Key Takeaways
- Rucking is walking with a weighted pack. The main number here comes from the US Army's LCDA metabolic model, in its 2024 form[4]. The older Pandolf equation[1] sits beside it.
- A 180 lb person carrying 35 lb for 12 miles in 3 hours burns about 1,640 kcal by LCDA and about 1,543 by Pandolf. The same walk with no pack comes to about 1,396 by LCDA.
- The two equations do not agree exactly. In the table below they differ by up to 7%. I show both and never average them.
- Hills and soft ground move the number a lot. For the 80 kg example below, a 10% grade takes LCDA from 401 to 799 kcal an hour.
- A weighted vest has its own term in the model. The 2024 paper found the backpack term fit vest data worse, so choose the right one[4].
- Everything here comes from lab walks by healthy, active, military-age adults. Treat the result as an estimate, not a measurement of you.
How the Estimate Works
LCDA is the Army's Load Carriage Decision Aid, a planning tool for marches[2]. Researchers at its Research Institute of Environmental Medicine published the metabolic model inside it in pieces: level and graded walking[3], backpack loads[2], and weighted vests[4].
The backpack term was fit on 30 adults (27 men, 3 women) who walked on a treadmill with packs up to 66% of their body mass, at 0.45 to 1.97 m/s. That is about 1.6 to 7.1 km/h[2].
Rate (W/kg) = rest + [0.21 + terrain × (1.78 × S0.58 + 0.27 × S4 + grade term)] × (1 + 1.96 × L1.36)
Grade term = 34 × S × G × (1 − 1.051 − 1.1100G + 32)
S = speed in m/s. G = grade as a decimal. L = pack weight divided by body weight.
Watts = W/kg × body weight. kcal per hour = watts × 3600 / 4184.
For a weighted vest, the load part becomes 1 + 1.38 × L1.21[4]. The 0.21 is the 2024 paper's value for the net cost of standing. The 2022 paper had 0.19[2].
In my checks, swapping one for the other moved the result by less than 3 kcal an hour for backpack loads up to 66% of body weight.
Worked example: 180 lb, 35 lb pack, 12 miles in 3 hours
Speed = 12 miles / 3 h = 4 mph = 1.79 m/s
L = 15.9 / 81.6 = 0.19, so the load factor is 1.21
Walking term = 1.78 × S0.58 + 0.27 × S4 = 5.25
Rate = 1.16 + (0.21 + 5.25) × 1.21 = 7.78 W/kg
7.78 × 81.6 kg = 635 W = 547 kcal/h
One number in that formula is mine. The 2022 study estimated resting rate from each person's lean mass, measured by a DXA scan[2], and a calculator cannot ask for that. I use 1 kcal per kg per hour instead.
The calculator also shows the result with resting energy taken out, which does not depend on that choice.
For an error range, the 2022 paper reports a mean difference of -0.08 ± 0.59 W/kg (mean ± standard deviation) against seven earlier data sets[2]. On the worked example that is about ±124 kcal. It is one standard deviation, not a 95% range.
How to use the calculator
- Pick metric or imperial, then say whether you carry a backpack or wear a weighted vest.
- Enter your body weight and the weight of the load.
- Choose what you know: your speed and time, or your distance and time.
- Pick the ground, and enter a grade or your total climb. Leave the grade at 0 for flat.
- Press the button and read the LCDA estimate, with the Pandolf figure beside it.
The Pandolf Equation and How It Compares
Most rucking calculators use the Pandolf equation from 1977. Pandolf, Givoni and Goldman published it to predict energy cost while standing or walking with a load[1].
M (W) = 1.5 W + 2.0 (W + L)(L / W)² + η (W + L)(1.5 V² + 0.35 V G)
W = body mass (kg). L = load (kg). V = speed (m/s). G = grade in percent, so a 10% grade is G = 10. η = terrain factor.
Worked example by hand: 82 kg, 14 kg pack, 1.56 m/s, level
Standing: 1.5 × 82 = 123 W
Load: 2.0 × 96 × (14 / 82)² = 5.60 W
Walking: 1.0 × 96 × 1.5 × 1.56² = 350.4 W
The paper prints no worked example, so that arithmetic is mine.
How the two compare
The 2022 paper tested both equations against measurements. On the authors' own walking data, Pandolf had a mean difference of -0.44 ± 0.74 W/kg and LCDA had 0.01 ± 0.63. On seven earlier data sets it was -0.46 ± 0.67 for Pandolf and -0.08 ± 0.59 for LCDA[2].
