speed: the same ratio taken over an interval so short that the speed cannot change within it. For a car on cruise control the two agree. For a city bus that stops every few hundred metres, the average can sit far below any speed the bus reaches while moving. Speed is a scalar, meaning it says how fast but not which way. Its directional counterpart, velocity, divides displacement, the straight-line change in position, by time. The SI unit of speed is the metre per second; 1 m/s is 3.6 km/h, and 1 mph is exactly 0.44704 m/s.

How to use this calculator.

1. 01Choose the unknown under Solve for: Speed when you know how far and how long, Distance when you know how fast and for how long, Time when you know how far and how fast. The field for the unknown is ignored, so whatever number sits in it does not affect the answer.
2. 02Set Speed unit, Distance unit and Time unit before typing values. They can be mixed freely, for example miles with km/h, and the answer is reported in the units you selected.
3. 03Enter each time as one number in one unit. One hour 45 minutes is 1.75 h or 105 min, never 1.45; when the decimal is awkward, switch Time unit to minutes and type the total.
4. 04For a journey, take the route distance from a map or the odometer rather than the straight-line distance, and decide which average you want: total elapsed time gives the door-to-door figure, while subtracting stops first gives the moving average.
5. 05Read the result together with the speed in metres per second. When time is the answer, convert the decimal part yourself: 0.25 h is 15 minutes and 0.1 h is 6 minutes.

The formula.

The relationship is v = d ⁄ t, where v is average speed, d is the distance travelled and t is the time taken. Multiply both sides by t and you have d = v × t; divide that by v and you have t = d ⁄ v. These are one equation solved for three different unknowns, not three separate laws.

Before solving, each input is put into SI units. Distances become metres (a kilometre is 1,000 m, a mile 1,609.344 m), times become seconds (a minute is 60 s, an hour 3,600 s), and speeds become metres per second (km/h divided by 3.6, mph multiplied by 0.44704). The equation is solved in metres and seconds and the answer converted back into the unit you asked for. Because every factor is a definition, the conversion adds no uncertainty of its own: the only error in the answer is whatever error was in the distance and time you entered.

The proportions are simple, but one of them surprises people. Distance and time scale together, so doubling the distance at a fixed speed doubles the time. Time and speed are inversely related, so a percentage rise in speed buys a smaller percentage cut in time: going 10% faster saves 9.09% of the time, and each further step up saves less than the one before. All three quantities have to be greater than zero; at zero speed no finite time covers any distance.

Nothing in the equation describes how the motion varied inside the interval. Give it a total distance and a total time and it returns the average across them. It cannot recover a peak speed, and it cannot say where an accelerating object will be halfway through; that takes d = ut + ½at², the constant-acceleration relation covered by the acceleration calculator.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811, 2008 Edition. National Institute of Standards and Technology, Gaithersburg, MD. Section B.8 'Factors for Units Listed Alphabetically' provides the exact unit-conversion factors used by this calculator (1 mi = 1 609.344 m, 1 km/h = 1/3.6 m/s, 1 mph = 0.447 04 m/s).
2. [2]Halliday, D., Resnick, R. & Walker, J. (2018). Fundamentals of Physics, 11th edition. Wiley. Chapter 2 'Motion Along a Straight Line', sections 2-1 through 2-3, on position, displacement, average speed, average velocity, and instantaneous speed. The textbook treatment behind every distinction made in this calculator's content.
3. [3]International Organization for Standardization (2019). ISO 80000-3:2019 'Quantities and units — Part 3: Space and time'. Defines the kinematic quantities length, distance, time, speed, and velocity, including their preferred SI units and the relationship v = ds/dt that underlies the calculator's formula.
4. [4]Bureau International des Poids et Mesures (2019). The International System of Units (SI), 9th edition. Section 2.3 'Coherent derived units in the SI'. Establishes m/s as the coherent SI unit of speed via the defining constants — the speed of light c = 299 792 458 m/s exactly fixes the metre, and the caesium hyperfine transition fixes the second.
5. [5]Khan Academy — Physics: One-Dimensional Motion. 'Distance, displacement and coordinate systems' and 'Average velocity and average speed'. Open educational resource used as the canonical curriculum reference for the introductory speed-distance-time material targeted by this calculator.
6. [6]International Astronomical Union (2012). Resolution B2 'On the re-definition of the astronomical unit of length'. Fixes 1 AU = 149 597 870 700 m exactly. The basis for the 8 min 19 s Sun-Earth light-time calculation cited in the FAQs.
7. [7]Graubard, S. T. & Higham, D. J. (1994). 'How to take averages of speeds'. The Mathematical Gazette, 78(481), 47-49. Short peer-reviewed paper on the harmonic-mean treatment of average speed across equal-distance segments — the result cited in this calculator's round-trip FAQ.