Grade-adjusted pace calculator

Enter an observed pace in seconds per kilometre and a signed grade percentage: positive for uphill, negative for downhill. The calculator applies a published polynomial running-cost curve and returns a flat-equivalent pace, a correction factor, and the modeled energy cost. It is deterministic and useful for comparing efforts, but it does not replace heart-rate, power, terrain, weather, or individual performance data.

Enter pace and grade consistently

Provide the observed pace as total seconds per kilometre. For example, a five-minute kilometre is 300 seconds. Grade is the signed vertical change divided by horizontal distance and multiplied by 100, so a climb gaining five metres over 100 horizontal metres is approximately +5%. Use a negative number for a descent. The calculator expects both fields because a pace without terrain cannot be adjusted, while terrain without an observed pace does not describe a running result. Use the average grade only for a reasonably consistent segment. A route that repeatedly alternates between steep climbs and descents should be divided into sections, calculated separately, and then combined by time or distance. Averaging a rolling route into zero percent can hide substantial climbing cost and downhill behavior. GPS elevation is often noisy over short segments, so prefer a mapped or smoothed grade when possible. The accepted range is deliberately limited to practical running slopes from −45% to +45%, and pace must fall between one and sixty minutes per kilometre.

Understand the polynomial correction

The calculation uses the Minetti polynomial energy-cost curve: cost equals 155.4g⁵ − 30.4g⁴ − 43.3g³ + 46.3g² + 19.5g + 3.6, where g is grade written as a decimal rather than a percentage. At zero grade the modeled cost is 3.6 joules per kilogram per metre. The correction factor is that flat cost divided by the cost at the supplied grade, and the observed seconds per kilometre are multiplied by this factor. An uphill cost above the flat value therefore produces a faster flat-equivalent pace. Moderate downhill running can also produce a faster equivalent pace than the observed pace, but the relationship is not a mirror image because descending has braking, impact, and muscle-damage costs. The returned energy cost is the polynomial value, not a direct calorie measurement. Results are rounded only after the full calculation, keeping repeated requests stable. This method describes energetic equivalence under its model; it does not claim that every runner can reproduce the adjusted pace on a track.

Interpret GAP as a comparison tool

Use grade-adjusted pace to compare segments or training efforts that would otherwise look misleading on a pace chart. A slow uphill split may represent a strong effort, while a fast descent may not be as demanding as its raw pace suggests. GAP is most informative when surfaces, altitude, wind, fatigue, and segment length are broadly comparable. Trail footing, sharp turns, stairs, mud, heat, and technical descending can dominate the result because the formula sees only pace and average grade. Individual running economy also varies, especially on steep descents where skill and eccentric muscle tolerance matter. Treat small differences as noise rather than as proof that one session was better. For structured analysis, preserve the raw pace and grade beside the adjusted output so the estimate remains auditable. The browser and API use the same pure JavaScript solver, and an API request costs $0.002. This makes the result suitable for repeatable logs and pipelines, while coaches and athletes should still interpret it alongside perceived exertion, heart rate, and the purpose of the workout.