Hill pace calculator: grade adjusted running pace

Updated: 2026-10-31

A pace of 6:00 per kilometre uphill and 6:00 on the flat are two different efforts, and the watch shows them the same. This calculator converts pace on a slope into the pace that would cost the same on the flat, and the other way round: from your flat pace it tells you how slowly you should run uphill so you do not burn out at the start of the course. The arithmetic rests on one of the most cited measurements in running physiology.

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Where the numbers come from

Minetti and colleagues measured in 2002 the energy cost of running in ten mountain runners on a treadmill inclined from minus 45 to plus 45 percent, from a steep descent to a steep climb. On the flat, running cost about 3.4 joules per kilogram of body mass and metre of distance, regardless of speed. Uphill the cost rose almost linearly: at 10 percent it was two thirds higher than on the flat, at 20 percent more than double. Downhill the cost first fell, reached a minimum around minus 20 percent, and on steeper descents rose again, because the muscles have to brake every step.

The authors described the whole curve with a single polynomial of the gradient, and that is what works in the calculator. The equivalent pace follows from a simple assumption: the same metabolic power, cost per metre times speed, means the same effort. If a metre uphill costs 1.3 times more, at the same effort you run 1.3 times slower.

How to read the result

At 6:00 per kilometre on a 5 percent climb the calculator shows about 4:37 on the flat: that is what the kilometre was "worth". At 10 percent the same pace corresponds to roughly 3:37 on the flat, a 10K race pace for many amateurs. The other way: if your easy pace on the flat is 5:30, on an 8 percent climb easy means about 8:15. Most runners charge into such a hill much faster and are surprised by their heart rate.

Limitations

The measurement was on a treadmill, in trained mountain runners, on an even surface. On trails there are rocks, mud and descending technique, which the polynomial knows nothing about. Downhill the energy cost is low, but muscle damage from braking is large, so "cheap" descending in the first half of a mountain race takes its revenge in the second. The converter speaks about energy, not about what the thighs will stand. Above 30 percent most people walk anyway, which Minetti measured separately.

Use in training

Write hill sessions in the plan by effort, not pace: instead of "6 times 400 metres in 1:45", "6 times 90 seconds uphill at interval effort" is better, and the calculator tells you what pace to expect at a given grade. When analysing a hilly run, look at heart rate and time in zones, because pace on a rolling course says nothing without the profile.

Frequently asked questions

Is this the same as "grade adjusted pace" in training services?

Same idea, different formulas. Services use their own, usually unpublished models fitted to user data. The calculator uses one published measurement and says where it comes from.

How do I calculate grade from elevation gain?

Elevation gain divided by horizontal distance times a hundred. A hundred metres up over two kilometres is 5 percent.

Why does a minus 30 percent descent cost more than minus 15?

Because on a steep descent muscle work goes into braking rather than propulsion. The minimum cost lies around minus 20 percent, one of the more important findings of the paper.

Does it work for walking?

No. Walking has a different cost curve, also measured by Minetti, but the calculator covers running only.

Sources

• Minetti A. E., Moia C., Roi G. S., Susta D., Ferretti G., Energy cost of walking and running at extreme uphill and downhill slopes, Journal of Applied Physiology, 2002. Running cost from minus 45 to plus 45 percent and the polynomial used in the calculator.