What is grade-adjusted pace (GAP)?
How hills change the effort of running, and how to pace a hilly route.
Short answer: grade-adjusted pace (GAP) is your pace converted to the pace that would take the same effort on flat ground. A 6:00/km climb up a steep hill may be as hard as 4:30/km on the flat. Running watches and apps show GAP so you can compare hilly runs with flat ones; turned around, it tells you how much slower to run each hill to keep your effort even.
Plan a hilly route in the GAP Planner
The science: the energy cost of running on slopes
The best-known model comes from Minetti et al. (2002). They had ten runners on a treadmill at gradients from −45% to +45% and fitted a formula for the energy cost of running at gradient i (rise over run, so 0.05 is a 5% slope):
C(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6 (J per kg per m)On the flat, C = 3.6 J/kg/m. Dividing the cost at each gradient by the flat cost gives how much harder each metre is:
| Gradient | −10% | −5% | 0% | +5% | +10% | +15% | +20% |
|---|---|---|---|---|---|---|---|
| Relative cost | 0.60 | 0.76 | 1.00 | 1.30 | 1.66 | 2.06 | 2.50 |
Running costs least on a gentle downhill (about −10% to −20%) and costs more again on steeper descents, where you're braking. Uphill, the cost rises steeply.
What it means for your pace
For the same effort, a stretch that costs 1.30 times the energy takes about 1.30 times as long. Here's the equal-effort pace on different gradients for a runner whose flat pace is 5:00/km (8:00/mi), using the Minetti model:
| Gradient | Relative cost | Equal-effort pace | Per mile |
|---|---|---|---|
| -10% | 0.60 | 2:59/km | 4:47/mi |
| -5% | 0.76 | 3:49/km | 6:06/mi |
| 0% | 1.00 | 5:00/km | 8:00/mi |
| +2% | 1.11 | 5:34/km | 8:54/mi |
| +5% | 1.30 | 6:30/km | 10:25/mi |
| +8% | 1.51 | 7:33/km | 12:04/mi |
| +10% | 1.66 | 8:17/km | 13:16/mi |
| +15% | 2.06 | 10:18/km | 16:29/mi |
Lab formulas describe the average runner on a treadmill. Real descents depend a lot on technique, terrain and how much you hold back to save your legs, so your own numbers can differ, especially downhill.
How the GAP Planner uses it
The GAP Planner uses this the other way round: from your flat pace, it predicts your pace and time for every split of a route you draw or import. It uses the Minetti model by default, or a personal pace-by-gradient model built from your own Intervals.icu runs, and can add a fatigue curve for long events. See the GAP Planner guide for how it works.
References
- Minetti AE, Moia C, Roi GS, Susta D, Ferretti G. Energy cost of walking and running at extreme uphill and downhill slopes. J Appl Physiol. 2002. PubMed
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- Marathon pace chart
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- 10K pace chart
- 5K pace chart
- All tool guides
RunTK's tools are for planning and education. They aren't medical advice, and the right numbers for you depend on your health, experience and goals.
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