Grade-adjusted running pace.

Energy cost by grade

Cost ratio is Cr(grade) divided by Cr(level). Above 1 means the same speed costs more energy than on the flat.

Worked example

You ran 5:30 per km up a steady +5% hill. Cr(0.05) = 4.69 J/kg/m against 3.60 on the level, a ratio of 1.301. Equal effort on the flat is 5:30 ÷ 1.301 = 4:14 per km (6:48 per mile). Going the other way, a 5:00 per km flat effort on that same +5% slope means holding 6:30 per km.

How it works

Minetti and colleagues measured the energy cost of running (Cr, in joules per kilogram per metre) on 10 runners on a treadmill inclined from -45% to +45%, and fitted a fifth-order polynomial (R² = 0.999), where i is the gradient as a fraction:

Cr(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6

Metabolic power is cost times speed, so holding power constant gives pace on slope = flat pace × Cr(i) / Cr(0). That last step is this tool's own simple rule, not a result in the paper. The paper reports Cr of 3.40 ± 0.24 on the level, 18.93 at +45%, a minimum of 1.73 at -20%, and 3.92 at -45%; the polynomial reproduces these within about 6%.

Limits: treadmill, steady state and 10 runners. It ignores terrain, technical footing, heat, fatigue, wind and walking breaks, and the real-world cost of steep descents depends on technique. No altitude penalty is applied because no primary source for a specific correction was verified; the tool omits it rather than guess. Several running apps use their own, different, grade models, so figures will not match theirs exactly.

Source (as of 2026-09-30): Minetti AE, Moia C, Roi GS, Susta D, Ferretti G, "Energy cost of walking and running at extreme uphill and downhill slopes," Journal of Applied Physiology 93(3):1039-1046, 2002, doi:10.1152/japplphysiol.01177.2001 (PubMed abstract).

FAQ

What is grade-adjusted pace?

The flat pace that would cost the same energy per second as your pace on a slope, so hill runs and flat runs can be compared.

Why is the steepest downhill not the fastest?

Cost is lowest near -20% and rises again on steeper descents because of braking. At -45% it is 3.92 J/kg/m, close to the level cost.

How do I get the grade?

Grade % = elevation change divided by horizontal distance × 100. A 50 m climb over 1 km is 5%.

Need the pace for a whole race? Use the running pace calculator or the race time predictor.