# How to convert difference in elevation into distance?

When you're running up a slope, you're running slower. Down the hill you may run faster, if your knees allow it. But how much?

In German, there is the notion of "Leistungskilometer", which is translated to "effective kilometers", "technical kilometers", "power kilometers" or "energy expenditure kilometers", depending on the source. The definition is that 100m difference in elevation are equivalent to 1 flat kilometer, at least for calculating hiking times.

I find that for running this is not true. Using a factor of 10 for the difference in elevation gives me virtual flat paces that are way beyond my abilities. Say you're running 6 km up a 500m hill in 45 minutes. This is a pace of 7:30; with a factor 10 the flat equivalent would 6 + 10x0.5 = 11 kilometers, giving a pace of 4:05.

I think a pace of 5:18 (which is using a factor of 5) would be more realistic.

Are there common conventions how to account for slopes when running?

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I don't know of any common conventions, but for the purposes of the original equation the pace was considered a constant. Using some Calculus skills would allow you to refine it a bit based on the pace you are running. However, to plot the results you have to have an accurate measure of pace. You'll also have to take different measures based on your speed. – Berin Loritsch Oct 4 '11 at 12:19

The best equivalent I know of is Naismith's rule. "Allow 1 hour for every 3 miles (5 km) forward, plus 1 hour for every 2000 feet (600 metres) of ascent."

Secondly, when it comes to run it will come down to how good you personally are at running up hills. You may need to calculate the factor yourself. Remember that Garmin devices display sea-level distance, not slope distance.

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Actually, some of the newer Garmins have a "correct for elevation" feature. – Ryan Miller Oct 6 '11 at 19:16
I haven't seen it on the Garmin but I have seen it on Garmin Connect, their website. That feature uses Digital Elevation Model (DEM) data, generally from a mission called the Shuttle Radar Topography Mission, to provide elevation data at fixed grid points. – Sarge Oct 7 '11 at 5:15
The issue is that using elevation to calculate slope distance is idiosyncratic because it depends on the exact choice of points. If you do a run one day and then do the same run the next day but the points that are sampled are 5 metres different at sea level then the elevation you get for each point will be different and the total distance will be different. During a run, the Garmin's I've tested will use sea level distance. Forgive me, here's a link to the article on my own site for Garmin Distance Calculation – Sarge Oct 7 '11 at 5:18
You can use this site to do Naismith's Rule calculations. – Eyal Jul 1 '12 at 14:07

The following calculator leverages more recent studies on determining the relationship between incline gradient, velocity, and calories in addition to in the field experiment data: Calcuator.

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