Converts uphill and downhill running pace into an estimated flat-equivalent pace for comparing effort across rolling terrain.

Grade Adjusted Pace (GAP)

Grade Adjusted Pace (GAP) converts your actual pace on uphill or downhill terrain into an estimated flat-equivalent pace with similar energy cost, using a biomechanical/energetic model.

It tries to answer the runner’s core question: “If I weren’t climbing this hill, what pace would I be running on flat ground at the same effort?”

Core idea

On rolling terrain, actual pace can be misleading:

Uphill: you do extra work against gravity; pace slows but physiological cost is high.
Downhill: gravity assists; pace speeds up but energy cost does not necessarily drop linearly (braking forces matter).

GAP reduces part of the terrain effect and provides a standardized pace so you can compare similar efforts across routes.

How it’s computed

Trainingload.ai computes GAP using an energy cost model based on Minetti (2002), which quantifies energy cost (EC) across grades.

Energy cost equation

C_r = 155.4 \times i^5 - 30.4 \times i^4 - 43.3 \times i^3 + 46.3 \times i^2 + 19.5 \times i + 3.6

Where:

$C_r$ : energy cost (J/kg/m)
$i$ : grade (e.g., 5% grade is 0.05)

GAP equation

GAP = Pace_actual / (C_r / C_flat)

At 0% grade, $C_{flat} \approx 3.6$ .
Uphill: $C_r > 3.6$ , so GAP is faster than actual pace (a smaller time value).
Gentle downhill: $C_r < 3.6$ , so GAP is slower than actual pace.
Note: on very steep downhills (often below -20%), heavy eccentric braking can increase energy cost again, making GAP “faster” again.

Typical applications

1. Trail and mountain running

On steep terrain, actual pace can be hard to interpret.

Example: you climb a 15% grade and your pace drops to 12:00/km.
GAP: shows 5:00/km.
Interpretation: the metabolic intensity may be much higher than the raw pace suggests.

2. Basis for rTSS

Trainingload.ai uses NGP (Normalized Graded Pace) to compute running load (rTSS), and GAP is the foundation of NGP.

Pace_actual  --(grade adjustment)-->  GAP  --(weighted smoothing)-->  NGP

3. Race pacing strategy

By analyzing course GPX data with GAP, you can plan what actual pace to run on different segments to keep effort more consistent.

How Trainingload.ai uses GAP

Terrain context: GAP helps explain why a slow uphill split may still be a high-intensity effort.
Foundation for NGP: Trainingload.ai uses GAP as the first step before computing NGP and rTSS.
Do not chase it blindly: GAP is a metabolic equivalence. It does not fully reflect musculoskeletal stress. Long, hard downhills may look manageable in GAP but still create high quad and knee load.
Prefer trends over instant values: GPS-grade estimates are noisy and delayed, which can make real-time GAP jumpy. Prefer lap averages or post-activity analysis.

References

Minetti, A. E., et al. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology.
Strava: Grade Adjusted Pace (GAP)

Grade Adjusted Pace (GAP)

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