Your pace on every gradient
The same effort, translated to each ramp. Look at the asymmetry: what you lose climbing at 10 % you do not get back descending at 10 %, not remotely.
| Gradient | Pace | Difference | Relative cost |
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Grade adjusted pace calculator
A 5:00 on the flat is not a 5:00 at 8 %. This calculator converts your flat pace into the equivalent pace on any gradient —and back again— and estimates what the total climbing of a whole race will cost you. It uses the Minetti energy cost curve, the same one behind grade adjusted pace.
8 %
The whole course
Equivalent pace on the gradient
—min / km
Relative cost
—
Difference
—
Speed
—
The whole course
Estimated time
—
If it were flat
—
It costs you
—
How grade adjusted pace is calculated
Running on a slope does not cost proportionally more: it costs vastly more uphill and only slightly less downhill. The reference for quantifying it is the work of Alberto Minetti and colleagues, who measured the energy cost of running at different inclines in the laboratory and fitted a fifth degree polynomial, with the gradient expressed as a fraction:
Cr(i) = 155.4·i⁵ − 30.4·i⁴ − 43.3·i³ + 46.3·i² + 19.5·i + 3.6
Cr = energy cost, in joules per kilo per metre
i = gradient as a fraction (0.08 = 8 %)
On the flat, Cr = 3.6 J/kg/m
The equivalent pace follows from a simple idea: if you hold the same energy expenditure per unit of time, your speed has to drop in the same proportion as the cost per metre rises.
pace on gradient = flat pace × Cr(i) / 3.6
grade adjusted pace = actual pace × 3.6 / Cr(i)
The asymmetry that ruins trail races
Climbing at 10 % multiplies the cost by 1.66. Descending at 10 % reduces it to 0.60. One kilometre up at 10 % and one down at 10 % together cost 13 % more than two flat kilometres, even though the net elevation is zero. At 6 % that same out-and-back penalty drops to 5 %, and at 20 % it explodes.
The cost has a curious minimum around −18 %, where running costs exactly half of what it costs on the flat. Beyond that it gets expensive again, because braking consumes energy: on a −40 % descent running costs the same as on the flat again, with the difference that the next day you cannot walk down stairs.
Why you never cash in the whole descent
Here is a trap almost no calculator warns you about. Apply the formula literally to an 18 % descent and it tells you that you can run at twice your flat speed: for someone at 5:00 per kilometre, a 2:30. That is 24 km/h, world-record 100 metre pace sustained downhill. Obviously it does not happen.
The reason is that the Minetti model describes energy cost, and on a steep descent your limit stops being oxygen: it becomes stride frequency, braking control and whatever your quadriceps will take. So this calculator applies the full curve uphill but caps the downhill gain at 20 % of pace, which is where empirical grade adjusted curves flatten out. You can see the difference in the table: the relative cost column follows the physics, and the pace column follows what can actually be run.
Against the rule of thumb
The popular rule says about 10 seconds per kilometre for each 1 % of gradient. For a runner at 4:00 per kilometre it lands reasonably close on ramps of 1 to 3 %, but it fails in two ways: the penalty is proportional to your pace, so someone running 6:00 loses considerably more than someone running 4:00, and beyond 8 % the curve accelerates and the rule falls badly short. At 15 %, a 5:00 runner does not lose 150 seconds per kilometre, they lose more than 300.
What this model does not include
Minetti measured on a treadmill, on an even surface, at submaximal speeds and without accumulated fatigue. A real mountain race adds technical ground, rocks, mud, altitude and the fact that on very steep ramps almost everyone switches to walking, which above 20 % is usually more efficient than running. Take the result as the floor of the effort: in the mountains it always takes a little longer.
The curve behind the numbers
What each gradient costs compared with running on the flat, according to the Minetti energy-cost curve. This is the curve the calculator uses, drawn from the same formula.
Notice the curve is not symmetric: a 10% climb costs 66% more than the flat, but a 10% descent only saves 40%. The minimum sits at −18%, where the formula says you spend half what you spend on the flat — meaning you could run twice as fast. You cannot: past a certain gradient what slows you down is braking. That is why the calculator caps the downhill gain at 20%.
Frequently asked questions
What is grade adjusted pace (GAP)?
It is your actual pace converted into the pace you would have run on the flat for the same effort. It lets you compare sessions run on different terrain: a 5:30 climbing at 5 % and a 4:35 on the flat are the same workout, even though the watch says otherwise.
How much slower do you run uphill?
About 5.5 % slower for each 1 % of gradient on gentle ramps, and considerably more beyond 8 % because the curve accelerates. For a runner at 5:00 per kilometre: 6:11 at 4 %, 7:33 at 8 % and 9:04 at 12 %. The penalty is proportional to your pace, so a slower runner loses more seconds than a fast one on the same hill.
How much do you gain running downhill?
Less than you lose climbing, and less than the physics suggests. Energetically the minimum sits at −18 %, where running costs half what it costs on the flat; but at that point the limit is technique and braking rather than oxygen. In practice the pace gain plateaus around 20 %, which is why this calculator caps it there.
What is the formula for the energy cost of running on a gradient?
Minetti and colleagues (2002): Cr(i) = 155.4·i⁵ − 30.4·i⁴ − 43.3·i³ + 46.3·i² + 19.5·i + 3.6, where Cr is the energy cost in joules per kilogram per metre and i is the gradient as a fraction. On the flat the cost is 3.6 J/kg/m.
Does it work for hiking in the mountains?
No. The model is for running. Walking follows a different energy cost curve and, above 20 % gradient, walking is usually more efficient than running, so the calculator will overestimate your time on very steep ramps.
Why does my Strava GAP not match exactly?
Because Strava applies the correction second by second on the instantaneous gradient of each segment, with its own smoothing of the elevation profile, while this calculator uses a constant average gradient. On very broken profiles the gap between the two grows.
Which flat pace should I enter?
The one you can hold for the race distance. If you do not know it, work it out with the running pace calculator and use marathon pace for long races or threshold pace for short ones.
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This calculator is an informational estimate and does not replace a coach or a laboratory test. Nothing you type ever leaves your browser.