Rucking Calorie Calculator: The Pandolf Load Carriage Equation

Rucking means walking with a weighted backpack, and the first question most people ask is how many calories it burns compared with the same walk without the pack. The most widely used answer is the Pandolf equation, published in 1977 by Pandolf, Givoni and Goldman at the US Army Research Institute of Environmental Medicine to predict the energy soldiers spend carrying loads. This rucking calories burned calculator runs it for your weight, pack, pace, grade and terrain.

Most rucking calculators print one large number. This one puts the same walk without the pack beside it, so you can see what the pack itself costs, and it says where every coefficient comes from and how far the equation has missed in published tests. It also refuses downhill grades instead of returning an impossible figure, for reasons explained below.

How the rucking calorie calculator works

The Pandolf equation predicts your metabolic rate, M, in watts. It needs your body mass W and the pack's mass L in kilograms, your walking speed V in meters per second, the uphill grade G in percent and a terrain factor η for the ground under your feet.

M = 1.5W + 2.0(W + L)(L/W)² + η(W + L)(1.5V² + 0.35VG)

• Standing, 1.5W. The cost of standing still without a load: 1.5 watts for every kilogram of body weight.
• Holding the load, 2.0(W + L)(L/W)². The extra cost of standing with a pack on. It grows with the square of the pack's share of your weight, so it is tiny for a light pack and climbs quickly for a heavy one.
• Moving, η(W + L)(1.5V² + 0.35VG). The cost of carrying your weight plus the pack at your speed and up your grade. Speed enters squared, so a faster pace costs more than its share, and each percent of grade adds a fixed amount for every meter per second you walk.
• Terrain, η. 1.0 on pavement or a treadmill, rising to 2.1 on loose sand, from Soule and Goldman (1972). The terrain section below lists all six.
• Calories. A watt is one joule per second and a kilocalorie is 4,184 joules, so watts × 0.86 gives kilocalories per hour. Multiply by the hours you ruck for the total.

For the default rucker, standing costs 1.5 × 81.6 = 122 W, holding the 13.6 kg pack adds 2.0 × 95.3 × (13.6 ÷ 81.6)² = 5 W, and moving at 1.34 m/s on flat pavement adds 95.3 × 1.5 × 1.34² = 257 W. That is 385 W in all, or 331 kcal an hour. With no pack, the same walk is 343 W, or 295 kcal an hour.

The coefficients come from Pandolf, Givoni and Goldman (1977) in the Journal of Applied Physiology. We could not open the 1977 paper online, so we took them as printed in Richmond, Potter and Santee (2015), a review by scientists at the same Army institute in the Journal of Sport and Human Performance, and checked them against that review's worked table. The calculator reproduces every Pandolf value in it to the watt, from 111 W for a 74 kg man standing unloaded to 520 W for the same man carrying 30 kg at 1.55 m/s.

Rucking vs walking calories: what the pack adds

The pack adds less than most people expect. For a 180 lb81.6 kg walker at 3 mph4.8 km/h on flat pavement, the equation gives 295 calories an hour with no pack and 331 with 30 lb13.6 kg, a 12 percent increase for a pack that is 17 percent of body weight. The standing cost stays tied to body weight alone, and the load term stays small until the pack gets heavy.

So the 10 to 30 lb packs common in recreational rucking add roughly 10 to 40 calories to an hour of walking. Looney et al. (2022), who built the Army's newer backpacking equation from walks with packs of up to 66 percent of body mass, describe the same shape: light loads cause small increases, and heavier loads cause disproportionately larger ones.

Hills, pace and ground matter more than pack weight

For the same 180 lb81.6 kg rucker, here is what each change does to an hour on the move.

Fifteen more pounds in the pack adds about as much as moving from pavement to a dirt road. Half a mile an hour more pace adds nearly four times as much, and a steady 4 percent climb adds seven times as much. Speed counts for so much because it enters the equation squared.

The six terrain factors

Soule and Goldman measured these factors on level ground at three walking speeds with three loads, and reported them as fairly independent of speed and load, as Richmond et al. (2015) summarize. The factor multiplies only the moving part of the cost, so standing still costs the same on sand as on pavement. Snow has its own factors that depend on how deep each footprint sinks (Pandolf, Haisman and Goldman 1976; Richmond et al. 2019), so it is not in the menu.

