About the Grade Adjusted Pace Calculator
This grade adjusted pace (GAP) calculator tells you what your pace on a hill is worth on flat ground. Running 6:00 per kilometre up a 6% climb takes far more energy than 6:00 on the flat, so the calculator converts it into the faster flat pace that would cost the same energy — and does the reverse for downhills.
Trail and mountain runners use GAP to judge effort on hilly routes, coaches use it to compare workouts on different courses, and road runners use it to plan race pacing on hilly marathons. Enter your actual pace and the average gradient of the segment; positive grades are uphill, negative grades downhill.
The model comes from laboratory measurements of the metabolic cost of running on slopes from −45% to +45% (Minetti and colleagues, 2002). It describes energy cost, not perceived effort or muscle damage, and very steep downhills are limited by braking and technique, so treat GAP on extreme grades as a guide only. GPS watches and apps use their own variants of this idea, so their numbers can differ slightly.
How to use the grade adjusted pace calculator
- 1Enter your actual pace for the hill segment in minutes and seconds.
- 2Choose whether that pace is per kilometre or per mile.
- 3Enter the average gradient — positive uphill, negative downhill.
- 4Read the grade adjusted pace: the flat pace that costs the same energy.
- 5Use the table to set a target pace for the same effort on other gradients.
Formula and method
C(i) is the metabolic energy cost of running in joules per kilogram per metre on a gradient i (rise ÷ run, so 5% = 0.05), from the polynomial fitted by Minetti et al. (Journal of Applied Physiology, 2002). On the flat it is 3.6 J/kg/m; it rises steeply uphill and is lowest at about −18% (roughly half the flat cost), below which braking makes running more costly again.
Grade adjusted pace assumes your metabolic power stays the same, so the equivalent flat speed is your actual speed multiplied by C(i) ÷ C(0). Pace is the inverse of speed, so GAP is your actual pace divided by the same ratio. The model is for steady running and ignores wind, surface and fatigue.
- i
- Gradient as a fraction (rise ÷ horizontal distance)
- C(i)
- Energy cost of running on gradient i (J/kg/m)
- GAP
- Flat-ground pace with the same energy cost
Worked examples
6:00/km up a 5% grade
At 5% the energy cost is 155.4(0.05)⁵ − 30.4(0.05)⁴ − 43.3(0.05)³ + 46.3(0.05)² + 19.5(0.05) + 3.6 ≈ 4.69 J/kg/m, 1.30 times the flat cost of 3.6. Dividing 360 s by 1.30 gives a flat-equivalent pace of about 4:37 per km.
8:30/mile on a 10% climb
A 10% grade costs about 5.97 J/kg/m, 1.66 times the flat value, so 510 s per mile on the climb is worth roughly 5:08 per mile on the flat.
5:00/km down a −8% slope
At −8% the cost falls to about 2.36 J/kg/m, only 0.65 of the flat value. A 5:00/km descent therefore represents the effort of about 7:38/km on flat ground.
Frequently asked questions
What is grade adjusted pace?+
Grade adjusted pace (GAP) is the pace you would run on flat ground for the same effort you are putting in on a hill. Uphill GAP is faster than your actual pace; on gentle downhills it is slower.
How much does a hill slow you down?+
Using the Minetti model, each 1% of uphill grade adds roughly 5–7% to the energy cost at moderate gradients. A 5% climb costs about 30% more than flat running, so at the same effort your pace is about 30% slower.
Why is my watch GAP different from this calculator?+
Apps such as Strava use their own models, some calibrated on large amounts of real-world heart rate data rather than lab oxygen measurements, and they work from second-by-second GPS elevation. Results are usually similar but not identical.
Is running downhill always easier?+
Energetically, yes down to about −18%, where cost is roughly half of flat running. Steeper than that, braking forces increase the cost again, and steep descents cause significant muscle damage even when they feel easy.
How do I find the gradient of a hill?+
Divide elevation gain by horizontal distance and multiply by 100. For example, climbing 60 m over 1.2 km is 60 ÷ 1200 × 100 = 5%. Most mapping and route-planning apps show segment gradients.