Tuesday, September 14, 2010

Miles per Hour and Minutes per Mile

Something that always fascinated me when I was running on the treadmill more was the relationship between Miles per hour and Minutes per mile. My watch would read out in MPM, but the treadmill should show MPH (unless I figured out how to change the settings.)

SO, as all we stats-obsessed runners know, sometimes you have to convert from minutes per mile to miles per hour, or vice versa. Mathematically, it's not too complex, you just convert to minutes and divide 60 by it:

MPH to MPM
9 miles per hour: 60/9 = 6.66 minutes per mile, or 6:40
7.5 miles per hour: 60/7.5 = 8 minutes per mile

or -

MPM to MPH
9:30 minutes per mile, or 9.5: 60/9.5 = 6.31 miles per hour
7 minutes per mile: 60/7 = 8.57 miles per hour

Of course, for ease of calculation, you can use an online pace calculator like the ones at coolrunning.com, arkansasrunner.com, or convertme.com.

One thing I had always wondered was at what point speed and pace numbers would be the same. You know - since a ten minute mile is six miles per hour, and a six minute mile is ten miles per hour, surely speed and pace cross at some nice round number, right?

Yeah, not so much. My math isn't up to figuring out a way to calculate it, so I used a spreadsheet program to draw a graph for me:



As you can see, the lines cross at about 7.75. So, 7.75 miles per hour equals a 7:45 mile. (It's closer to 7.746, to take it one more decimal point out.)








So if you were curious, there you go.

3 comments:

SnowLeopard said...

Is there a "Like" button for us statistic-obsessed runners for this post? 'Cause I'd click it~ ;)

Anonymous said...

SnowLeopard,

If there were one, I would click on your comment first and beforehand! :D

Anonymous said...

It's the square root of 60. X miles/60 minutes = 1 mile/ X minutes. Rearrange and you get X^2 = 60 or X = square root of 60, which is 7.74596...