How it works
GAP = pace × C(0) / C(grade), C from Minetti’s gradient-cost curve
Minetti and colleagues measured how much metabolic energy running costs at different slopes and fitted a fifth-order curve: C(i) = 155.4·i⁵ − 30.4·i⁴ − 43.3·i³ + 46.3·i² + 19.5·i + 3.6 joules per kilogram per metre, where i is the gradient as a fraction (0.05 = 5% up). On the flat the cost is 3.6. Because at a given effort your speed is inversely proportional to that cost, the flat-equivalent pace is your actual pace multiplied by C(0) ÷ C(grade). Uphill costs more, so a hard climb at 6:00/km on a 10% grade is worth about 3:37/km on the flat; a gentle downhill costs less, so the same pace there is worth a slower flat pace. Note that very steep downhills start to cost more again as braking dominates — the curve captures that too.
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
What is grade-adjusted pace?
It is the flat-ground pace that would require the same effort as your actual pace on a hill. Because climbing is harder and descending is easier, GAP lets you compare a hilly run fairly against a flat one and judge your true effort.
How is GAP calculated?
From the energy cost of running at a slope. This calculator uses Minetti’s measured cost-of-gradient curve: your flat-equivalent pace is your actual pace scaled by the ratio of flat cost to the cost at your grade. Uphill scales you faster, gentle downhill slower.
Why does my uphill GAP look so fast?
Because running uphill is genuinely costly — a 10% grade roughly doubles the per-metre energy demand. Your slow climbing pace therefore represents a much faster flat effort. The steeper the grade, the bigger the adjustment.
Does downhill always make GAP slower?
For gentle to moderate descents, yes — gravity helps, so the effort equals a slower flat pace. But on very steep downhills the cost rises again because braking and eccentric muscle work become expensive, and the model reflects that turnaround.
Is GAP the same as Strava’s GAP?
It is the same idea and built on the same kind of physiological cost model. Exact numbers can differ slightly between implementations because of smoothing and the specific cost curve used, but the concept and the typical adjustments line up closely.
What grade should I enter?
The average gradient of the segment as a percentage — rise over run × 100. A 30-metre climb over 600 metres is 5%. Use positive numbers for uphill and negative for downhill; the calculator handles both.
GAP is an estimate from a population energy-cost model and the average grade you enter; real cost varies with pace, surface, fatigue and running form. Use it to compare efforts, not as an exact measurement. General information for training, not medical advice.