What is grade-adjusted pace?

Grade-adjusted pace (GAP) is the pace on flat ground that would require exactly the same metabolic energy as running your actual pace on a slope. An 8% uphill at 6:00 min/km might convert to a GAP of 4:30 min/km, meaning your body is working as hard as if you were running 4:30 on flat — even though your GPS shows 6:00.

What formula does this calculator use?

It uses the Minetti et al. (2002) empirical metabolic cost polynomial published in the Journal of Experimental Biology. The energy cost of running at fractional grade i is C(i) = 155.4i^5 - 30.4i^4 - 43.3i^3 + 46.3i^2 + 19.5i + 3.6 joules per kilogram per metre. GAP is derived by multiplying actual pace by the ratio of flat cost to graded cost: GAP = pace x C(0) / C(i). Garmin, TrainingPeaks, and Strava all use variants of the same Minetti model.

Why does downhill running not give free speed?

Gentle downhills (around -5% to -10%) are slightly easier than flat and produce a GAP greater than actual pace. However very steep downhills (below roughly -15%) become metabolically expensive again because the eccentric braking load on your quads increases dramatically. The Minetti model captures this non-linear behaviour, which is why the GAP factor does not simply keep falling as grade becomes more negative.

Is GAP the same as effort pace?

GAP is a metabolic effort estimate — it normalises for the extra energy cost of climbing and the eccentric load of steep descending. It is not the same as heart-rate-adjusted effort, power-based effort, or perceived effort, which also depend on heat, fatigue, altitude, wind, and surface. Use GAP as a useful guide for comparing workouts, not a rigid physiological truth.

What grade range is the model accurate for?

Minetti measured subjects on a motorised treadmill at grades from -45% to +45%. Accuracy is highest between -20% and +30%. Extreme values (below -30% or above +40%) extrapolate beyond the dense part of the original data and should be treated with more caution. The calculator accepts inputs within -40% to +45% and warns you outside that window.

Can I use this for trail running and ultra-marathons?

Yes. Grade-adjusted pace is especially useful for trail and ultra planning because elevation gain dominates pacing decisions. Plug in the average grade of a climb segment to estimate how it compares to your flat training paces, or use it to analyse a Strava or Garmin activity lap by lap. Remember that trail surfaces, cumulative fatigue, and altitude can make actual effort higher than GAP alone predicts.

Grade Adjusted Pace Calculator (GAP)

Grade-adjusted pace (GAP) answers the practical question every hill runner faces: “Was that climb as hard as it felt, and how does it compare to my flat running?” This calculator takes your recorded pace and the slope percentage and converts it into the flat-equivalent pace that would demand exactly the same metabolic energy — using the precise empirical formula published by Alberto Minetti and colleagues in the Journal of Experimental Biology in 2002.

How it works

The key insight is that running on a hill costs more (or sometimes less) energy per metre than running on flat ground. Minetti measured oxygen consumption in trained runners on a motorised treadmill across twenty-one gradients from −45% to +45% and fitted a fifth-order polynomial to the data:

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

where i is the fractional grade (5% = 0.05) and C(i) is the metabolic cost in joules per kilogram per metre. On flat ground C(0) = 3.6 J/kg/m. On a +10% slope the cost rises to roughly 6.0 J/kg/m — about 1.7 times harder per metre.

The GAP factor is the ratio of flat cost to graded cost:

factor = C(0) ÷ C(i)

And grade-adjusted pace is just:

GAP = actual pace (s/unit) × factor

A factor below 1.0 means the slope is harder than flat (GAP is faster than actual pace). A factor above 1.0 means the slope is easier (mild downhills). Because the polynomial is non-linear, very steep downhills eventually become harder again as the braking demand increases — the model reflects this correctly.

This is the same underlying model used by Garmin (Running Dynamics), Strava (Relative Effort), and TrainingPeaks (GAP) — so results align with what you see on those platforms.

Worked example

Suppose you record a 6:00 min/km pace on a segment with +8% grade:

Flat cost: C(0) = 3.6 J/kg/m
Cost at 8% (i = 0.08): C(0.08) = 155.4(0.08)⁵ − 30.4(0.08)⁴ − 43.3(0.08)³ + 46.3(0.08)² + 19.5(0.08) + 3.6 ≈ 0.000 − 0.001 − 0.022 + 0.296 + 1.560 + 3.6 ≈ 5.433 J/kg/m
GAP factor: 3.6 ÷ 5.433 ≈ 0.6626
GAP: 360 s × 0.6626 ≈ 239 s = 3:59 min/km

So a 6:00/km climb at 8% is metabolically equivalent to running 3:59/km on flat — comfortably sub-4-minute pace. Your body was working far harder than the GPS number suggests. This explains why hill repeats build fitness so efficiently even when the pace looks pedestrian.

Grade	Actual pace	GAP	Effort vs flat
+5%	6:00 min/km	4:37	+30% harder
+8%	6:00 min/km	3:59	+51% harder
+15%	6:00 min/km	2:55	+106% harder
-5%	6:00 min/km	7:52	-24% easier
-10%	6:00 min/km	10:02	-40% easier

Notice how a -10% descent is substantially easier than flat at this grade. Steeper descents (-15% to -30%) become progressively easier until extreme grades where eccentric braking loads start to reverse the trend.

Formula note

The polynomial coefficients are from Minetti AE, Moia C, Roi GS, Susta D, Ferretti G (2002). “Energy cost of walking and running at extreme uphill and downhill slopes.” J. Exp. Biol. 205, 1759–1767. The model is valid from approximately −40% to +45%. Outside this range the polynomial extrapolates beyond the measured data.

GAP is a metabolic estimate, not a direct power or heart-rate reading. Factors like heat, altitude, fatigue, surface texture, and running economy can all cause actual effort to diverge from the GAP prediction. Use it as a consistent, physics-grounded tool for comparing workouts across varying terrain, not as a substitute for a physiological assessment.

All calculations run locally in your browser — no pace data, grades, or results are ever uploaded to any server.