Calculate your grade adjusted pace (GAP) from a running pace and hill grade, or find the pace to run on a hill to hold a target flat effort.
Grade Adjusted Pace Formula
Grade adjusted pace converts the pace you actually run on a slope into the pace that would take the same effort on flat ground. It divides your actual pace by a grade adjustment factor:
GAP = P / f
The calculator can also run this backwards. If you know the flat effort you want to hold, it multiplies that target by the same factor to give the pace to run on the hill:
P_hill = GAP_target * f
The factor f depends only on the grade. This tool uses a curve calibrated to real running, which adds roughly 2.5 percent of effort for every 1 percent of uphill grade and gives a downhill credit that peaks near 10 percent down before steep braking cancels it out. Writing the grade steepness as a positive number G in percent:
f uphill = 1 + 0.025 G + 0.0006 G^2 f downhill = 1 - 0.015 G (to 10 percent down) f steep down = 0.85 + 0.02 (G - 10)
Variables:
- GAP is the grade adjusted pace, the flat-ground pace that represents the same effort
- P is your actual pace on the slope, in minutes per mile or per kilometer
- GAP_target is the flat effort you want to hold, used in the reverse mode
- P_hill is the pace to run on the slope to hold that target effort
- f is the grade adjustment factor for the slope
- G is the grade of the slope in percent, found as elevation change divided by distance, times 100
Pick what you want to find at the top of the calculator. In the first mode you enter your actual pace and the grade, and the tool returns your grade adjusted pace along with the adjustment factor and how much harder or easier the slope is than flat. In the reverse mode you enter a target grade adjusted pace and the grade, and the tool returns the pace to run on that slope so the effort matches your flat target. You can type the grade directly, or enter an elevation change and the distance it covers and let the tool work out the grade for you.
Grade Adjustment Factor by Slope
This table lists the adjustment factor at common grades. The last column shows the raw metabolic cost ratio from the Minetti (2002) treadmill study, the research the whole idea is built on. Notice that the measured energy cost climbs much faster than the pace factor: a 10 percent climb costs about 66 percent more energy per stride, yet your sustainable pace only slows by about a third, because you cannot hold that energy output for long. The pace factor is the number that actually predicts how you run.
| Grade | Adjustment factor | Effort vs flat | Minetti cost ratio |
|---|---|---|---|
| 15% downhill | 0.95 | 5% easier | 0.51 |
| 10% downhill | 0.85 | 15% easier | 0.60 |
| 6% downhill | 0.91 | 9% easier | 0.72 |
| 3% downhill | 0.96 | 4.5% easier | 0.85 |
| Flat (0%) | 1.00 | same | 1.00 |
| 3% uphill | 1.08 | 8% harder | 1.17 |
| 6% uphill | 1.17 | 17% harder | 1.37 |
| 10% uphill | 1.31 | 31% harder | 1.66 |
| 15% uphill | 1.51 | 51% harder | 2.06 |
The second table turns the reverse mode into a pacing sheet. It shows the pace to run at each grade for a runner whose flat-ground target is 9:00 per mile, so the effort stays even across a rolling course. This is why holding your flat pace up a climb spikes your effort: to keep it honest you have to give back time on the way up and take it back on the way down.
| Grade | Pace to run (9:00/mi flat target) | vs flat |
|---|---|---|
| 10% downhill | 7:39/mi | 1:21 faster |
| 6% downhill | 8:11/mi | 0:49 faster |
| 3% downhill | 8:36/mi | 0:24 faster |
| Flat (0%) | 9:00/mi | even |
| 3% uphill | 9:43/mi | 0:43 slower |
| 6% uphill | 10:33/mi | 1:33 slower |
| 10% uphill | 11:47/mi | 2:47 slower |
Example Problems
Example 1: find grade adjusted pace from your run.
You run 9:00 per mile up a steady 6 percent climb. First find the factor: f = 1 + 0.025(6) + 0.0006(6 squared) = 1 + 0.15 + 0.0216 = 1.17. Then divide your pace by it: GAP = 9:00 / 1.17, which is about 7:41 per mile. The climb held your clock pace at 9:00, but the effort was that of a 7:41 flat mile.
Example 2: find the pace to hold a target effort uphill.
Your plan calls for an 8:00 per mile effort, and the next segment is an 8 percent climb. The factor is f = 1 + 0.025(8) + 0.0006(8 squared) = 1.24. Multiply the target by it: P_hill = 8:00 x 1.24, which is about 9:54 per mile. Running the climb near 9:54 keeps the effort where the 8:00 flat target wanted it, instead of blowing up trying to force 8:00 up the hill.
Frequently Asked Questions
Why is my grade adjusted pace faster than my actual pace uphill?
Because the hill slowed your clock pace without lowering your effort. Grade adjusted pace asks what flat pace would have cost the same effort, and on a climb that flat pace is faster than the pace you actually ran. Downhill it works the other way: gravity does part of the work, so your grade adjusted pace is slower than the pace on your watch. On a moderate downhill of about 10 percent the effect is largest, worth roughly a 15 percent credit.
Does this match Strava’s grade adjusted pace?
It will be close but rarely identical. This calculator uses a transparent curve calibrated to the same cost-of-running research Strava started from, the Minetti (2002) study. Strava later rebuilt its model from millions of runs using heart rate, and it smooths GPS elevation before applying the curve, so a noisy track can shift the number a few seconds per mile either way. Use this tool for a deliberate what-if before a run, and use Strava to see what actually happened.
Why does steep downhill running stop getting easier?
Below about 10 percent down, the cost curve bends back up. Your quadriceps have to fire in long braking contractions to stop you from accelerating out of control, which burns more oxygen per step and causes far more muscle damage than pushing uphill does. That is why the factor stops falling past 10 percent down and starts rising again, and why a fast, rocky descent can trash your legs even when the pace on your watch looks easy.
