Grade-Adjusted Running Pace Calculator
Explore a Minetti-based running energy-cost adjustment for a constant gradient, with a terrain curve and flat-equivalent pace estimate.
Terrain energy model workspace
Constant-gradient energy-cost scenario
Your terrain-adjusted scenario
00:04:37 flat-equivalent time per km
Equal-metabolic-power polynomial scenario
Full result table
| Gradient % | Cost J/kg/m | Ratio to level | Equivalent min/km |
|---|---|---|---|
| -20 | 1.800032 | 0.500009 | 11.999787 |
| -18 | 1.781369 | 0.494825 | 12.125506 |
| -16 | 1.806419 | 0.501783 | 11.957359 |
| -14 | 1.876259 | 0.521183 | 11.51227 |
| -12 | 1.991372 | 0.553159 | 10.846794 |
| -10 | 2.151706 | 0.597696 | 10.038546 |
| -8 | 2.356735 | 0.654649 | 9.165221 |
| -6 | 2.605518 | 0.723755 | 8.290098 |
| -4 | 2.896757 | 0.804655 | 7.456613 |
| -2 | 3.228861 | 0.896906 | 6.689665 |
| 0 | 3.6 | 1 | 6 |
| 2 | 4.008169 | 1.11338 | 5.388994 |
| 4 | 4.451247 | 1.236457 | 4.852573 |
| 6 | 4.927054 | 1.368626 | 4.383958 |
| 8 | 5.433414 | 1.509282 | 3.975401 |
| 10 | 5.968214 | 1.657837 | 3.619173 |
| 12 | 6.529461 | 1.813739 | 3.308083 |
| 14 | 7.115344 | 1.976484 | 3.035693 |
| 16 | 7.724295 | 2.145638 | 2.796372 |
| 18 | 8.355046 | 2.320846 | 2.585264 |
| 20 | 9.006688 | 2.501858 | 2.398218 |
A simplified constant-gradient, equal-metabolic-power scenario. The fitted polynomial intercept is 3.6, not the study’s measured level mean. Restricted here to −20% through +20%. Wind, surface, biomechanics, technical descents and personal economy are not represented.
Let’s work it out.
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How to use Grade-Adjusted Running Pace Calculator
- Enter the average pace and a signed gradient for one segment.
- The calculation uses the published running-cost polynomial and assumes equal metabolic power between the slope and a level surface.
- The curve shows how the same mathematical assumption behaves across the supported gradient range.
Worked example
At zero gradient, the cost ratio is one and the flat-equivalent pace exactly matches the observed pace. At an uphill gradient the same observed pace implies a faster flat-equivalent scenario.
Formula, accuracy & limitations
With gradient g as a decimal, running cost C(g) = 155.4g⁵ − 30.4g⁴ − 43.3g³ + 46.3g² + 19.5g + 3.6 J/kg/m. Model flat-equivalent pace = observed pace × C(0)/C(g). Energy-cost ratio = C(g)/C(0).
A simplified constant-gradient, equal-metabolic-power scenario. The fitted polynomial intercept is 3.6, not the study’s measured level mean. Restricted here to −20% through +20%. Wind, surface, biomechanics, technical descents and personal economy are not represented.
These outputs use the stated model and your supplied inputs. A mathematically consistent model can still differ from personal measurements. Scenario curves and formula comparisons are not statistical confidence intervals.
Source and method context ↗Describe one reasonably constant segment
Enter the average pace and a signed gradient for one segment. A positive percentage is uphill and a negative percentage downhill. A hilly route with equal climbing and descending is not equivalent to a flat route merely because its net elevation change is zero.
Read the adjustment as a model comparison
The calculation uses the published running-cost polynomial and assumes equal metabolic power between the slope and a level surface. It then converts the ratio into a flat-equivalent pace. This is an energy-model scenario, not a personal physiological measurement or a proprietary watch algorithm.
Use the terrain curve within its limits
The curve shows how the same mathematical assumption behaves across the supported gradient range. It does not include braking, unstable footing, wind or fatigue. Technical downhill performance can differ sharply from an energetic model, so the page avoids promising real-world pace gains.
Separate fitted cost from measured level-running cost
The polynomial used on this page has an intercept of 3.6 J/kg/m. The original experiment also reports a measured level-running mean, which is a different reported quantity. Using 3.6 consistently in the numerator and denominator makes the zero-gradient ratio exactly one. Replacing only one of those values with a different level cost would break that identity. The resulting equivalent pace still assumes the same metabolic power and cannot capture an individual runner’s uphill technique, downhill braking or preferred gait.
Frequently asked questions
Why does zero gradient return the original pace?
Both costs are C(0), so their ratio is exactly one. This identity is included in the numerical checks.
Is the model a calorie calculator?
The primary output is an equivalent-pace scenario based on energy cost per mass and distance. Body mass is not entered and total calories are not calculated.
Can I use average route gradient for rolling hills?
A nonlinear cost curve means the cost at an average slope need not equal the average cost of separate climbs and descents. Analyse segments separately.
Why limit the gradient to 20%?
The interface uses a narrower practical scope than the experimental extreme slopes. That does not eliminate individual or terrain-related model error.
