Speed answers a simple question: how much distance, in how much time? The formula is one division — speed equals distance divided by time — and everything else in this subject is either unit conversion, or the distinction between the speed of a whole journey and the speed at one instant, or the distinction between speed and velocity. This guide covers the formula with worked examples in road, running, and scientific contexts, the unit conversions that cause the most errors, and the average-speed traps: the harmonic-mean trap of out-and-back journeys, the effect of stops, and the difference between speed and pace. Pace — minutes per kilometre or per mile, the runner’s unit — is covered in its own guide, linked at the end; this guide stays with speed.

The speed formula, and its three rearrangements

The formula is speed = distance ÷ time. With distance in kilometres and time in hours, the answer is in kilometres per hour. With distance in miles and time in hours, miles per hour. The same triangle rearranges two ways: distance = speed × time, and time = distance ÷ speed. Every speed problem in school, driving, and sport is one of these three, with the units converted to match.

Worked examples. A car covers 240 km in 3 hours: speed = 240 ÷ 3 = 80 km/h. A train travels at 120 km/h for 2.5 hours: distance = 120 × 2.5 = 300 km. A cyclist must cover 45 km at 18 km/h: time = 45 ÷ 18 = 2.5 hours, or 2 hours 30 minutes. A marathon runner covers 42.195 km in 4 hours: average speed = 42.195 ÷ 4 = 10.55 km/h. The arithmetic is trivial; the errors come from units — mixing minutes with hours, or miles with kilometres — so convert first, calculate second, and write the unit on every intermediate number.

Time conversions deserve care. 2 hours 30 minutes is 2.5 hours, not 2.30 hours. 45 minutes is 0.75 hours. 20 minutes is one-third of an hour (0.333…). A journey of 30 km in 45 minutes averages 30 ÷ 0.75 = 40 km/h; computed as 30 ÷ 45 = 0.67, the answer is kilometres per minute, which converts to 40 km/h by multiplying by 60. Either route works; mixing them — dividing kilometres by minutes and calling the result km/h — is the standard error.

Average speed, instantaneous speed, and the stops that count

Average speed divides the whole journey: total distance over total elapsed time, including traffic lights, fuel stops, and rest breaks. Instantaneous speed is the speedometer at one moment. The two coincide only on a journey at constant speed, which real journeys never are. A driver who covers 120 miles in 2 hours 30 minutes averages 48 mph, even if the speedometer read 70 mph for most of the moving time — the slow stretches and stops are in the denominator, and they pull the average down more than intuition suggests, because time spent slow contributes disproportionately.

That asymmetry is the key insight of average speed. An hour at 30 mph followed by an hour at 60 mph averages 45 mph (equal times, so the simple mean works). But 60 miles at 30 mph followed by 60 miles at 60 mph averages 40 mph, not 45: the first leg takes 2 hours, the second 1 hour, so total distance 120 miles over 3 hours is 40 mph. Equal distances average by the harmonic mean: 2 ÷ (1/30 + 1/60) = 40. The rule is: equal times, use the ordinary average; equal distances, use the harmonic mean. Out-and-back journeys at different speeds are the classic equal-distance case, and the naive average overstates the result every time.

Speed versus velocity: direction changes the answer

Velocity is speed with direction: displacement divided by time, where displacement is the straight-line distance from start to finish. On a straight road in one direction, speed and velocity have the same magnitude and the distinction is pedantic. On any journey that turns, it matters. A 400-metre lap run in 60 seconds has an average speed of 6.67 m/s and an average velocity of 0 m/s, because the runner finishes where they started. A delivery van that drives 30 miles east and 30 miles west in two hours has an average speed of 30 mph and an average velocity of 0 mph.

Physics problems usually say which they want: “velocity” means displacement and direction; “speed” means distance. In everyday language the two are interchangeable, and no harm follows, because everyday questions are about how fast, not about displacement. But a navigation or physics answer that reports a round trip’s velocity as its speed has answered a different question from the one asked.

Unit conversions: the table, and the traps

Convert with exact factors, and convert before calculating. The exact factors: 1 mile = 1.609344 km; 1 km = 0.621371 miles; 1 metre per second = 3.6 km/h = 2.23694 mph; 1 knot = 1 nautical mile per hour = 1.852 km/h = 1.15078 mph; 1 foot per second = 0.3048 m/s = 1.09728 km/h = 0.681818 mph. The speed of light, 299,792,458 m/s, and the speed of sound, about 343 m/s in air at 20°C, are the scientific reference points; a passenger jet cruises at about 250 m/s (900 km/h, 560 mph).

Two traps. First, converting a speed is not converting a distance: multiplying a speed in mph by 1.60934 converts it to km/h, but the time unit must also match — a speed in miles per minute needs the minutes converted too. Second, pace and speed are reciprocals: a pace of 5 minutes per kilometre is a speed of 12 km/h (60 ÷ 5), and a pace of 6 minutes per mile is 10 mph (60 ÷ 6). The runner’s pace guide linked at the end covers pace charts in full; here, remember only that faster means a smaller pace number and a larger speed number, and the confusion between them is the source of most training-plan errors.

Speed in science: from falling objects to escape velocity

In physics, speed appears in contexts where the distance-time formula is only the start. A falling object accelerates: near Earth’s surface, speed increases by about 9.8 m/s every second (ignoring air resistance), so after 3 seconds of fall it moves at about 29.4 m/s, having covered about 44 metres. Terminal velocity — the speed at which air resistance balances weight — is about 53 m/s (190 km/h) for a skydiver in a spread position. Escape velocity, the speed needed to leave Earth’s gravity without further thrust, is about 11.2 km/s. Orbital velocity in low Earth orbit is about 7.8 km/s.

Relative speed governs encounters: two cars approaching at 50 km/h each close at 100 km/h; a car overtaking at 60 km/h past one travelling at 50 km/h gains at 10 km/h, so passing a 5-metre car with a safe gap takes far longer than the speedometer suggests. Sound and light give the everyday examples: thunder heard 3 seconds after lightning means the strike was about 1 km away (sound at ~343 m/s), and the light arrives essentially instantly. These are all the same formula, applied to different distances and times.

Frequently asked questions

How do I calculate average speed?

Divide total distance by total time, including stops: average speed = distance ÷ time. A 240 km journey in 3 hours averages 80 km/h. Convert time to hours (or minutes) consistently before dividing.

What is the difference between speed and velocity?

Speed is distance over time, without direction. Velocity is displacement (straight-line distance from start to finish, with direction) over time. On a round trip, average speed is positive and average velocity is zero.

How do I convert km/h to mph?

Divide by 1.60934 (or multiply by 0.621371). 100 km/h = 62.1 mph. To convert mph to km/h, multiply by 1.60934: 60 mph = 96.6 km/h.

Why is my average speed lower than my cruising speed?

Because average speed includes all elapsed time — slow stretches, traffic, and stops. Time spent at low speed contributes disproportionately: equal distances at different speeds average by the harmonic mean, which sits below the simple mean.

What is a knot in speed?

One nautical mile per hour: 1.852 km/h, or 1.151 mph. Knots are used in aviation and maritime navigation because a nautical mile is one minute of latitude, which makes chart work simple.

How fast is 10 metres per second in km/h?

36 km/h. Multiply metres per second by 3.6 to get km/h. 10 m/s is also 22.4 mph and 19.4 knots.