How it works
GAP = pace × C(0) / C(grade), C from Minetti’s gradient-cost curve
Minetti’s lab measurements of running economy across steep slopes produced a fifth-order cost curve, C(i) = 155.4·i⁵ − 30.4·i⁴ − 43.3·i³ + 46.3·i² + 19.5·i + 3.6, in joules per kilogram per meter, with the grade i written as a decimal (0.05 for a 5% incline). Level running costs 3.6 J/kg·m. Speed at a fixed effort scales inversely with that cost, so multiplying your pace by C(0) ÷ C(grade) yields the flat-equivalent number. The curve also captures a quirk runners feel but watches ignore: mild descents genuinely cost less, yet very steep ones get expensive again as braking forces take over.
Sources
- Minetti gradient-cost model Minetti, A. E., Moia, C., Roi, G. S., Susta, D., & Ferretti, G. (2002). “Energy cost of walking and running at extreme uphill and downhill slopes.” Journal of Applied Physiology 93(3), 1039–1046.
- GAP concept Grade-adjusted pace expresses hill running as the equivalent flat pace at equal metabolic effort, allowing fair comparison of efforts on different terrain.
- Velocity and energy cost At a fixed metabolic power, running velocity is inversely proportional to the energy cost per metre — the basis for scaling pace by C(0)/C(grade).
FAQ
When should I use the grade adjusted pace calculator?
After hilly runs, when raw splits undersell a climb or flatter a descent, and before hilly races, when a goal flat pace needs converting into realistic uphill splits. It is also the fair way to compare workouts run on very different routes.
What inputs matter most?
Grade accuracy drives everything. Work it out as rise over run times 100 — climbing 30 meters across 600 meters of trail is a 5% grade — and use the segment average, not the steepest pitch. Enter negative values for descents; the pace fields take minutes and seconds per mile or per kilometer.
How should I read the result?
As the flat pace that would demand the same energy. A slow-looking 10% climb often converts to a strikingly quick flat equivalent, because that gradient roughly doubles the energy cost of every meter. Use it to judge effort honestly, not to predict a downhill race split.
Does this work in miles and kilometers?
Yes — set the pace unit to per-mile or per-kilometer and the adjusted result comes back in the same unit. The grade percentage is dimensionless, so nothing else changes between the two systems.
Why might my real-world result differ?
Minetti’s curve describes average physiology on a controlled surface. Trail footing, mud, wind, altitude, descending skill, and your individual economy on slopes all shift true cost, and GPS elevation noise can distort the grade you feed in. Different apps also smooth data differently, so this figure and Strava’s GAP may disagree slightly.
Can beginners use it?
Yes — it actually helps most when hills still feel demoralizing, because it reveals the fitness hiding inside a slow uphill split. Just resist chasing the adjusted number on the next climb; run by effort and let GAP do the accounting afterward.
Grade-adjusted pace applies a population-average energy model to the single average grade you supply; individual economy, footing, and weather sit outside the math. Read the output as an effort comparison for training review, not a performance guarantee or medical guidance.