What grade-adjusted pace means
Two runs at 10:00 per mile are not the same run if one went up a mountain. Grade-adjusted pace answers a single question: what pace on flat ground would have cost me the same energy? It lets you compare a hilly effort with a flat one honestly, instead of either ignoring the hills or giving yourself unlimited credit for them.
How it is calculated
Minetti and colleagues (2002) put runners on a treadmill at gradients from −45% to +45% and measured the oxygen cost at each one. They fitted a fifth-order polynomial to the result, with the gradient i expressed as rise ÷ run:
Cost (J/kg/m) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6
Factor = cost at your gradient ÷ 3.6
Grade-adjusted pace = your pace ÷ factor
On the flat the formula returns 3.6 J/kg/m, the long-accepted cost of level running, so the factor is exactly 1 and nothing is adjusted. The shape of the curve is the interesting part: cost rises steeply uphill, falls to a minimum at about −20%, and then rises again on steeper descents, because braking starts to cost more than gravity gives back.
Grade adjustment chart
The last column is what a 10:00 mile on that gradient is worth on the flat.
| Gradient | Cost (J/kg/m) | Effort vs flat | 10:00 mile is worth |
|---|---|---|---|
| -20% | 1.80 | 0.50× | 20:00 |
| -15% | 1.84 | 0.51× | 19:37 |
| -10% | 2.15 | 0.60× | 16:44 |
| -5% | 2.75 | 0.76× | 13:07 |
| -2% | 3.23 | 0.90× | 11:09 |
| 0% | 3.60 | 1.00× | 10:00 |
| +2% | 4.01 | 1.11× | 8:59 |
| +5% | 4.69 | 1.30× | 7:41 |
| +8% | 5.43 | 1.51× | 6:38 |
| +10% | 5.97 | 1.66× | 6:02 |
| +15% | 7.42 | 2.06× | 4:51 |
| +20% | 9.01 | 2.50× | 4:00 |
Where this model stops being useful
The numbers above are energy cost and nothing else, and that is a narrower thing than “effort”. Three limits worth knowing before you quote your GAP at anyone:
- Steep downhills flatter you. At −20% the model says running costs half what it does on the flat. Your quads disagree: the braking forces that make downhill running wreck your legs are eccentric work the oxygen cost barely sees.
- Steep uphills break the conversion. A 10:00 mile at +20% converts to a 3:00 flat mile. That is arithmetically correct and practically meaningless — nobody can turn that effort into that speed. Above roughly 10–15% most runners are power-hiking, and the running curve no longer describes what they are doing.
- Average gradient hides the run. Ten kilometres that climb 500 m steadily and ten that climb 500 m in two savage pitches both read 5%. The second is much harder.
Is this the number Strava shows?
Similar uphill, more generous downhill. Strava publishes its own GAP model and damps the adjustment on descents, which is a reasonable engineering choice for exactly the reason above. This page applies Minetti's curve as it was published, without a correction we would have no source for. If your figure here looks kinder than Strava's on a steep descent, that is the difference.
Using it in training
The practical use is week-to-week comparison. If last week's flat tempo ran at 7:30 and this week's rolling one shows a grade-adjusted 7:28, you held your fitness even though the raw pace looked worse. For pacing a race, the honest version is to look at the gradient of each section rather than the average, because the average is the one number the course will not give you.
If you run indoors, the treadmill pace calculator covers the related question of what a belt speed is worth outdoors, and why 1% is the usual setting.
Frequently asked questions
What is grade-adjusted pace?
Grade-adjusted pace (GAP) is the pace you would have run on flat ground for the same energy cost. Running up a hill costs more per mile, so a slow uphill pace converts to a faster flat-equivalent one. It lets you compare a hilly run with a flat one without pretending the hills were not there.
How is grade-adjusted pace calculated?
From the energy cost of running on a slope. Minetti et al. (2002) measured the oxygen cost of running at gradients from −45% to +45% and fitted a curve to it. Divide the cost at your gradient by the cost on the flat (3.6 J/kg/m) and you get a factor; divide your pace by that factor and you get the flat-equivalent pace.
Why does downhill running barely help?
Energetically it helps a lot — the curve bottoms out around −20%, where running costs half what it does on the flat. But the model only counts energy. It does not count the braking forces that beat up your quads, or the fact that you cannot turn your legs over fast enough to cash in the saving. On steep descents GAP will flatter you.
Is this the same number Strava shows?
Close, but not identical. Strava's GAP uses its own model and damps the adjustment on steep descents. This page applies Minetti's published curve as it was fitted, so uphill figures are similar and steep downhill figures are more generous than Strava's.
What gradient counts as a hill?
Below about 2% the adjustment is small enough to ignore — a 10:00 mile at 1% is worth 9:27. At 5% it is 7:41, and at 10% it is 6:02. Most road races sit under 2% average even when they feel hilly; trail races are where this calculator earns its keep.
Sources
The formula on this page comes from the published work below. We check the numbers against the worked examples in these sources with automated tests, and re-read the page against them when we review it.
- Minetti AE, Moia C, Roi GS, Susta D, Ferretti G. Energy cost of walking and running at extreme uphill and downhill slopes. J Appl Physiol. 2002;93(3):1039–1046. pubmed.ncbi.nlm.nih.gov/12183501/
- Bontemps B, Vercruyssen F, Gruet M, Louis J. Downhill running: what are the effects and how can we adapt? A narrative review. Sports Med. 2020;50(12):2083–2110. pubmed.ncbi.nlm.nih.gov/33037592/
General fitness information, not medical advice. Results are estimates; check with a doctor or qualified coach before major changes to diet or training. Formula and copy last reviewed 12 October 2026.