How much slower should you run uphill?

The cost curve behind the numbers

In 2002 A. E. Minetti and colleagues published measurements of the energy cost of running on slopes from -45% to +45% in the Journal of Applied Physiology. The abstract reports a level cost of 3.40 J per kg per metre, independent of speed; 18.93 at +45%; a lowest measured value of 1.73 at -20%; and 3.92 at -45%. They also fitted a fifth-order polynomial to their data, which is what the grade-adjusted pace calculator and the course pace planner use:

Cr = 155.4i⁵ - 30.4i⁴ - 43.3i³ + 46.3i² + 19.5i + 3.6

Cr is in joules per kilogram per metre and i is the grade as a decimal (0.05 for 5%). The constant, 3.6, is the fitted value on the flat; it differs from the measured 3.40 because one is a curve through all the data and the other a mean of the level runs.

The model's logic for pacing is simple: if a metre of slope costs Cr and a metre of flat costs 3.6, then at the same energy per second, time per metre scales with Cr. So an even-effort pace on a slope = flat pace × Cr(i) / 3.6.

How much slower uphill: the per-percent rule

Near the flat, the slope of the curve is set by the 19.5i term: 19.5 / 3.6 = 5.42% more cost per 1% of grade. Worked by hand for a 1% climb: Cr(0.01) = 3.800, so the ratio is 3.800 / 3.6 = 1.055 and an 8:00 mile (480 seconds) becomes 480 × 1.055 = 507 seconds, or 8:27.

The rule does not stay linear. The i² term pushes the cost up faster as the hill steepens: the ratio is 1.113 at 2%, 1.236 at 4%, 1.509 at 8% and 1.658 at 10%. A 10% grade is not ten times a 1% grade; in this model it costs as much as 65.8% more than the flat, against 5.5% for 1%.

Even-effort pace on each grade

What to run on each slope to hold the same energy per second as a flat 8:00 or 10:00 per mile (or 5:00 per km), computed with RUN.minettiCr:

I stopped the downhill rows at -6% on purpose. The energy model keeps promising faster paces on steeper descents (at -10% it would say 4:47 for an 8:00 effort), but those speeds are limited by footing, braking and leg impact, none of which the curve measures. For steeper descents, use the next table to judge an effort, not to set a target pace.

Flat-equivalent pace from -20% to +20%

The opposite question: you held 8:00 or 10:00 per mile on a slope; what is that worth on the flat? Flat-equivalent pace = pace on the slope × 3.6 / Cr(i).

The +20% row is the reason grade-adjusted figures on steep climbs look heroic: holding 10:00 per mile up a 20% slope is, in energy terms, a 4:00 mile on the flat. Few runners hold 10:00 there for long, which is the point.

The cheapest downhill slope, computed

To find the lowest point of the fitted curve I set its derivative to zero:

dCr/di = 777i⁴ - 121.6i³ - 129.9i² + 92.6i + 19.5 = 0

Solving numerically between -30% and -10% gives one root, at i = -0.1814. The cost there is Cr = 1.781 J/kg/m, a little under half the flat value (1.781 / 3.6 = 0.495). The measured data in the abstract put the lowest cost at -20% (1.73), so the curve and the measurements agree that the minimum sits close to -18 to -20%. At -20% the curve gives 1.800; beyond the minimum the cost rises again, to 4.03 at -45% on the fitted curve (3.92 measured).

That is a much steeper slope than most race courses contain, so on ordinary road descents the rule is simply: steeper is cheaper, but each extra percent saves less.

A single hill in seconds

Paces per mile hide how short most hills are, so here is one hill worked through. A 400 m climb at 6% for a runner whose flat effort is 8:00 per mile: on the flat, 400 m at that pace takes 480 × 400 / 1,609.344 = 119.3 seconds. At 6% the cost ratio is 1.369, so the same effort takes 119.3 × 1.369 = 163.3 seconds, 44.0 seconds longer. Coming back down the same 400 m at the same effort takes 119.3 × 0.724 = 86.3 seconds, 33.0 seconds quicker than flat. Net: 11 seconds lost on the round trip, for one short hill.

For a 10:00 per mile runner on an 800 m drag at 4%, the flat time is 298.3 seconds and the even-effort time 368.8 seconds: 70.5 seconds more. If the plan says to hold 10:00 there anyway, those 70 seconds have to come from extra effort on the climb instead of from the clock.

Why a hill does not cancel out

Because the curve bends upward, the climb costs more than the matching descent gives back. For an out-and-back over the same grade, at even effort, the average pace is the flat pace × (Cr(i) + Cr(-i)) / (2 × 3.6):

Gentle rolling hills cost almost nothing (2.5 seconds per mile at 2%), but the penalty grows quickly with grade. This is also why a course with the same start and finish height is not "net zero" for time.

Even effort on a whole course

The course pace planner applies the same idea to a real route: it reads a GPX file in your browser, resamples the track every 10 m to measure the grade, and shares your goal time out in proportion to Cr, so climbs get more time and descents less while the finish time stays the same. That is the even-effort plan. An even-pace plan from a pace band or the split calculator ignores the hills, which on the numbers above means working well above your average effort on every climb. On a treadmill, where the slope never changes and there is no downhill, the treadmill pace chart uses the simpler ACSM equation; the treadmill incline guide compares the two.

Limits

The curve is an energy model for steady running on a uniform slope. It does not include the braking load and muscle damage of long descents, rough ground, the cost of constant changes of grade, wind, or heat. Minetti's equation is a fit to group data, so an individual runner's costs can differ. Fitness apps that show their own grade-adjusted pace may use other models, so their numbers can disagree with these. And the faster downhill paces in the even-effort table are energy equivalents, not a promise that your legs can or should run them.

Run your own numbers: grade-adjusted pace calculator, course pace planner, treadmill pace chart.

Sources: Minetti AE et al. (2002), Energy cost of walking and running at extreme uphill and downhill slopes, J Appl Physiol 93:1039-1046; di Prampero PE (2015), Mechanical efficiency, work and heat output in running uphill or downhill, Annales Kinesiologiae (quotes the Minetti polynomial). Rules checked 7 October 2026. Found a problem? Tell us.

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