The rucking calorie calculator uses the Pandolf equation to estimate the energy cost of loaded walking from body weight, pack weight, speed, grade, and terrain. Researchers at the US Army Research Institute of Environmental Medicine (USARIEM) published the equation in 1977, and it remains a widely used model in load-carriage research.
Need the calculator, not the math? Use our Pandolf equation rucking calorie calculator to run the formula online with your body weight, ruck weight, pace, terrain, and grade. This page explains the rucking calorie calculation behind the tool so you can see what each input changes.
Below: the formula, the variables, the terrain table, a worked example, and the models that came after.
The formula
The full Pandolf equation predicts metabolic rate (M, in watts) as:
M = 1.5W + 2.0(W+L)(L/W)² + η(W+L)[1.5V² + 0.35VG]
Where:
| Variable | Meaning | Units |
|---|---|---|
| M | Metabolic rate | watts |
| W | Body weight | kg |
| L | Load (pack + plate + contents) | kg |
| V | Walking velocity | m/s |
| G | Grade (slope) | percent |
| η | Terrain coefficient | unitless (see table below) |
The three terms each model a separate component of energy expenditure:
- 1.5W: the cost of standing still without a load, scaled to body weight
- 2.0(W+L)(L/W)²: the extra cost of standing while supporting a load, which grows with the square of the load-to-body-weight ratio
- η(W+L)[1.5V² + 0.35VG]: the cost of walking, which scales with total mass (body plus load), speed, grade and terrain
The squared load term looks dramatic on paper, but at ordinary rucking loads it's small. In the worked example below it adds under 6 watts, while moving the same 14 kg through the walking term adds about 50. For most ruckers, then, the pack's cost comes mainly from carrying more total mass, which rises roughly in step with the weight; the squared term only starts to bite when the load is heavy relative to body weight. Because the burn tracks the weight you carry, a known, fixed load is the cleanest way to dial in and progress it. We compare the common options in our ruck plate guide.
Pandolf, Givoni, and Goldman extended an earlier USARIEM walking equation (Givoni and Goldman, 1971) so it also covered standing and very slow walking, which is where the paper's title comes from. Later studies tested it against heavier, faster military loads. Drain et al. (2017) had 16 men walk at 2.5 to 6.5 km/h carrying 22.7 or 38.4 kg and found the equation under-predicted metabolic rate in every condition, by 12% to 33%. Looney et al. (2022) likewise reported that existing equations underestimate heavy military backpacking. Treat the result as an estimate, not a personal metabolic measurement.
Terrain coefficients
The η term accounts for how the surface underfoot changes energy cost. Pandolf's equation took its terrain factor from earlier USARIEM work, chiefly Soule and Goldman (1972), with snow values from a 1976 study by Pandolf, Haisman and Goldman. The commonly cited values:
| Terrain | η (terrain coefficient) |
|---|---|
| Blacktop road or treadmill | 1.0 (baseline) |
| Dirt road | 1.1 |
| Light brush | 1.2 |
| Heavy brush | 1.5 |
| Swampy bog | 1.8 |
| Loose sand | 2.1 |
| Soft snow, 15 cm (about 6 in) deep | about 2.5, rising with depth |
The categories are military ones, so a hiking trail doesn't map neatly onto any single row. A smooth dirt path sits near the dirt-road value; a rooty, rocky trail behaves more like brush.
This is why the same 30-pound ruck at the same pace burns roughly 70% more calories on a sandy beach than on pavement (about 575 against 330 an hour for a 180-pound person at 3 mph). The terrain coefficient multiplies the entire walking term of the equation, so the harder the surface is to move across, the steeper the cost.
A worked example
Here are the numbers for a typical recreational rucker:
- Body weight (W): 82 kg (180 lb)
- Load (L): 14 kg (30 lb, plate + pack + water)
- Speed (V): 1.56 m/s (3.5 mph)
- Grade (G): 0% (flat)
- Terrain (η): 1.0 (paved road)
Plug into the equation:
Term 1 (standing, no load): 1.5 × 82 = 123 W
Term 2 (standing with the load): 2.0 × (82 + 14) × (14 / 82)² = 2.0 × 96 × 0.0291 = 5.6 W
Term 3 (walking): 1.0 × (82 + 14) × [1.5 × (1.56)² + 0.35 × 1.56 × 0] = 96 × [3.65 + 0] = 350 W
Total M = 123 + 5.6 + 350 = 478 watts
Convert watts to calories per hour:
478 W × 0.86 = ~411 kcal/hr
(The 0.86 factor is a plain unit conversion: one watt sustained for an hour is 3,600 joules, or about 0.86 kcal. The result is gross energy cost, including what you'd burn standing still, which is the figure most calorie estimates report.)
