Grade adjusted
pace calculator

Turn your pace on a hill into the flat-equivalent pace that costs the same effort, using the Minetti cost-of-running curve — the one Strava-style GAP is built on. With the reason a steep downhill isn't the free ride most calculators print.

How the math works

A slope changes the energy it costs to cover a metre of ground. Minetti et al. (2002) measured that cost across gradients from −45% to +45% and fitted it to a curve. The energy cost of running Cr, in joules per kilogram of body mass per metre, is a 5th-order polynomial in the gradient i (a fraction: +10% → 0.10, a −10% descent → −0.10).

At a steady effort your metabolic power is Cr(i) × speed. Hold that power constant and the flat speed of equal effort is speed × Cr(i)/Cr(0) — so in pace terms the grade-adjusted pace is your clock pace scaled by Cr(0)/Cr(i). Uphill, Cr(i) is larger than 3.6, so the factor is below 1 and the flat-equivalent pace is faster than your watch: grinding uphill is worth a quick flat pace. Downhill, the factor is above 1 and the flat-equivalent pace is slower — gravity did some of the work. The factor depends only on the grade, not on how fast you are going.

Worked example

A runner holds a 10:00/mi (6:13/km) clock pace up a steady 6% grade. The Minetti cost at i = 0.06 is Cr = 4.93 J/kg/m versus 3.6 on the flat — 1.37× the cost, or +37% energy.

• GAP factor: 3.6 / 4.93 = 0.731
• Grade-adjusted pace: 10:00/mi × 0.731 = 7:18/mi (4:32/km)

So the 10:00/mi you are actually running up the hill costs what a 7:18/mi flat run would — the climb is worth a much faster flat pace than your watch shows. Now the descent: that same runner drops a 10% grade at 7:30/mi (4:40/km). The cost at i = −0.10 is 2.15 J/kg/m (−40% energy), a GAP factor of 1.673, so the grade-adjusted pace is 12:33/mi (7:48/km). Running 7:30/mi downhill costs the energy of a 12:33/mi flat jog, which is exactly why downhills flatter your average pace.

When this calculator is wrong

Grade-adjusted pace treats every downhill as a bigger discount, but the energy cost of running bottoms out near −20% grade and climbs back toward the flat cost — a steep descent is barely cheaper than level ground. On the Minetti curve the cost falls as the grade turns down, reaches a minimum near −18% to −20% (about 1.8 J/kg/m, half the flat 3.6), and then rises again: by −40% it is back to roughly 3.6 — the same as flat — and at −45% it is higher. So the discount a descent earns peaks at a moderate grade and shrinks to nothing on a cliff-like drop, because the eccentric braking your legs do to not fall costs real energy. Three limits bite.

• The steep-descent end. Past about −20% a steeper descent is not cheaper. A tool that keeps slowing the flat-equivalent pace as the drop steepens is wrong there; this page flags it. The honest range for the downhill discount is roughly −5% to −20%, where most runnable descents sit.
• The steep-climb end. GAP is an effort equivalence, not a pace you can hold. A 10:00/mi up a 10% grade has a flat-equivalent near 6:02/mi — a true statement about energy cost, but faster than you could actually run. Read a steep-uphill GAP as "this effort equals roughly a 6:00/mi flat effort," not as a split you should chase.
• Outside the measured range. Minetti fitted the curve on −45% to +45% grades with ten trained runners on a treadmill. Past ±45% the polynomial is extrapolation, and real trail running adds footing, rocks, mud, and air resistance the lab curve never saw. Treat the number as effort bookkeeping, not a measurement.

What to do with the result

Use the grade-adjusted pace to keep hilly runs honest. On a climb, your clock pace undersells the effort — log the GAP so a slow hill rep sits next to your flat efforts on an equal footing, and set the effort by the GAP rather than fighting to hold a flat split uphill (which spikes your heart rate for no gain). On a descent, the GAP is slower than your watch, so don't read a fast downhill split as fitness; it is mostly gravity. To compare a hilly route to a flat one, average the GAP over the route, not the raw pace.

Then calibrate against something you can measure. The curve is a group average; your heart rate at a given effort is yours. Run a familiar flat easy pace, note the heart rate, then on a hill hold the belt-and-grade combination the calculator calls that same effort — if your heart rate runs high, trust the heart rate and ease off. Over a few weeks the gap between your GAP-for-effort and your heart rate tells you more than either number alone.

Common questions

What is grade adjusted pace?

The flat pace that would cost the same energy as the pace you actually ran on a hill. It lets you compare a hilly run to a flat one on equal terms. Uphill, the grade-adjusted pace is faster than your watch (the climb was harder than the clock shows); downhill, it is slower (gravity helped). It is the number Strava, Garmin, and COROS show as "GAP" under splits with elevation.

How is grade adjusted pace calculated?

From the energy cost of running on a slope. This page uses the Minetti et al. 2002 cost-of-running curve, Cr(i) = 155.4·i⁵ − 30.4·i⁴ − 43.3·i³ + 46.3·i² + 19.5·i + 3.6 in J/kg/m, and scales your clock pace by Cr(0)/Cr(i), where Cr(0) = 3.6 is the flat cost. Many calculators instead use a flat rule of thumb like "2.5% of effort per 1% of grade" — close on gentle ground, but it misses the way the curve bends at the steep ends.

Does running downhill really save energy?

Up to a point. The cost of running drops as a descent steepens, reaching a minimum near −18% to −20% (about half the flat cost). Past that it climbs back: by −40% grade a descent costs about the same as running on the flat, and steeper than −45% it costs more, because your legs brake hard to keep from falling. So a gentle downhill is genuinely cheap; a cliff-like one is not.

Is grade adjusted pace the same as my race pace on hills?

No. GAP is an effort equivalence, not a pace you can hold. On a steep climb the flat-equivalent pace runs faster than anyone could actually run — it tells you the effort matches a fast flat run, not that you should run that split. Use it to pace by effort and to compare runs; use real splits and heart rate to judge what you can hold.

How much does a 10% hill slow me down?

In energy terms a 10% climb costs about 66% more than flat running (Cr rises from 3.6 to about 6.0 J/kg/m), so holding the same effort means running roughly 40% slower up it. A 10% descent costs about 40% less, so the same effort runs faster — which is why your average pace on a rolling course rarely matches the flat pace the climbs and descents each imply.

Why does the calculator warn on steep downhills?

Because the cost curve turns around. Below about −20% grade a steeper descent stops being cheaper and starts being more costly, so a naive "steeper = bigger discount" model over-credits it. When you enter a descent past the cost minimum, the page says so rather than printing a flat-equivalent pace that is too slow.