LCDA was fit on that first set of data, so it has the advantage there. The seven earlier sets are the fairer test.
Drain and colleagues tested 16 men at 2.5 to 6.5 km/h with 22.7 and 38.4 kg loads. They found Pandolf read 12 to 33% low[6]. That is one study with specific loads, so I did not turn it into a correction factor.
For weighted vests the picture changes. In the 2024 paper, Pandolf had a mean difference of -0.12 ± 0.71 W/kg on twelve earlier vest data sets, and the authors call it acceptably accurate for vests[4]. They also note it overestimates the cost of standing with heavy loads.
Pandolf has no downhill answer. Its grade term just goes negative, and measured downhill cost bottoms out near -8% before rising again[7]. The calculator hides Pandolf on downhill and says why.
| Pack | LCDA | Pandolf | Pandolf vs LCDA |
|---|---|---|---|
| 0% (0 kg) | 300 | 289 | -4% |
| 10% (8 kg) | 319 | 309 | -3% |
| 20% (16 kg) | 348 | 333 | -4% |
| 30% (24 kg) | 384 | 361 | -6% |
| 40% (32 kg) | 424 | 394 | -7% |
80 kg walker at 3 mph on level pavement, backpack. Kilocalories per hour by pack size
What the Load Adds
For the worked walk, the same 12 miles with no pack comes to about 1,396 kcal by LCDA. The 35 lb pack adds about 243 kcal, which is 17.4% more.
The table shows LCDA kilocalories per hour at 3 mph on level pavement, for a backpack. Each column is a pack as a share of body weight.
| Body weight | No pack | 10% pack | 20% pack | 30% pack |
|---|---|---|---|---|
| 60 kg (132 lb) | 225 | 239 | 261 | 288 |
| 70 kg (154 lb) | 262 | 279 | 305 | 336 |
| 80 kg (176 lb) | 300 | 319 | 348 | 384 |
| 90 kg (198 lb) | 337 | 358 | 392 | 432 |
| 100 kg (220 lb) | 375 | 398 | 435 | 480 |
LCDA kilocalories per hour at 3 mph, level pavement, backpack, by body weight and pack share
Those numbers include resting energy. For the extra cost of walking and carrying only, use the "above resting" figure in the calculator.
Backpack or weighted vest
The same weight costs less in a vest than in a pack, according to the 2024 model[4]. For an 80 kg person at 3 mph on level pavement:
| Load | Backpack | Vest |
|---|---|---|
| 10% (8 kg) | 319 | 319 |
| 20% (16 kg) | 348 | 343 |
| 30% (24 kg) | 384 | 371 |
LCDA kilocalories per hour at 3 mph, 80 kg, level pavement, same load in a backpack and in a vest
That is why the calculator asks which one you carry. The paper found the backpack term, applied to the vest trials, was off by 0.41 ± 0.64 W/kg, against 0.00 ± 0.56 for the vest term (mean ± standard deviation)[4].
If you only want a walk without a load, the Steps to Calories Calculator is built on treadmill data for plain walking.
Hills and Downhill
Grade is rise over run, in percent. A 10% grade rises 10 units for every 100 you walk. For a hilly route, the calculator can turn your total climb into an average grade.
That average is an approximation, because it hides how the climb is spread out along the route.
| Grade | LCDA | Pandolf |
|---|---|---|
| -10% | 275 | not shown |
| -5% | 306 | not shown |
| 0% | 401 | 389 |
| 5% | 573 | 605 |
| 10% | 799 | 822 |
80 kg walker, 16 kg pack, 5.4 km/h, paved. Kilocalories per hour by grade
Downhill is cheaper than flat, but not free. Santee and colleagues had 16 people walk at 1.34 m/s with loads of 0, 9.1 or 18.1 kg. Cost was lowest at -8% grade, among the slopes they tested down to -12%[7].
The graded term in LCDA covers -40% to 45%, from 95 people in 11 studies[3]. I could not confirm how well that term holds for the heaviest packs on the steepest slopes, so treat those combinations with extra caution.
Ground and Terrain
Soft ground costs more. The terrain factor multiplies the walking and grade terms in both equations, and a treadmill or paved road is 1.0.
The factors here come from Richmond, Potter and Santee, a 2015 review by US Army researchers. Both LCDA papers cite their work for terrain coefficients[5].
Older calculators use Soule and Goldman's 1972 values from level ground: dirt road 1.1, light brush 1.2, heavy brush 1.5, swamp 1.8, sand 2.1[8].
