What grade adjusted pace is
Running uphill costs more energy than running on the flat, and gentle downhills cost less. Grade adjusted pace (GAP) converts your pace on a slope into the flat pace that would take the same effort, so hilly runs can be compared with flat ones.
The Minetti model
Physiologist Alberto Minetti and colleagues measured the energy cost of running on a treadmill at grades from −45% to +45% (2002). Their fitted curve, in joules per kilogram per meter, is:
C(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6
where i is the grade as a fraction (6% = 0.06). On the flat, C = 3.6 J/kg/m. The flat-equivalent pace is:
GAP = actual pace × 3.6 ÷ C(i)
Reference values
| Grade | Energy cost vs flat | 10:00/mi on the slope equals |
|---|---|---|
| +10% | 166% | 6:02 flat |
| +5% | 130% | 7:41 flat |
| 0% | 100% | 10:00 |
| −5% | 76% | 13:07 flat |
| −10% | 60% | 16:44 flat |
| −20% | 50% | lowest cost |
Example
An 11:00 mile on a 6% climb, which gains about 317 ft per mile, costs 137% of the flat energy. It equals about 8:02 per mile on the flat.
Limits of the model
- Minetti’s curve describes metabolic cost at steady state. Apps such as Strava use models fitted to heart-rate data from many runners, which give smaller adjustments on moderate climbs. Treat this calculator’s result as an upper estimate of the effort.
- Steep downhills are cheap in oxygen but hard on muscles: eccentric loading of the quadriceps causes soreness that the energy figure does not show.
- On very steep terrain, power hiking is often more efficient than running.
Uses
- Pacing hilly races by effort rather than by pace.
- Comparing a trail run with a road run.
- Setting treadmill incline workouts. Many runners add a 1% incline to mimic outdoor air resistance.