Free calculator
Grade-adjusted pace calculator
Turn a pace on a hill into its flat equivalent, or find the pace to hold on a climb for a given effort. Same model as the grade-adjusted pace OpenAthlete computes on your runs.
min:ss per km
Negative for a descent. Capped at ±30%, as in the app.
Flat-equivalent pace (GAP)
3:37/km
Each metre costs 1.66 × a flat metre.
Same effort as 3:37/km on the flat
| Gradient | Cost vs flat | Pace |
|---|---|---|
| -20% | ×0.50 | 1:49* |
| -15% | ×0.51 | 1:51* |
| -10% | ×0.60 | 2:10 |
| -5% | ×0.76 | 2:46 |
| 0% | ×1.00 | 3:37 |
| +5% | ×1.30 | 4:43 |
| +10% | ×1.66 | 6:00 |
| +15% | ×2.06 | 7:27 |
| +20% | ×2.50 | 9:03 |
| +25% | ×2.98 | 10:47 |
| +30% | ×3.49 | 12:39 |
* On steep descents the model gives the pace your heart could afford, not the one your quads, the ground and your brakes will allow.
How it is calculated
Grade-adjusted pace answers one question: what would this effort be worth on flat ground? It uses the energy cost of running on a slope, measured by Minetti and colleagues on a treadmill between −45% and +45%: C(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6, in joules per kilogram per metre, where i is the gradient as a fraction (0.10 for 10%). On the flat, C = 3.6. Flat-equivalent pace = pace on the slope × 3.6 / C(i). The other way round, the pace to hold on a slope = flat pace × C(i) / 3.6.
flat pace = pace × 3.6 / C(i)
pace on slope = flat pace × C(i) / 3.6
Example: 6:00/km on a 10% climb. C(0.10) = 5.97, 1.66 times the flat cost, so 6:00/km uphill is worth 3:37/km on the flat. The other way: to keep a 5:00/km flat effort on that climb, hold 8:17/km.
OpenAthlete applies the same curve to every run and trail run you sync: the gradient is read from altitude over 10 m windows and capped at ±30%, because steeper readings are usually GPS or barometer noise.
Source: 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 93, 2002 (doi:10.1152/japplphysiol.01177.2001).
Send these targets to your watch
Write your sessions in OpenAthlete with targets as a percentage of your VMA or max heart rate. They reach your Garmin, Suunto or COROS with the paces filled in.
Questions
The pace you would have run on flat ground for the same energy. 7:00/km on a 12% climb is worth about 3:52/km on the flat, a harder effort than 4:30/km on the road. GAP puts both on the same scale, so you can compare a hilly run with a flat one, or check you held the right effort on a climb.
Strava uses its own model, which it says it built from its athletes' heart rate data rather than from lab measurements of energy cost. It gives less credit on descents than Minetti's curve. Neither is wrong; they answer slightly different questions. OpenAthlete uses Minetti, written out in its open-source code, and so does this page.
On paper, yes. The curve bottoms out around −20%, where a metre costs half as much as on the flat, then rises again on steeper ground. In practice, past about −10%, braking, footing and the load on your quads limit speed before energy does. That is why a 4:30/km descent at −10% shows a flat equivalent of 7:32/km: easy for the heart, not always for the legs.
The curve is for running. Minetti's team measured walking too, and on steep climbs walking costs less than running at the same speed, which is why everyone starts hiking past a certain gradient. On a power-hiked climb, read the flat-equivalent pace as a rough guide.
Yes: type the incline as the gradient. 5:00/km at 5% is worth about 3:51/km on the flat. Minetti's measurements were made on a treadmill, so there is no air resistance in them; many runners set 1% to make up for its absence on a flat treadmill run (Jones and Doust, 1996).
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