Formula, in endurance

Marathon Pace Elevation Formula

Elevation adds running-economy cost beyond what a flat-course pace predicts. Minetti 2002 quantified the energetic cost of grade; at marathon effort it reduces to a simple rule matching Daniels' Running Formula: each metre of gross climb adds about 1.5 seconds to your finish time, each metre of descent about 0.75 seconds. Climbs cost about twice what descents recover, so even a net-zero rolling course runs slower than flat.

5 variables. Published May 14, 2026. By AI Fit Hub.

Education, not medical advice. The result comes only from the published formula and your inputs. How we check our formulas.

Formula

adjusted_pace_sec_per_km = flat_pace_sec_per_km +
   (ascent_m_per_km × uphill_cost) − (descent_m_per_km × downhill_credit)
   uphill_cost ≈ 1.5 sec/m of finish time (Daniels; Minetti 2002 consistent)
   downhill_credit ≈ 0.75 sec/m (2:1 asymmetric — climbs cost twice what descents recover)

Variables

flat_pace_sec_per_km

Flat-course goal pace

Target marathon pace on a perfectly flat, sea-level course. Use a recent flat-marathon result or a Riegel-extrapolated time. Pace expressed in seconds per kilometer.

ascent_m_per_km

Average ascent per km

Total cumulative elevation gain divided by race distance. NYC Marathon ~8 m/km, Berlin ~2 m/km, Boston ~10 m/km (net downhill but with rolling profile).

descent_m_per_km

Average descent per km

Total cumulative elevation loss divided by race distance. Downhill credit is smaller than uphill cost in magnitude — quad fatigue grows faster than free pace.

uphill_cost

Uphill energetic cost

Finish-time penalty per meter of vertical gain. Steeper grades cost more nonlinearly above ~10%, but marathon courses rarely sustain that. Use about 1.5 sec/m as a rule of thumb (Daniels; ~1.3 for well-trained runners who hold form on climbs, up to ~2 for recreational runners). Consistent with Minetti's 2002 grade energy-cost curve at marathon effort.

downhill_credit

Downhill recovery

Finish-time credit per meter of vertical loss, about 0.75 sec/m — roughly half the uphill cost, because eccentric quad load accumulates and gravity only partly pays back the climb. Above 5% grade, credit drops further as runners brake.

Step by step

1

Get a flat-course goal pace. If your last race was hilly, normalize via Riegel + this formula in reverse.

Flat goal: 4:30 marathon = 270 min ÷ 42.195 km = 6:24 min/km = 384 sec/km.
2

Get course profile: total ascent and total descent in meters.

Boston Marathon: ~262m total ascent, ~390m total descent over 42.195 km.
3

Compute per-km averages: ascent_m_per_km, descent_m_per_km.

Boston: 262 / 42.195 = 6.2 m/km ascent; 390 / 42.195 = 9.2 m/km descent.
4

Apply formula with appropriate constants.

Adjusted = 384 + (6.2 × 1.5) − (9.2 × 0.75) = 384 + 9.3 − 6.9 = 386.4 sec/km. Boston's descents recover only half of what its climbs cost, so it comes out slightly slower than flat even though it is net-downhill.
5

Recompute target time. Beware: even Boston's net downhill DOES add quad damage that costs in later miles. Add 30-60s overall for fatigue compounding.

Pace 386.4 sec/km × 42.195 = 4:31:44. Add 60s for cumulative quad fatigue → 4:32:44 realistic target.

Worked example

Runner with 4:30 flat-marathon ability targeting Boston Marathon

Flat-course goal pace

6:24 min/km (384 sec/km)

Course ascent

262m (6.2 m/km)

Course descent

390m (9.2 m/km)

Adjusted = 384 + (6.2 × 1.5) − (9.2 × 0.75) Adjusted = 384 + 9.3 − 6.9 = 386.4 sec/km Total time = 386.4 × 42.195 = 16,304 sec = 4:31:44

Boston's descents recover only about half of what its climbs cost, so despite being net-downhill it still runs about 1.7 minutes slower than flat on raw pace math. Quad damage from Heartbreak Hill (mile 20) and the prior descents adds another 30-90s — final target 4:32-4:33 instead of 4:30 flat.

Common variations

Minetti 2002 raw cost: at 0% grade running costs 3.6 J/kg/m. Each 1% uphill adds about 0.4 J/kg/m. The pace conversion approximates this at marathon paces; very fast runners (sub-3 hour) need slightly lower cost coefficients.

Steeper grades break linearity: above 10% grade most runners are walking, and the energetic cost flattens. Marathon courses rarely sustain >5% grade; trail marathons need a different formula (Skiba 2007).

Altitude correction is separate: above 1500m elevation, VO2 max drops ~3% per 300m. NYC Marathon is sea level so no correction. Mexico City, Denver marathons need ~5-8% pace adjustment beyond the per-km formula.

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Questions people ask next

How much does elevation gain slow your marathon pace?

Each metre of gross climb adds about 1.5 seconds to your finish time — roughly 15 seconds per kilometre on a sustained 1% uphill grade. Over a full marathon, 1000m of total ascent adds about 1500 seconds, near 25 minutes, before any descent is counted back. This rule of thumb matches Daniels' Running Formula and is consistent with Minetti's 2002 grade energy-cost curve at marathon effort.

Why is the downhill credit smaller than the uphill cost?

Each metre of descent gives back only about 0.75 seconds — half the 1.5-second cost of a metre climbed — because eccentric quad load accumulates and gravity only partly repays the climb. Climbs therefore cost about twice what descents recover, so even a net-zero rolling course runs slower than a flat one. Above about a 5% grade the credit shrinks further as runners brake on the descent.

Does net elevation or total ascent matter more?

Both matter. The net figure — total ascent costed at 1.5 sec/m minus total descent credited at 0.75 sec/m — drives the raw pace math, but total ascent still adds quad damage on top. Boston Marathon (~262m ascent, ~390m descent) comes out about 1.7 minutes slower than flat on the raw math, because its climbs cost more than its descents give back despite the net downhill. The eccentric damage from those descents then adds another 30-90 seconds in the late miles.

Do I need a separate adjustment for high-altitude marathons?

Yes. Altitude is a separate correction from the per-kilometre elevation formula. Above 1500m, VO2 max drops about 3% per 300m, so courses like Mexico City or Denver need roughly a 5-8% pace adjustment on top of the ascent/descent math. Sea-level races such as NYC need no altitude correction.

Sources

Minetti, Moia, Roi, Susta & Ferretti (2002). Energy cost of walking and running at extreme uphill and downhill slopes. , Journal of Applied Physiology — foundational energy-cost paper across grades
Townshend, Worringham & Stewart (2010). Spontaneous pacing during overground hill running. , Medicine & Science in Sports & Exercise — hill-running pacing validation
Skiba — Publications and Lectures (PhysFarm) , Physfarm — Running Stress Score methodology incl. elevation
Vernillo et al. (2017). Biomechanics and physiology of uphill and downhill running. , Sports Medicine — eccentric load + quad fatigue on descents