Your hill pace, converted to flat
At the same effort: what your uphill or downhill pace is worth on the flat, or the pace to hold on a slope. Plus two runners at the same effort, so you can see it.
Outlined in blue: your pace converted to flat
Two runners, same effort
How it's calculated
- The model: the energy cost of running on a slope, measured by Minetti et al. ("Energy cost of walking and running at extreme uphill and downhill slopes", Journal of Applied Physiology 93:1039-1046, 2002) on ten runners, on a treadmill, from −45% to +45%. It boils down to a fifth-order polynomial: C(i) = 155.4 i⁵ − 30.4 i⁴ − 43.3 i³ + 46.3 i² + 19.5 i + 3.6, in joules per kilogram per meter, where i is the grade (0.08 for 8%). On the flat, this cost doesn't depend on speed: that's why the ratio between your two paces depends only on the grade.
- The equivalence: at the same effort, you burn the same energy every second. So your speed on the flat equals your speed on the slope multiplied by C(grade) ÷ C(0), and the reverse when you start from the flat. It's the exact grade-adjusted pace calculation the Cadevia app uses, rounded to the second just like on your watch.
- Reference points: at +10%, each meter costs 1.66 times the flat; at +30%, 3.49 times. Going down, the cost drops until −18% (the polynomial's minimum; the study measured it around −20%), where it's half the flat, then it climbs back up: any steeper and you're braking with every stride.
- The colors: green while a meter costs less than 1.25 times the flat (from −18% to +4%); amber from 1.25 to 2 times (from +5% to +14%) and on descents steeper than −18%; red from 2 times the flat (+15% and up).
- Time and elevation: the time on your slope = your pace × its length; its elevation change = its length × the grade, the "elevation ÷ distance" rule turned around.
- The two runners: they start together and run for one minute burning the same energy. Each tick on their path marks 10 seconds, and their pulses land at the same instant. The slope is drawn at its true angle.
- The limits: the model was measured on a treadmill, at a steady speed; it knows nothing about the terrain (rocks, mud, steps), your downhill technique or fatigue. On very steep grades, people often hike: this calculation assumes you're running. And the effort it talks about is energy spent, not your heart rate, which takes a while to catch up.
Frequently asked questions
How do I convert an uphill pace to a flat pace?
At the same effort, your flat speed equals your speed on the grade multiplied by the energy cost of a meter on that grade, divided by the cost of a meter on the flat (Minetti et al., 2002). Example: 10:28 per mile on a +8% grade is worth 6:56 per mile on the flat.
How much harder is running uphill?
At +10%, each meter costs 1.66 times a flat meter; at +30%, 3.49 times. These are the measurements of Minetti et al. (Journal of Applied Physiology, 2002), taken on a treadmill from −45% to +45%.
Is running downhill always easier?
Down to about −18% (the study measured it near −20%), yes: each meter costs less and less, down to half of the flat. Steeper than that, the cost climbs again, because you brake with every stride.
What is grade-adjusted pace?
It's your pace converted to its flat equivalent at the same effort. The Cadevia app calculates it during your workout with the same model as this tool.