The terrain coefficient, written as η, multiplies the movement term of the load-carriage equation. Blacktop is 1.00 by definition. Every other surface is measured against it, and the differences are much larger than most people assume.
| Surface | Coefficient | Notes |
|---|---|---|
| Blacktop or paved road | 1.00 | Baseline surface in the original studies. |
| Dirt road or hard-packed trail | 1.10 | |
| Light brush or packed grass | 1.20 | |
| Hard-packed snow | 1.30 | |
| Heavy brush or loose dirt | 1.50 | |
| Wet or muddy trail | 1.65 | Highly variable, 1.5 to 1.8 depending on depth. |
| Soft snow, ankle deep | 1.60 | Rises steeply with depth. |
| Loose sand | 2.10 | The most costly common surface, and the one most tools get wrong. |
Where these numbers come from
They are frequently attributed to Pandolf’s 1977 paper. But that is wrong. The 1977 work used blacktop, and the coefficients come from Soule and Goldman’s 1972 study, which measured energy cost across surfaces directly.
Snow is the exception. Snow coefficients come from later work by Richmond and colleagues, which established something important: what costs you energy is not snow as such but how far you sink into it. Hard-packed snow is barely worse than dirt road. Soft snow rises steeply with depth and has no single correct value.
Sand is the one that matters
Loose sand is 2.10. Moving over it costs more than twice what the same ruck costs on pavement, because every step displaces ground that gives way under you and returns none of the energy.
A 180 lb person carrying 45 lb at 3 mph burns roughly 440 kcal/hr on pavement and roughly 765 kcal/hr on soft sand. Same load, same pace, 74% more energy.
Many rucking calculators use something near 1.2 for sand. So did this one. That under-reports a beach ruck by about 35%, and if you have ever finished a sand ruck feeling far more destroyed than the numbers suggested, this is why. The correction is logged in the changelog.
View the numbers behind this chart
| Pace | Blacktop or paved road | Dirt road or hard-packed trail | Loose sand | Soft snow, ankle deep |
|---|---|---|---|---|
| 2 mph | 259 | 271 | 394 | 333 |
| 2.5 mph | 335 | 354 | 550 | 452 |
| 3 mph | 430 | 459 | 747 | 603 |
| 3.5 mph | 546 | 586 | 987 | 786 |
| 4 mph | 684 | 737 | 1,273 | 1,005 |
| 4.5 mph | 845 | 915 | 1,609 | 1,262 |
Picking a coefficient for real ground
Real routes are mixed and the table is a set of reference points, not a lookup for every surface you will meet.
- Sidewalk, road, track: 1.0.
- Groomed gravel path or fire road: 1.1. Most park trails sit here.
- Singletrack, grass, packed field: 1.2.
- Rooty, rocky or loose trail: 1.5. Also where you will be slowest, which compounds the cost.
- Wet or muddy: 1.5 to 1.8, depending on how much your foot sinks and whether the ground pulls back.
- Beach: wet packed sand near the waterline behaves closer to 1.2. Dry loose sand above the tide line is the full 2.1. On most beach rucks you are switching between the two.
- Mixed routes: weight by time spent, not distance. You move slower on the hard ground, so it takes a larger share of your session than the mileage implies.
What the coefficient does not capture
It is a single multiplier standing in for a genuinely complicated interaction between ground, footwear, gait and stability. It does not account for footing that forces you to shorten your stride, uneven ground that demands constant stabilising work, or rock-hopping that is closer to bounding than walking. In broken terrain the coefficient probably understates the true cost.
It also does not model snow depth, which as Richmond’s work showed is the variable that actually matters in snow.
Run your own numbers
Estimated burn
406 kcal ±10%
- 478 kcal per hour
- 135 kcal per mile
- +91 vs. walking it unloaded
All inputs within validated ranges.
Engine v1.1.0 · How this is calculated · What changed
Sources
Soule RG, Goldman RF. Terrain coefficients for energy cost prediction. Journal of Applied Physiology 1972;32(5):706-708. PMID 5028188Establishes: Measured terrain coefficients across surfaces, establishing that loose sand costs roughly 2.1 times blacktop at equivalent pace and load.
Used for: The terrain coefficient table. This is the source most calculators attribute incorrectly to Pandolf 1977.
Establishes: Terrain coefficients for snow, showing cost rises sharply with sinking depth rather than snow presence alone.
Used for: The hard-packed and soft snow entries in the terrain table.
How the coefficient sits inside the wider model is covered on the Pandolf equation page and in the methodology.