So a 180-lb rucker with a 30-lb pack at 3.5 mph on pavement comes out at roughly 410 kcal/hr. Unloaded, the same walk is about 365, so the pack adds about 13% on the flat. Use our calculator if you want to skip the arithmetic.
What changes when you go uphill
Grade enters through the third term: 1.5V² + 0.35VG. The grade term scales with both velocity AND grade, so a 10% climb at 3.5 mph adds proportionally more energy cost than a 10% climb at 2.0 mph.
Re-running the worked example above with G = 10% (a steady, noticeable hill):
Term 3 becomes 1.0 × 96 × [3.65 + 0.35 × 1.56 × 10] = 96 × [3.65 + 5.46] = 96 × 9.11 = 875 W
Total M = 123 + 5.6 + 875 = 1,003 watts
That's a 2.1x increase in metabolic rate from going to a 10% grade, or about 860 kcal/hr. Each 1% of grade adds roughly 45 kcal/hr in this example, which is more than another 20 lb in the pack would add on the flat. Grade is the variable casual calorie estimates most often leave out.
A 10% grade means 10 feet of climb for every 100 feet you walk, or about 130 feet of climb over a quarter mile. If your route has hills, your calorie burn is almost certainly higher than a flat-route estimate suggests.
Where the original equation breaks down
The original equation has known weak spots:
1. Downhill grades. Plug a negative grade into the original equation and the grade term simply subtracts, so steep descents come out implausibly cheap. In measured data the cost of walking downhill bottoms out and then rises again on steeper descents, as your legs work to brake and stay stable; Santee et al. (2001) found the minimum at about an 8% descent. Our calculator uses the original equation and accepts uphill grades only (0 to 15%), so it doesn't model descents.
2. Faster walking with heavy loads. In Drain et al. (2017), the equation under-predicted at every speed tested, with the smallest errors (12% to 17%) at moderate speeds of 4.5 to 5.5 km/h and larger errors at the slowest and fastest speeds. Once your gait breaks into a jog, a walking equation no longer applies at all.
3. Heavy loads. Those trials used military loads of roughly 50 to 85 lb, and the equation read low. Looney et al. (2022) built a separate backpacking equation for the Army for exactly this reason. Treat heavy-load estimates as conservative.
4. Individual differences. The equation predicts an average. Your own fitness, gait and how the pack sits will move your real cost above or below it.
The takeaway: Pandolf is a reasonable estimate for steady walking on level to uphill ground at moderate loads, and it tends to read low as loads get heavy. For long descents it's the wrong tool.
Apple Watch vs Pandolf: why wrist-based estimates can undershoot
Apple Watch, Fitbit and most consumer wearables don't use Pandolf. They estimate energy from heart rate, motion and your personal details, and Apple's Workout app has no field for pack weight. Your heart rate does rise under load, so the watch isn't blind to the pack, but it can't use a number it doesn't have.
The implication: if your wearable scores the walk as unloaded (about 365 kcal/hr at 3.5 mph for a 180-lb person) while you're carrying a 30-lb plate, it misses roughly 45-50 kcal/hr on flat ground, about 12% of the Pandolf estimate, and about 80 kcal/hr up a 5% grade.
Garmin has added a Rucking activity with a pack-weight field, and its May 2025 software update extended pack weight to hiking and walking on supported watches. Garmin's announcement names the Instinct 3 line, which includes the Garmin Instinct 3 Solar, and the Forerunner series without listing every model, so check compatibility for a specific watch such as the Forerunner 265. On an Apple Watch, third-party rucking apps add the missing pack-weight field.
For comparing the prediction with what your body actually did, pair a load-aware calculation with a chest strap heart rate monitor, which reads heart rate more directly than a wrist sensor. A Garmin HRM-Pro Plus is one option that pairs with Garmin watches.