Richmond and colleagues compared those with the Pandolf equation. Their results suggested the old values do not carry over, so they recommend newer ones, and I use those.
| Ground | Factor at 5.4 km/h | LCDA | Pandolf |
|---|---|---|---|
| Paved road or treadmill | 1.00 | 401 | 389 |
| Gravel or dirt road | 1.20 | 462 | 444 |
| Grass or brush | 1.18 | 457 | 440 |
| Sand | 2.08 | 729 | 689 |
| Swamp or very soft ground | 3.50 | 1,161 | 1,086 |
| Hard wet clay or ice | 1.70 | 614 | 584 |
80 kg walker, 16 kg pack, 5.4 km/h, level. Terrain factor and kilocalories per hour by ground
Sand and grass or brush depend on your speed, so the factor changes as you change speed in the calculator. The sand factor is 1.5 + 1.3 / V², with V in m/s, and grass and brush use a cubic formula[5].
The authors note that for some ground types, load and speed may have an extra effect their factors do not capture.
On this walk, sand takes LCDA from 401 to 729 kcal an hour.
The sand data behind the formula covers 0.85 to 1.95 m/s, which is 3.1 to 7.0 km/h. I could not confirm a range for grass and brush. The calculator warns outside that window.
A rough hiking trail has no factor of its own. Richmond and colleagues list rough terrain as unknown and say to treat the roughness as part of the surface you pick[5]. Snow and mud are also left out, because their factors need measurements I cannot ask you for.
Two cautions from the sources. Richmond and colleagues say there is very little data to support these factors on slopes other than zero[5]. The 2024 LCDA paper adds that terrain coefficients may need refining to carry treadmill findings over to walking outdoors[4].
What This Calculator Leaves Out
A pack and a vest at the same time. The model has a term for each, but this tool takes one load at a time.
Hand-carried loads, weapons and protective clothing. The 2024 authors say clothing like bomb-disposal suits cannot be estimated with the backpack and vest equations[4].
Faster walking and running. The same authors say the model should not be used above 1.96 m/s, about 4.4 mph[4].
Heat, cold, fatigue and very long efforts. The 2022 data are steady-state treadmill walks in temperate laboratory conditions[2], so a hot, tiring, hilly day outdoors can land elsewhere.
How heavy a pack to carry. I found no source I trust for a target weight, so this page does not give one. Ask a coach or doctor if you are building up a load.
Two things I could not fully verify. I could not read Soule and Goldman's 1972 paper, only a table reproducing it[5]. And the 2024 paper's table of formulas did not copy cleanly, so I built the model from its printed vest equation and its written description.
For running, use the Jogging Calorie Calculator. For all-day movement outside workouts, try the NEAT Calculator. For a climbing machine, see the StairMaster Calorie Calculator.
One watt is 0.86 kcal per hour, and I round half up. I apply no correction factor on top of either equation.
Frequently Asked Questions
Sources & References
- Predicting energy expenditure with loads while standing or walking very slowly (full text read from DTIC report ADA047699). Pandolf KB, Givoni B, Goldman RF. Journal of Applied Physiology (1977)
- Modeling the Metabolic Costs of Heavy Military Backpacking. Looney DP, Lavoie EM, Vangala SV, Holden LD. Medicine & Science in Sports & Exercise (2022)
- Estimating Energy Expenditure during Level, Uphill, and Downhill Walking. Looney DP, Santee WR, Hansen EO, Bonventre PJ, Chalmers CR, Potter AW. Medicine & Science in Sports & Exercise (2019)
- Metabolic Costs of Walking with Weighted Vests (formula table did not copy cleanly; model built from the printed vest equation and the text). Looney DP, Lavoie EM, Notley SR, Holden LD, et al.. Medicine & Science in Sports & Exercise (2024)
- Terrain Factors for Predicting Walking and Load Carriage Energy Costs: Review and Refinement. Richmond PW, Potter AW, Santee WR. Journal of Sport and Human Performance (2015)
- The Pandolf equation under-predicts the metabolic rate of contemporary military load carriage. Drain JR, Aisbett B, Lewis M, Billing DC. Journal of Science and Medicine in Sport (2017)
- A proposed model for load carriage on sloped terrain. Santee WR, Allison WF, Blanchard LA, Small MG. Aviation, Space, and Environmental Medicine (2001)
- Terrain coefficients for energy cost prediction (original not read; the 1972 values quoted here come from the table reproduced in Richmond et al. 2015). Soule RG, Goldman RF. Journal of Applied Physiology (1972)
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Disclaimer: This calculator provides estimates based on published formulas and population averages. Results are for informational and personal logging purposes only. Individual results may vary.