Why downhill grades are not computed

Pandolf's grade term is a straight line, so a negative grade subtracts cost, and on a steep descent the total falls below the cost of standing still. For the default rucker, the uncorrected equation gives a negative number at a 10 percent descent. The 1977 equation was built without any downhill data (Richmond et al. 2015), and measured descents behave differently. In a field study at 3 mph with packs of 0 to 27 kg, Santee, Small and Blanchard (2003) found that oxygen uptake fell on descents of 4 to 12 percent, and the earlier studies they review place the lowest walking cost on a downhill slope, not at the bottom of a straight line.

Army researchers added a downhill correction to Pandolf's equation (Santee et al. 2003), which their planning models use and which the accuracy section covers. We could only read it as reprinted in a review, not in the original technical note, so this calculator does not compute it. For a route that climbs and descends, run the climb at its average grade and the descent at 0 percent as two separate rucks, then add them. Gentle descents cost a little less than flat ground, so that total reads slightly high.

Worked examples: calories burned rucking for eight rucks

Eight rucks run through the calculator. The last column is the same walk without the pack.

Three patterns stand out. On flat ground, body weight and pace do most of the work: the 200 lb90.7 kg rucker at 3.5 mph5.6 km/h burns 44 percent more an hour than the 180 lb81.6 kg rucker at 3 mph4.8 km/h. A steady 6 percent climb on a dirt road takes the default ruck from 331 to 607 calories an hour, 83 percent more. And the 12-mile ruck march costs about 1,700 calories, 283 of them from the 45 lb20.4 kg pack.

If you ruck to lose weight, pairing your rucks with two or three strength sessions a week helps you keep muscle while you lose fat. Our comparison of the best workout apps for weight loss looks at which apps build that strength work into the plan.

Why the walking calorie calculator gives a different number for the same walk

FitCraft's walking calorie calculator also takes a backpack, and for the same walk it gives a higher number than this page. Here are four walks run through both.

The gap, 9 to 16 percent in these four walks, comes from three modeling choices.

• The base cost. The walking calculator starts from the 2024 Compendium of Physical Activities value for a 2.8 to 3.4 mph walk, 3.8 METs (Herrmann et al. 2024). Pandolf's own cost for level walking at 3 mph comes out lower, close to the ACSM walking equation that the walking calculator shows as its second figure.
• The pack. The walking calculator multiplies the whole cost, standing included, by your weight plus the pack divided by your weight, so a 30 lb pack on a 180 lb walker adds 17 percent. Pandolf leaves the standing cost on body weight alone and adds a load term that grows with the square of the pack's share, so the same pack adds 12 percent. The two methods only agree on the pack's effect when it reaches half your body weight.
• Speed and ground. Pandolf's moving cost rises with the square of speed, and its terrain factor multiplies only the moving part, 2.1 on loose sand. The walking calculator steps between Compendium pace bands and multiplies the whole cost by its surface factor, 1.8 on soft sand.

The 9 to 16 percent gap between the two is smaller than the 12 to 33 percent the Pandolf equation has missed by in some tests, so neither number is wrong. Use this page when a pack, a climb or rough ground is the point of the walk, and the walking calculator for everyday walks by pace, distance or steps.

Why some rucking calculators show 400 to 700 calories an hour

Figures of 400 to 700 calories an hour are common on rucking sites. They match the 2024 Compendium's code 17012, backpacking or hiking with a daypack, at 7.8 METs, which works out to about 446 calories an hour at 120 lb and 743 at 200 lb (Compendium walking codes). That code describes hiking terrain, not a flat sidewalk. The same table lists walking with a day pack on level ground in the city, code 17011, at 3.5 METs, about 300 calories an hour at 180 lb, close to this calculator's 331. In Pandolf's terms, a 180 lb rucker with 30 lb at 3 mph reaches the backpacking figure only on a climb of about 9 percent. FitCraft's calories burned calculator uses the 7.8 MET code for hiking with a daypack.

How accurate is this rucking calorie calculator?

The calculator runs the Pandolf equation exactly, so the real question is how close the equation comes to what people actually burn. It has been tested many times since 1977, mostly with soldiers, and its error depends on the pack, the pace and the ground. In most tests it read low, by up to 33 percent; in one it came within about 1 percent on average; and one outdoor study at a self-chosen pace found it reading 13 to 17 percent high.

