Grade Adjusted Pace (GAP) Calculator
Convert your running pace on an uphill or downhill grade into the equivalent flat-ground effort (grade adjusted pace) using Minetti's energy cost of running on slopes.
How it works
Energy cost C(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6 J/kg/m (i = grade as a decimal) · GAP = actual pace × 3.6 ÷ C(i)
Minetti et al. (2002) measured the metabolic energy cost of running on treadmill slopes from −45% to +45% and fitted a fifth-order polynomial: 3.6 J/kg/m on the flat, rising steeply uphill and falling to a minimum near −20% before braking makes steeper descents costlier again. Dividing the flat cost by the cost on the grade turns your actual pace into the pace that would take the same energy on level ground — the idea behind grade adjusted pace in training apps. Real-world GAP models (such as Strava's, based on heart-rate data) penalise moderate climbs a little less than the pure metabolic curve.
Worked example
Running 6:00 /km up a 5% grade: C = 155.4 × 0.05⁵ − 30.4 × 0.05⁴ − 43.3 × 0.05³ + 46.3 × 0.05² + 19.5 × 0.05 + 3.6 = 4.69 J/kg/m, 30.1% more than flat. GAP = 360 s × 3.6 ÷ 4.69 = 276.6 s = 4:37 /km.
Sources: Minetti AE et al. (2002) Energy cost of walking and running at extreme uphill and downhill slopes. J Appl Physiol 93:1039–1046 · Strava Engineering — An improved GAP model
Frequently asked questions
What is grade adjusted pace?
GAP is an estimate of the pace you would run on flat ground for the same effort. Uphill sections show a faster GAP than your actual pace and gentle downhills a slower one, which makes hilly runs comparable with flat runs.
Why is a steep downhill not always easier?
Minetti's data show the energy cost is lowest around −10% to −20%. On steeper descents you spend energy braking, so the cost rises again, and your flat-equivalent pace slows.
Why does my watch app show a different GAP?
Apps use their own models — Strava's current GAP is fitted to heart-rate data from millions of runs and is gentler on moderate climbs than the laboratory energy-cost curve. Expect differences of a few seconds per kilometre.
Should I use average grade for a whole run?
Use it for a single climb or descent of steady grade. For a rolling route, average grade hides the fact that uphills cost more than downhills save, so calculate each section separately.
Related calculators
This calculator gives an estimate for general fitness and education only. It is not a diagnosis — field tests and prediction equations can differ from laboratory measurements, so talk to a doctor or qualified exercise professional before acting on the result, especially before maximal testing.