Grade-Adjusted Pace Calculator
Running uphill takes more energy than flat running at the same pace. Grade-adjusted pace (GAP) converts your actual pace on a slope to the flat-ground pace that requires the same metabolic effort, using the Minetti (2002) polynomial model.
Calculate
Choose a mode, enter a pace and a grade.
You ran at a certain pace on a slope. What flat pace required the same effort?
Or calculate grade from segment below.
Calculate grade from segment distance and elevation
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What is grade-adjusted pace? When you run uphill, each metre of horizontal distance costs more energy than on flat ground. GAP converts your actual running pace on a slope to the flat-ground pace that would require the same metabolic effort. A 6:30/km uphill at 8% grade might be equivalent to a 5:15/km flat effort. Apps like Strava use this to make hill training comparable to flat training.
Why does GAP sometimes get slower on steep downhills? At grades steeper than about -10% to -15%, the braking cost of running downhill increases, and the metabolic cost rises again. The Minetti polynomial captures this non-monotonic behaviour. Very gentle downhills (around -5%) are where the cost is lowest and GAP is most generous.
For heat and altitude pace adjustments, use the Pace Adjustment Calculator.
How this calculator works
Minetti et al. (2002) metabolic cost polynomial: C_r(i) = 155.4i^5 - 30.4i^4 - 43.3i^3 + 46.3i^2 + 19.5i + 3.6 (J/kg/m), where i is the gradient as a decimal fraction. The flat metabolic cost C_r(0) = 3.6 J/kg/m. GAP mode: flat-equivalent speed = actual_speed x C_r(i) / C_r(0), so pace inverts. Inverse mode: expected on-grade speed = flat_speed x C_r(0) / C_r(i). Grade is clamped to approximately +/-45%, the validated range of the polynomial.
Assumptions
- • Minetti polynomial applies to trained runners on hard surfaces
- • Individual braking efficiency varies, especially on steep descents
- • No wind, altitude, or heat effects are included
Limitations
- • Steep downhill braking cost is modelled but varies widely by technique
- • Surface type (trail, road) affects cost but is not included
Who this is for
- • Runners and triathletes comparing effort across hilly and flat courses
- • Athletes setting effort-based targets for hill workouts
- • Triathletes analysing Garmin, Strava or Coros GAP data
Who this is not for
- • Grades outside approximately +/-45% (polynomial extrapolates unreliably)
- • Accurate energy accounting for non-running activities