Grade Adjusted Pace Calculator (Running Uphill and Downhill)
The flat-ground pace that costs the same energy as your pace on a slope, so hill runs can be compared with flat ones, from Minetti's measured cost of running.
Results
The dashed line marks the value you entered.
What this tool does
In 2002 Minetti and colleagues measured the energy cost of running on slopes from −45 % to +45 % and fitted a fifth-degree polynomial: 3.6 J per kilogram per metre on the flat, about 5.4 at +8 %, with a minimum near −20 %, where braking begins to cost more than gravity gives back. Equal effort means equal energy per second, so the equivalent flat pace is your pace times 3.6 divided by the cost on the slope. It ignores fatigue, surface and the technical skill of downhill running, and is not the same model as any watch or app uses.
Formula
C(i) = 155.4 i⁵ − 30.4 i⁴ − 43.3 i³ + 46.3 i² + 19.5 i + 3.6 J/(kg·m) (i = gradient as a fraction) · flat pace = pace × 3.6 ÷ C(i)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pm | Pace on the slope: minutes per km | min |
ps | and seconds | s |
gr | Gradient (positive uphill) | % |
FP | Equivalent pace on the flat | s/km |
FM | Equivalent flat pace in minutes per km | min/km |
CO | Energy cost of running on this slope | J/(kg·m) |
RE | Effort compared with the flat | % |
Worked example
- Pace on the slope: minutes per km6 min
- and seconds0 s
- Gradient (positive uphill)8 %
- Equivalent pace on the flat239 s/km
- Equivalent flat pace in minutes per km3.98 min/km
- Energy cost of running on this slope5.43 J/(kg·m)
- Effort compared with the flat151 %
Limitations
- This tool is informational only. It does not diagnose, treat or replace a qualified health professional. Speak to a doctor before making decisions about your health.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.