I know that I can jog a mile in 8 minutes--perhaps 10 if I haven't run in a while, but when I try to work out on the elliptical, it says that I've only finished a mile after ~20-25 minutes. Why is this?
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The distance reported on an elliptical doesn't mean much. I suspect it is adding up the motion of your feet but it does not correlate well with running. A better way to compare an elliptical workout with a running workout is to wear a heart rate monitor. Whether you run 30 minutes at 70% max heart rate or use an elliptical for 30 minutes at 70% max heart rate, the cardiovascular benefit is the same.
If you keep a running log and want to convert elliptical time to running miles then again assuming that your heart rate is the same, divide the elliptical time by your average pace for that heart rate. Some runners are more conservative and only count 75% of the elliptical miles calculated this way as running miles. If you don't have a heart rate monitor then you can still divide the time by your average running pace to get a rough equivalent distance (this assumes that you do the elliptical at the same perceived effort as you run).
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