Read together, the tests show a pattern by pace and pack. The equation comes closest at a brisk pace of about 3 to 3.7 mph with moderate to heavy packs on firm ground, as in Duggan and Haisman's study and Vine's 40 and 50 kg walks. It read low at slow paces in every study above that tried them, and low with loads that hamper movement, such as bomb-disposal suits. It read high only with the heaviest packs, 60 to 70 kg at 3 mph, and on a real outdoor course at a self-chosen pace. Looney et al. (2022) sum up the older Army equations as underestimating heavy military load carriage, particularly at slower walking speeds, on steep downhill grades and with contemporary military equipment.

For a typical recreational ruck, the closest test is Duggan and Haisman's, where packs of 4 to 37 kg at a brisk pace left the equation within about 1 percent on average. For one person on one ruck, expect the true figure within about 15 to 20 percent of the estimate, judging by the spread of individual errors in these studies, and more often above it than below in laboratory tests.

How good are the terrain factors?

They are less settled than the equation itself. Soule and Goldman fitted their factors to an earlier Army equation by Givoni and Goldman, not to Pandolf's. When Richmond et al. (2015) recalculated them for the Army's corrected version of Pandolf's equation, the factors shifted with speed and load. Pavement averaged 0.83 across studies, although 1.0 stayed their recommended value. For dirt and gravel roads they recommend 1.2 rather than 1.1, and sand ranged from about 1.8 to over 3 at walking speeds, with their recommended formula, 1.5 + 1.3V², giving about 3.8 at 3 mph. Read the pavement result as fair and the sand, swamp and brush results as likely low.

Downhill corrections and newer equations

The Army's planning models pair Pandolf's equation with a downhill correction from Santee et al. (2003). On a 10 km mixed-terrain course with packs of 30 and 45 percent of body mass, that combination had the smallest error of six equations tested, an average bias of −13 W (±87 W) (Looney et al. 2018). Fed with GPS speed and grade data on a complex trail, it showed no significant bias, −2 W (±12 W) (Potter et al. 2018).

Newer Army equations go further. The Load Carriage Decision Aid graded walking equation estimated uphill and downhill walking within 0.09 ± 0.40 W per kg on average across grades from −40 to 45 percent (Looney et al. 2019), and its backpacking version was more accurate than Pandolf's with heavy packs (Looney et al. 2022). The backpacking version needs your resting metabolic rate, and we could not open the 2019 graded paper to check its coefficients, so both are reported here rather than computed.

When to ignore this calculator

The equation was built and tested in healthy adults, most of them young soldiers. In these cases, skip the number or ask a clinician first.

• Pregnancy. Your weight, balance and posture change week to week, and a pack adds load to your back and pelvis. Ask your obstetric care team before rucking.
• Heart, lung or circulation conditions. A pack raises the effort of every step. See a doctor before adding one if walking brings on chest pain, faintness or breathlessness out of proportion to the effort.
• Back, hip, knee or foot problems. A recent disc injury, joint replacement, stress fracture or plantar fasciitis needs a physical therapist's plan before you add load.
• Eating disorders or recent recovery. Counting exercise calories can feed a harmful cycle. A clinician or registered dietitian who treats eating disorders is the right guide.
• Teenagers and children. The equation and its tests come from adults, so young people need separate advice on packs and loads.
• Long rucks in the heat. Calorie numbers say nothing about heat strain or fluid loss. The sweat rate calculator estimates how much fluid you lose per hour from a before-and-after weigh-in.

