Average vs Instantaneous Speed Calculator
Combine two legs of a trip to see why the overall average speed is not the average of the two leg speeds.
How it works
average speed = total distance ÷ total time · leg speed = distance ÷ time · instantaneous speed = limit of distance ÷ time over a vanishing interval
Average speed is always total distance divided by total time — never the plain average of the individual leg speeds, because the slower leg usually takes more time and therefore deserves more weight. Instantaneous speed is what a speedometer reads: the value the leg speed approaches as the measured interval shrinks toward a single instant. A trip can have any number of instantaneous speeds but only one average.
Worked example
Walk 100 m in 20 s (5 m/s), then run 100 m in 10 s (10 m/s). Total distance 200 m over 30 s gives an average of 6.67 m/s. Averaging 5 and 10 would suggest 7.5 m/s — too high, because you spent twice as long at the slower 5 m/s.
Sources: Speed — Wikipedia
Frequently asked questions
Why isn’t average speed just the average of the two speeds?
Because each speed acts over a different amount of time. Averaging the speeds treats both legs as equally long in time; the correct method weights each by its own duration, which total distance ÷ total time does automatically.
What is instantaneous speed?
It is the speed at a single moment — the limit of distance ÷ time as the time interval shrinks to zero. Your car’s speedometer shows an instantaneous speed, while a trip meter gives you the average.
When do average and instantaneous speed agree?
Only when the speed is constant. If you never change pace, every instant reads the same value and it equals the average for the whole trip.
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This calculator is for educational purposes. Double-check important results before acting on them.