The formula we use
The primary calculation is the Pandolf equation for loaded walking. It predicts metabolic rate in watts:
M = 1.5W + 2.0(W + L)(L / W)^2 + eta(W + L)(1.5V^2 + 0.35VG)| Variable | Meaning | Our input |
|---|---|---|
| M | Metabolic rate in watts | Calculated |
| W | Body mass in kilograms | Body weight |
| L | External load in kilograms | Ruck weight |
| V | Walking speed in meters per second | Pace |
| G | Grade as a percent | 0-15% uphill grade |
| eta | Terrain coefficient | Paved, gravel, trail, or sand |
Terrain coefficients (eta)
The terrain coefficient term in the Pandolf equation comes from a separate primary source: Soule & Goldman's 1972 paper in the Journal of Applied Physiology. They measured energy cost across six surface types and produced the multipliers still used today.
| Surface | eta value | Used in calculator |
|---|---|---|
| Treadmill / blacktop / paved | 1.0 | Paved |
| Dirt road | 1.1 | Gravel (rounded to 1.2) |
| Light brush | 1.2 | Gravel |
| Heavy brush | 1.5 | Trail |
| Swampy bog | 1.8 | Not exposed in UI |
| Loose sand | 2.1 | Sand |
Soule RG, Goldman RF. Terrain coefficients for energy cost prediction. J Appl Physiol. 1972;32(5):706-708.
Implementation details
- Body weight and ruck weight are converted from pounds to kilograms when imperial units are used.
- Pace is converted from minutes per mile into meters per second.
- Grade is clamped between 0% and 15%. The current tool models flat and uphill rucking. Downhill cost requires the Santee correction below and is not yet exposed in the UI.
- Terrain uses eta values of 1.0 for pavement, 1.2 for gravel or packed dirt, 1.5 for trail, and 2.1 for sand.
- Watts are converted to kcal/hour using the standard approximation of 1 watt = 0.86 kcal/hour.
- Total calories are calculated from either the entered duration or the duration implied by distance and pace.
- Comparison activities (walking, jogging, running) use MET values from the 2024 Adult Compendium of Physical Activities (Herrmann et al., 2024, PMID 38242596).
Validation envelope - where the model applies
The Pandolf equation was developed and validated for a specific envelope. Inside that envelope it is accurate. Outside it, expect drift:
- Loads up to roughly 40 kg (88 lbs).
- Walking speeds up to roughly 6.0 km/h (3.7 mph, or about 16 min/mile).
- Grades 0% to 10% uphill on consistent surfaces.
- Original validation cohort was young, fit, military-aged males. Reliability decreases for women, older adults, and obese populations.
Underprediction at modern military loads
Drain et al. (2017, PMID 28919496) found that the Pandolf equation under-predicts the metabolic rate of contemporary military load carriage by 12-33%, with a mean bias of +124.9 watts across the tested envelope. If you are rucking in the 30-50% body-mass load range, the true cost is likely higher than this calculator shows. The Looney 2022 LCDA equation (PMC8919998) is the modern correction for that regime and is on the build roadmap as a toggle.
The Santee downhill correction
Pandolf was designed for level and uphill walking. Applied uncorrected to downhill grades, it overestimates by 20-30%. Santee et al.'s 2001 USARIEM technical report (T01-11) introduced the correction factor for negative grades. Looney et al. (2018, PMID 29860513) found that "the Pandolf et al equation with the correction factor from Santee et al is most suitable for estimating metabolic demands when traversing complex terrain."
The current calculator UI clamps grade to 0-15% uphill. Until the downhill toggle ships, treat estimates for routes with significant descent as upper bounds.
Why this beats a generic walking calculator
A normal walking calculator usually knows body weight and speed. It does not know pack weight, terrain coefficient, or grade. Those are the variables that make rucking different from walking. A 30 lb pack on flat pavement is a different session from the same person carrying the same pack uphill on sand.
Fitness watches are useful for trend tracking, but most do not directly model external load. That means they can underestimate the cost of loaded walking or confuse a ruck with an ordinary walk unless you manually adjust the activity context.
Where the estimate can be wrong
- Individual metabolic efficiency, body composition, and fitness can move real calorie burn 10-20% above or below the estimate.
- Modern military-style heavy loads are systematically under-predicted by the Pandolf equation per Drain 2017.
- Validation data is overwhelmingly young military males. Female, older, and non-athletic populations are under-represented.
- Wind, heat, altitude, mud, route interruptions, and technical footing are not modeled.
- The comparison table uses MET values only for non-rucking activities. The rucking number still comes from the Pandolf equation.
How to use the number
Use the estimate to compare sessions and plan weekly training load. Do not treat it as a precise license to eat back calories. For fat loss, the useful pattern is consistency: similar route, similar load, similar pace, and a conservative nutrition plan.