What is the Minetti gradient cost model?
A fifth-order polynomial fitted to measured oxygen cost across gradients from −45% to +45%. It is the basis for essentially every grade-adjusted pace calculation in use.
Minetti and colleagues measured the energy cost of running at gradients from −45% to +45% and fitted a polynomial to the result. The curve gives the cost in joules per kilogram per metre at any gradient in that range, with a level-ground reference cost of about 3.6 J/kg/m.
Two features of the curve matter for runners. It has a minimum at a slightly negative gradient — running very gently downhill is cheaper than running on the flat — and above that minimum the cost rises steeply with gradient while below it, on steep descents, the cost rises again as braking becomes expensive.
That shape produces the asymmetry that dominates hill pacing: a 5% climb costs far more than a 5% descent saves. Over a rolling course with equal climbing and descending, the net effect is a slower time than the flat equivalent, which is why "it all evens out" is one of the more expensive myths in marathon pacing.
The limits are worth knowing. The polynomial is valid only within its measured domain of ±45%, it was fitted on a treadmill rather than on real terrain, and it models metabolic cost alone — the eccentric muscle damage that makes long descents so punishing late in a race is entirely outside it.
Key numbers
| Level-ground cost | 3.6 J/kg/m | the reference value |
|---|---|---|
| Valid domain | −45% to +45% | gradient |
| Cost minimum | slightly downhill | not at 0% |
Work it out for yourself
Marathon course profiles — See the model applied to real elevation profiles, kilometre by kilometre.
Frequently asked questions
Is downhill running easier than flat running?
Metabolically, gentle downhill running is cheaper than flat — the cost curve has its minimum at a slightly negative gradient. Steep descents get expensive again because braking costs energy, and they cause eccentric muscle damage that the metabolic model does not capture at all.
Why does the model stop at 45%?
Because that is the range over which the original measurements were made. Beyond roughly ±45%, running gives way to scrambling or controlled descent, which are different activities with different costs, so extrapolating the polynomial there would be inventing data.
Sources
- Minetti et al. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology.
- Vernillo et al. (2017). Biomechanics and physiology of uphill and downhill running. Sports Medicine.
Related explainers
Glossary: Minetti Gradient Cost, GAP (Grade-Adjusted Pace)