What is grade-adjusted pace?

It is the pace that costs the same metabolic effort on a hill as your reference pace does on the flat. Uphill it is slower, and on moderate downhills it is faster, so you run by effort rather than chasing a fixed flat-ground number.

What is Minetti's equation?

Minetti and colleagues measured the energy cost of running, in joules per kilogram per metre, as a fifth-order polynomial in gradient. The tool uses that curve to scale your flat pace by the ratio of hill cost to flat cost.

Why does running get cheaper on a slight downhill?

Gravity assists forward motion on gentle descents, so the metabolic cost dips below flat ground. Minetti's data shows the minimum cost is around minus ten to minus fifteen percent grade, after which braking forces raise the cost again.

Does this model muscle damage on long descents?

No. It only adjusts for metabolic energy cost. Long or steep downhills cause eccentric muscle damage and require their own pacing and conditioning, which this tool does not account for.

What grade range is valid?

Minetti's measurements covered roughly minus forty-five to plus forty-five percent, so the tool restricts input to that range. Extrapolating far beyond it would be unreliable.

Running Hill Grade Pace Adjuster

Run hills by effort, not by the watch

On hilly courses a fixed pace target is meaningless: holding 5:00/km up a 10% climb is a completely different effort than holding it on the flat. This tool converts your flat-ground pace into the equivalent pace for any gradient, so you keep a steady metabolic effort over rolling terrain — slowing the right amount uphill and, on moderate descents, speeding up to take advantage of gravity.

How it works

The energy cost of running depends strongly on gradient. Minetti et al. (2002) fitted the cost, in joules per kilogram per metre, as a polynomial in the fractional grade i:

C(i) = 155.4*i^5 - 30.4*i^4 - 43.3*i^3 + 46.3*i^2 + 19.5*i + 3.6

On the flat (i = 0) the cost is 3.6 J/kg/m. At a fixed metabolic effort, sustainable speed is inversely proportional to cost, so the equivalent pace on a grade is your flat pace scaled by the cost ratio:

pace_hill = pace_flat * C(i) / C(0)

A positive grade raises the cost and slows you; a moderate negative grade lowers it and speeds you up.

Example and notes

For a flat target of 5:00/km on an 8% climb, the cost ratio pushes your equivalent pace well past 6:00/km — that slower number represents the same effort, not a loss of fitness. Conversely, on a gentle downhill the tool returns a faster pace, reflecting the energy gravity gives back. The cheapest running of all sits around a 10 to 15% downhill, where the curve dips below flat before steeper descents drive the cost up again through braking. Remember this captures only metabolic cost: long descents still batter your quadriceps through eccentric loading, so pace those by feel and build the specific durability through training.

Running Hill Grade Pace Adjuster

Email me this result

Run hills by effort, not by the watch

How it works

Example and notes