Speed and Average Speed
Speed is the rate at which an object covers distance, and average speed is the total distance traveled divided by the total time taken: v = d ÷ t. In brief: the SI unit of speed is meters per second (m/s), and 1 m/s = 3.6 km/h. Speed is a scalar. The average speed over a whole trip is not the mean of the speeds in each part unless the times are equal.
Speed tells how fast something moves, but not in which direction. It is used for cars, runners, sound and light. This guide defines speed and average speed, shows the formula and its rearrangements, describes typical speeds, compares units in a table, works through examples including a trip with two parts and corrects common mistakes.
What is speed?
Speed measures how much distance is covered per unit of time. If an object moves at a constant speed, it covers equal distances in equal times. The formula is
v = d ÷ t, or d = v × t, or t = d ÷ v,
where v is speed, d is distance traveled and t is time. Common units are m/s, km/h and mi/h. To convert: multiply km/h by 1 ÷ 3.6 to get m/s (72 km/h = 20 m/s), and multiply m/s by 3.6 to get km/h.
Instantaneous speed is the speed at a particular moment, such as the reading of a car’s speedometer. It can change during a trip.
What is average speed?
Average speed = total distance ÷ total time. It is the constant speed that would cover the same distance in the same time. The total time includes any stops. It does not tell how the speed varied during the trip.
When a journey has parts at different speeds, find the total distance and total time first. Only if the two parts take equal times is the average speed equal to the arithmetic mean of the speeds. If the two parts cover equal distances, the average speed is the harmonic mean: 2v1v2 ÷ (v1 + v2).
Typical speeds
| Object | m/s | km/h |
|---|---|---|
| Walking person | 1.4 | 5 |
| Cyclist | 5 | 18 |
| Car on a highway | 30 | 108 |
| Passenger jet | 250 | 900 |
| Sound in air (20 °C) | 343 | 1,235 |
| Light in a vacuum | 3.00 × 108 | 1.08 × 109 |
Worked example: average speed of a trip
A cyclist rides 12 km in 30 minutes, stops for 10 minutes, and then rides 8 km in 20 minutes.
- Total distance: 12 km + 8 km = 20 km.
- Total time: 30 + 10 + 20 = 60 minutes = 1.0 h (the stop is included).
- Average speed: 20 km ÷ 1.0 h = 20 km/h = 20 ÷ 3.6 = 5.6 m/s.
- Speed in the first part: 12 km ÷ 0.50 h = 24 km/h. Second part: 8 km ÷ (20 ÷ 60) h = 8 ÷ 0.333 = 24 km/h.
The average speed (20 km/h) is lower than the speed while riding (24 km/h), because of the stop.
Equal distances: a car drives 60 km at 40 km/h and then 60 km at 60 km/h. The times are 60 ÷ 40 = 1.5 h and 60 ÷ 60 = 1.0 h, so the average speed is 120 km ÷ 2.5 h = 48 km/h, not 50 km/h (the mean of 40 and 60). The result agrees with the formula 2 × 40 × 60 ÷ (40 + 60) = 4,800 ÷ 100 = 48 km/h.
How was speed measured?
Galileo tried to measure the speed of light with lanterns on hills in the 1600s, but it was too fast. Ole Rømer estimated it from the moons of Jupiter in 1676. Speedometers for cars were introduced in the early 1900s, and radar and GPS now measure speed. Since 1983 the meter has been defined from the speed of light, which is exactly 299,792,458 m/s.
Where is speed used?
Speed limits on roads, the planning of journey times, the training of athletes (pace in minutes per kilometer is the inverse of speed), and calculations in navigation and in physics all use speed.
Which mistakes are common?
Mistake 1: Averaging the speeds
Average speed is total distance over total time, not the mean of the speeds, unless the times are equal.
Mistake 2: Leaving out the stops
Waiting time is part of the total time.
Mistake 3: Mixing units
Do not combine kilometers with seconds without conversion. Use km and h, or m and s.
Mistake 4: Confusing speed and velocity
Speed is a scalar. Velocity is a vector and has a direction.