Quick answer: 10:00 per mile up a 5% grade costs as much energy as 7:41 per mile on the flat. Down a 5% grade, the same 10:00 is worth only 13:07 on the flat, because descending at that slope is cheaper than level running.
How to use it
Type the pace you held on the climb or descent, choose miles or km, and enter the grade in percent: rise over run x 100, so 5 m of climbing over 100 m is 5%. Use a minus sign for downhill. The headline is the flat-equivalent pace. The last tile answers the planning question in reverse: if your normal flat effort is the pace you typed, it shows what the same effort looks like on that slope.
Worked example
Minetti and colleagues measured the energy cost of running, Cr, in joules per kilogram per metre. Their fitted curve gives Cr = 3.6 on the flat and 4.685 at a 5% grade (i = 0.05). The cost per metre is 30% higher, so the same energy buys 30% more speed on the flat: 600 seconds x 3.6 / 4.685 = 461 seconds, or 7:41 per mile. At -10% the cost falls to 2.152, and 6:00 per km becomes 10:02 per km of flat effort.
The formula
Cr = 155.4i^5 - 30.4i^4 - 43.3i^3 + 46.3i^2 + 19.5i + 3.6, with i the grade as a decimal, from Minetti et al., Journal of Applied Physiology, 2002. They measured slopes from -45% to +45%, so the tool stops outside that range. The curve is lowest at about -18%; the paper reports its lowest measured cost, 1.73, at -20%. Below that, running downhill costs more again.
Limits
This is an energy model for steady running. It does not count the braking load on your legs on steep descents, poor footing on trails, or the extra effort of changing grade constantly. Fitness apps that show their own grade adjusted pace may use other models, so their figures can differ.
On a treadmill, the treadmill pace chart shows what an incline is worth. Plan the race itself on the split calculator or the pace calculator. To plan a whole hilly race, load the course into the course pace planner.
Sources: Minetti AE et al. (2002), Energy cost of walking and running at extreme uphill and downhill slopes, J Appl Physiol 93(3):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 . Found a problem? Tell us.
Questions
What is grade adjusted pace?
The pace on flat ground that would cost the same energy as the pace you ran on a hill. Uphill it is faster than your actual pace; on gentle descents it is slower.
How much slower should I run uphill?
On a 5% grade, the same effort as 10:00 per mile on the flat is about 13:01 per mile, by the Minetti energy cost curve.
How do I work out the grade of a hill?
Divide the height gained by the horizontal distance and multiply by 100. Climbing 30 m over 600 m is a 5% grade.
Why does a steep downhill not count as easy?
The energy cost of running is lowest around -18% to -20% and rises again on steeper descents. The model also ignores the braking work your muscles do, which tires the legs on long descents.