The models that came after
Pandolf 1977 is the foundation. Two later papers tackled the slopes it handles poorly:
Santee et al. 2001 measured 16 people walking at 1.34 m/s on grades from -12% to +12% with loads of 0, 9.1 or 18.1 kg, and proposed a model that treats downhill walking separately, because its cost can't be extrapolated from the uphill line.
Looney et al. 2019 pooled data from 95 participants across 11 studies, on grades from -40% to +45%, and developed a graded walking equation for the Army's Load Carriage Decision Aid that covers uphill and downhill walking with one formula.
If a calculator's documentation mentions a downhill correction or the Load Carriage Decision Aid equations, it is doing more than raw Pandolf 1977. Many online calculators don't say which method they use; raw Pandolf is fine for flat and uphill routes and shouldn't be trusted for long descents.
Frequently asked questions
For steady recreational rucking on flat to uphill ground with a moderate load, it's a reasonable estimate. Studies with heavy military loads found it reads low, so treat heavy-load numbers as conservative. In practice the bigger errors usually come from your inputs: underestimating pack weight (water adds up), misjudging grade on hilly routes, and picking the wrong terrain setting. Log your weight, load, route and time accurately and the estimate is useful for comparing one ruck with the next.
The (L/W)² term means the cost of supporting a load scales with the ratio of load to body weight, squared. A 150-lb person carrying 30 lb (20% of body weight) pays a bigger load term than a 200-lb person carrying the same 30 lb (15%). Doubling the pack more than quadruples that term, but it starts small: for a 180-lb rucker at 3.5 mph on the flat, going from 20 lb to 40 lb raises the total estimate from about 395 to 430 kcal an hour. Most of that increase comes from moving more total mass.
Pavement and sidewalk are η = 1.0. The published table puts a dirt road at 1.1, light brush at 1.2, heavy brush at 1.5 and loose sand at 2.1. Our calculator offers four settings: paved (1.0), dirt or gravel road (1.1), trail (1.5, the heavy-brush value) and sand (2.1). Pick the one closest to most of your route. Terrain isn't a rounding error: for a 180-lb rucker with 30 lb at 3.5 mph, moving from 1.0 to 1.1 adds about 30 kcal an hour, and the trail setting adds about 150.
It works for both. The equation doesn't distinguish between "rucking" and "hiking"; it calculates the metabolic cost of moving a loaded body across terrain. A hiker with a 25-lb daypack at 2.5 mph on a 5% grade (about 415 kcal an hour for a 180-lb person) fits the model as cleanly as a rucker with a 25-lb plate on flat pavement at 3.5 mph (about 400). The difference shows up in the V and G inputs, not the model itself.
METs (Metabolic Equivalent of Task) assign a fixed multiplier to each activity, taken from the Compendium of Physical Activities. That's fine for rough comparisons between activities, but a MET value doesn't change with your pack weight, speed, grade or terrain. Pandolf does, which makes it the better tool for estimating a specific ruck.
Pandolf KB, Givoni B, Goldman RF. "Predicting energy expenditure with loads while standing or walking very slowly." Journal of Applied Physiology 43(4): 577-581, 1977. The PubMed record lists the citation; most university libraries carry the journal, and Google Scholar can point you to available copies.
Use the equation
If you want to skip the arithmetic, our rucking calorie calculator runs the original Pandolf equation with four terrain settings built in. Plug in body weight, pack weight, pace, distance or time, and an uphill grade, and it returns calories per hour and total burn for the session.
For tracking real-world effort against the prediction, a chest-strap heart rate monitor like the Garmin HRM-Pro Plus reads heart rate more directly than a wrist sensor under shoulder straps. Our GPS watch guide explains when wrist and chest-based measurements are useful. A load-aware calculator plus a chest strap is a practical setup for comparing predicted and observed effort.
Related reading
- Rucking calorie calculator: the tool that runs this equation
- The complete rucking calorie guide: field application of the formula
- Rucking afterburn (EPOC) effect: what the equation doesn't capture, post-exercise metabolism
- Progressive overload for rucking weight loss: how to manipulate the equation's variables for adaptation
- Zone 2 rucking guide: heart-rate-based intensity tracking
