Every study this calculator depends on, what each one establishes, and which part of the engine relies on it. Each entry links to a resolvable PubMed ID or DOI so you can read the source yourself.
This page exists because an earlier version of this site cited papers by the wrong year, described one as a “re-analysis” that was nothing of the sort, and attributed terrain coefficients to a paper that did not contain them. None of it was linked, so none of it was checkable. That is a poor way to earn anyone’s trust, and this is the correction.
The papers
Predicting energy expenditure with loads while standing or walking very slowly
Pandolf KB, Givoni B, Goldman RF. Predicting energy expenditure with loads while standing or walking very slowly. Journal of Applied Physiology 1977;43(4):577-581. PMID 908672Establishes: The foundational predictive equation for the metabolic cost of walking under load, derived from US Army Research Institute of Environmental Medicine treadmill work.
Used for: The base metabolic rate calculation. Step 1 of every result on this site.
Terrain coefficients for energy cost prediction
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.
Load carriage model development and testing with field data
Santee WR, Blanchard LA, Small MG, Gonzalez JA, Blanchard LA. Load carriage model development and testing with field data. USARIEM Technical Report T01-11 2001;T01-11.Establishes: A correction factor for downhill walking. The base equation returns values below basal metabolism on descent, which the correction resolves.
Used for: Step 2, applied only at negative grades. Validated at 4 km/h and above, loads to 27 kg, grades to -12%.
Metabolic costs of standing and walking in healthy military-age adults: a meta-regression
Looney DP, Santee WR, Hansen EO, Bonventre PJ, Chalmers CR, Potter AW. Metabolic costs of standing and walking in healthy military-age adults: a meta-regression. Medicine & Science in Sports & Exercise 2019;51(2):346-351. PMID 30253591Establishes: The Load Carriage Decision Aid walking equation, from a meta-regression of standing and level walking energy cost in military-age adults.
Used for: The unloaded walking baseline used to calculate how much extra a ruck costs. Never folded into the ruck figure itself.
The Pandolf equation under-predicts the metabolic rate of contemporary military load carriage
Drain JR, Aisbett B, Lewis M, Billing DC. The Pandolf equation under-predicts the metabolic rate of contemporary military load carriage. Journal of Science and Medicine in Sport 2017;20(S4):S104-S108. PMID 28919496Establishes: Measured under-prediction by the base equation of 12-17% at 2.8 mph and 21-33% at 4 mph when carrying 22.7 kg.
Used for: The load-ratio correction in Step 3, and the basis for the correction being scaled by load-to-body-weight ratio rather than applied flat.
Terrain coefficients for predicting energy costs of walking over snow
Richmond PW, Potter AW, Looney DP, Santee WR. Terrain coefficients for predicting energy costs of walking over snow. Applied Ergonomics 2019;74:48-54. PMID 30487107Establishes: 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.
Predicting metabolic energy cost
Givoni B, Goldman RF. Predicting metabolic energy cost. Journal of Applied Physiology 1971;30(3):429-433. PMID 5544128Establishes: The earlier predictive framework that the 1977 load-carriage equation was built on.
Used for: Background and lineage on the methodology page. Not used directly in calculation.
Prediction of energy expenditure from heart rate monitoring during submaximal exercise
Keytel LR, Goedecke JH, Noakes TD, Hiiloskorpi H, Laukkanen R, van der Merwe L, Lambert EV. Prediction of energy expenditure from heart rate monitoring during submaximal exercise. Journal of Sports Sciences 2005;23(3):289-297. PMID 15966347Establishes: Sex-specific equations estimating energy expenditure from heart rate, body mass and age.
Used for: The optional heart-rate cross-check, shown alongside the primary estimate rather than replacing it.
How these are maintained
Every entry is re-verified against the primary source each quarter: authors, year, journal, volume, pages, and that the identifier still resolves. Nothing enters this list without a PubMed ID or DOI. Where a source is a technical report rather than a journal article, it is labelled as one.
If you spot an error here, please tell us. Corrections are made and logged rather than quietly edited.
Reading the research yourself
Most of this work came out of the US Army Research Institute of Environmental Medicine, which has studied soldier load carriage for over fifty years. Abstracts are free on PubMed; several of the full papers are open access. If you only read one, make it Pandolf, Givoni and Goldman (1977). It is short, and every rucking calculator you will find online is built on it, whether or not they say so.