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I don't understand what you mean by computing it over distance. Could you give an example of what that equation would look like? –  jimirings Jun 15 '13 at 21:07
@jimirings One useful definition: calculate the average pace and then calculate its reciprocal –  anatolyg Jun 16 '13 at 21:33
To me, this would make sense in case of speeders in traffic, because the road dangers appear relative to distance and not to time. So if some bloke flies through an all-through-dangerous town, you wouldn't say anymore that he was causing danger for the very little time he was coming past the town, but that he actually caused danger all along the road. So speeders would get a more appropriate judgement. –  Sam Sep 3 '14 at 21:15
Except you do regain it on the downhill, because you cover a great distance in a short amount of time. –  whatsisname Sep 7 '14 at 19:22

8 Answers 8


On the flat I maintain a constant 20 miles/hour.
On the descent I maintain a constant 30 miles/hour.

My average speed for this would be:

By the proposed calculation I would have:


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+1 because mathematics is always right. –  Carey Gregory Jun 15 '13 at 22:59
Can you always assume that your speed difference is the same for uphill and downhill? You can say that the force is always the same (mgsin(theta)), but there's also wind resistance (and other factors, I'm willing to bet) to factor in. –  Scott Jun 15 '13 at 23:05






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+1 for identifying average power as the measure that the poster is looking for. –  amcnabb Jun 16 '13 at 13:49


Arithmetic Mean







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You cant't compare it - that's a good reason. –  Uooo Jun 19 '13 at 8:25


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+1 Well put! This is indeed the right answer –  Javier Jun 19 '13 at 18:55





  1. Difficult to track
  2. Mathematically incorrect


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Agreed, I just wanted to add that the points you have apply more to human tracking, and aren't much of a factor to modern electronics. –  Ehryk Jun 19 '13 at 8:25





The Mode is the most commonly occurring average speed.

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It would at least likely match the algorithm used within Expresso exercise bikes when stating the speed of the "pacer". –  Daniel R Hicks Jun 21 '13 at 1:03
Exactly. When we have a set of different data we can simplify by replacing them all with the average and still get the same result in some calculation that we care about. If someone travels at various speeds on a route we can simplify by replacing each speed with the average speed and we still get the same duration. –  bdsl Jan 19 at 17:40

Indeed your average speed is total distance over total time

Regarding sampling this is where you go wrong:
No they are not equally weighted. The denominator is time (not distance). You need to take even samples in time. You cannot sample on distance if you want to average the sample.

20 miles up the hill and 20 miles down the hill.
Up assume 10 mph and down assume 30 mph.

First total distance over total time
Total distance is 40 miles
Total time is 20 miles / 10 mph + 20 miles / 30 mph = 2 hour up + 2/3 hour down = 8/3 hour

Average speed = total distance over total time = 40 miles / 8/3 hours = 120 / 8 mph
= 15 mph

The average speed is not the 10 + 30 / 2 = 20 mph because spent more time at 10 mph. Spent 3 times as long at 10 mph compared to 30 mph.

If you sampled every mile then indeed you would get the wrong answer of 15 mph average.

But if you sampled every minute you would get the right answer.
Up the hill you would have 120 samples at 10 mph and down the hill you 40 samples at 30 mph.
(120 * 10) + (40 * 30) / 120 + 40 = 1200 + 1200 / 160 = 240 / 16 = 15.
If you want to average the sample then the sample needs to based on the denominator.

But it is easier to just use total time over total distance.

If you had a magic hill that was 10 miles up and 30 miles down then your average speed would be the average as you would spend the same amount of time going up as down.

You can use any number you want for up versus down the hill. 18 mph up and 20 mph down. The average speed will not be speed up + speed down / 2. Because you will spend more time at the lower speed.
Average speed is caluculation:
d is total distance
su is speed up and sd is speed down
total distance / total time
d / (d / 2*su + d / 2*sd)
d / ( sd*d/2*su*sd + su*d/2*sd*su )
d / ( (sd*d + su*d) / 2*sd*su ) d*2*sd*du / d(su + sd)
2*sd*su / (su + sd)
hill same distance up as down
average speed = 2*sd*su / (su + sd)
in statistics it is called the harmonic mean
try 10 and 30 and get 15
try 20 and 20 and get 20
try 18 and 20 and get 19.95

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