Related reading

References

1. Pandolf KB, Givoni B, Goldman RF. "Predicting energy expenditure with loads while standing or walking very slowly." J Appl Physiol Respir Environ Exerc Physiol. 1977;43(4):577-581. doi:10.1152/jappl.1977.43.4.577, PubMed 908672. Coefficients as printed in reference 3.
2. Soule RG, Goldman RF. "Terrain coefficients for energy cost prediction." J Appl Physiol. 1972;32(5):706-708. doi:10.1152/jappl.1972.32.5.706, PubMed 5038861. Factors as printed in reference 3.
3. Richmond PW, Potter AW, Santee WR. "Terrain factors for predicting walking and load carriage energy costs: review and refinement." J Sport Hum Perf. 2015;3(3):1-26. Open-access article page
4. Duggan A, Haisman MF. "Prediction of the metabolic cost of walking with and without loads." Ergonomics. 1992;35(4):417-426. doi:10.1080/00140139208967822, PubMed 1597173
5. Drain JR, Aisbett B, Lewis M, Billing DC. "The Pandolf equation under-predicts the metabolic rate of contemporary military load carriage." J Sci Med Sport. 2017;20 Suppl 4:S104-S108. doi:10.1016/j.jsams.2017.08.009, PubMed 28919496
6. Vine CAJ, Coakley SL, Blacker SD, et al. "Accuracy of metabolic cost predictive equations during military load carriage." J Strength Cond Res. 2022;36(5):1297-1303. doi:10.1519/JSC.0000000000003644, PubMed 32398631
7. Looney DP, Lavoie EM, Vangala SV, et al. "Modeling the metabolic costs of heavy military backpacking." Med Sci Sports Exerc. 2022;54(4):646-654. doi:10.1249/MSS.0000000000002833, PMC8919998
8. Ludlow LW, Weyand PG. "Energy expenditure during level human walking: seeking a simple and accurate predictive solution." J Appl Physiol. 2016;120(5):481-494. doi:10.1152/japplphysiol.00864.2015, PubMed 26679617
9. Weyand PG, Ludlow LW, Nollkamper JJ, Buller MJ. "Real-world walking economy: can laboratory equations predict field energy expenditure?" J Appl Physiol. 2021;131(4):1272-1285. doi:10.1152/japplphysiol.00121.2021, PMC8560389
10. Bach AJ, Costello JT, Borg DN, Stewart IB. "The Pandolf load carriage equation is a poor predictor of metabolic rate while wearing explosive ordnance disposal protective clothing." Ergonomics. 2017;60(3):430-438. doi:10.1080/00140139.2016.1173233, PubMed 27110873
11. Looney DP, Santee WR, Karis AJ, et al. "Metabolic costs of military load carriage over complex terrain." Mil Med. 2018;183(9-10):e357-e362. doi:10.1093/milmed/usx099, PubMed 29860513
12. Potter AW, Santee WR, Mullen SP, et al. "Complex terrain load carriage energy expenditure estimation using global positioning system devices." Med Sci Sports Exerc. 2018;50(10):2145-2149. doi:10.1249/MSS.0000000000001669, PubMed 29944605
13. Looney DP, Santee WR, Hansen EO, Bonventre PJ, Chalmers CR, Potter AW. "Estimating energy expenditure during level, uphill, and downhill walking." Med Sci Sports Exerc. 2019;51(9):1954-1960. doi:10.1249/MSS.0000000000002002, PubMed 30973477
14. Santee WR, Small MG, Blanchard LA. "Application of energy cost algorithms for load carriage to field data." J Human-Environ Syst. 2003;6(2):69-76. doi:10.1618/jhes.6.69
15. Looney DP, Lavoie EM, Notley SR, et al. "Metabolic costs of walking with weighted vests." Med Sci Sports Exerc. 2024;56(6):1177-1185. doi:10.1249/MSS.0000000000003400, PubMed 38291646
16. Herrmann SD, Willis EA, Ainsworth BE, et al. "2024 Adult Compendium of Physical Activities: a third update of the energy costs of human activities." J Sport Health Sci. 2024;13(1):6-12. doi:10.1016/j.jshs.2023.10.010, PMC10818145. Walking codes: pacompendium.com
17. Pandolf KB, Haisman MF, Goldman RF. "Metabolic energy expenditure and terrain coefficients for walking on snow." Ergonomics. 1976;19(6):683-690. doi:10.1080/00140137608931583, PubMed 1009916
18. Richmond PW, Potter AW, Looney DP, Santee WR. "Terrain coefficients for predicting energy costs of walking over snow." Appl Ergon. 2019;74:48-54. doi:10.1016/j.apergo.2018.08.017, PubMed 30487109

How this calculator differs from typical rucking calorie calculators

Most online rucking calorie calculators either multiply a single MET value, often the 7 to 8 METs of backpacking, by your weight and minutes, or run the Pandolf equation without saying where its coefficients and terrain factors come from. The single-value approach ignores pace, grade and ground. A Pandolf calculator that accepts downhill grades without a correction can return less than the cost of standing still on a steep descent.

This calculator runs Pandolf's three terms with coefficients checked against a published Army review, uses the six published terrain factors, and shows the same walk without the pack, so you can see what the pack itself costs. It reports calories for the ruck, per hour, per mile and in watts, refuses downhill grades rather than computing an impossible number, and gives the published error by pack, pace and ground. Its numbers are lower than many rucking calculators show, because a pack on flat ground adds less than most people expect. Every input is checked against realistic ranges, and no number appears for a pack heavier than half your body weight.