Ruck calorie burn estimator

The equation, in full

Every coefficient below is read from the code that computed your answer, so what you see is what ran.

What each symbol means

Kilocalories are watts times seconds divided by 4184, which is how many joules there are in a kilocalorie.

A pound is 0.45359237 kilograms, a mile is 1609.344 metres and a minute is 60 seconds. All three are exact definitions rather than approximations.

Where the equation comes from

• Pandolf KB, Givoni B, Goldman RF. Predicting energy expenditure with loads while standing or walking very slowly. Journal of Applied Physiology 1977 Oct;43(4):577-581. doi:10.1152/jappl.1977.43.4.577.
• Soule RG, Goldman RF. Terrain coefficients for energy cost prediction. Journal of Applied Physiology 1972 May;32(5):706-708. doi:10.1152/jappl.1972.32.5.706.
• 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.
• Richmond PW, Potter AW, Santee WR. Terrain factors for predicting walking and load carriage energy costs: review and refinement. Journal of Sport and Human Performance 2015;3(3):1-26. doi:10.12922/jshp.0067.2015.

What this equation cannot do

The equation was built for military load carriage over firm ground, at walking speeds, from a small and entirely male sample, and from steady bouts rather than from stop and start days out. Loads in the source studies reached about 55 kilograms. It had no downhill data at all in its development, which is why this page never offers you a descent and never credits one. Inside that envelope it is the best published option there is. Outside it, it is extrapolating.

The published equation has a terrain factor for the surface underfoot, and this page holds it at 1 for every terrain, which is the value for blacktop and treadmill. That means anything softer than a firm path reads low here. The published table further down gives you the correction: the factor multiplies the movement term of the equation, the third one, and loose sand roughly doubles it.

The terrain choice is not a surface. It is an equivalent steady grade applied across the whole distance: 2 percent for mixed and 4 percent for hilly, which works out at 106 and 211 feet of climbing a mile. If you know your route climbs more than that, the estimate is low for you. This approximation is the single largest source of error on this page.

This is a walking equation and it stops applying where walking stops. This page draws that line at about 13.4 minutes a mile, and the line is ours rather than one the paper sets. What the research does support is that the estimate gets less reliable the faster you go.

Unloaded walking is its weakest case. With nothing on your back the load term drops out completely and the estimate leans entirely on the 1.5 watts per kilogram standing term and on the movement term, neither of which was the point of the study.

No descent credit is modelled. The 2 percent applied to mixed ground charges you for every foot of climbing and neither charges nor credits you for the descending, because walking downhill at a gentle grade is a little cheaper than walking on the level rather than free.

The two assumptions this page adds pull in opposite directions, and neither one is tuned against the other. Holding the terrain factor at 1 reads low on anything softer than blacktop. Charging the climbing with no descent credit reads slightly high on a rolling route. They are named separately because correcting one against the other would be tuning rather than physiology.

Measured energy cost is typically 10 to 30 percent away from what this equation predicts. It is at its most accurate between 17.6 and 21.5 minutes a mile, which is slower than most people actually ruck, and it gets worse at both slower and faster paces than that.

The direction of that error is not uniform, so this page does not pick a side. Published checks find the equation reading low at light and moderate loads and reading high at very heavy ones, and long efforts drift further as the hours add up. That is why the number comes with a percentage either way rather than with a promise that it errs in your favour. The 10 to 30 percent band is the honest one.

The honest reading of any single output here is a range rather than a number. Individual metabolic efficiency varies by a wide margin either way, and the 10 to 30 percent band is where to hold it.

How this estimator works

The equation adds three costs together. The first is what your body spends holding itself up, 1.5 watts for every kilogram of you. The second is the price of carrying something on your back, and it grows with the square of the load as a share of your body weight, which is why a heavy ruck costs far more than the same number of pounds of extra body weight. The third is the cost of moving, which scales with your speed squared and with the grade, and it is the only term the terrain touches.

Terrain here is about hills rather than about what the ground is made of, so it feeds the grade term and nothing else. Flat is 0 percent, mixed is 2 percent and hilly is 4 percent, applied as a steady grade across the whole distance. In feet that is 0, 106 and 211 feet of climbing a mile, so you can check the assumption against a route you already know.

Two numbers come out of that one equation and nothing is added to make the second one. The total is all three terms. The net figure is the total minus one thing and one thing only: the 1.5 watts per kilogram the equation charges you for holding yourself up, which you would have spent existing for that long whether you rucked or not. Everything else stays in, the cost of wearing the load included, because carrying it is part of what the ruck cost. There is no MET table here, no resting metabolic rate constant and no second source of physiology - the baseline that comes out is already inside the published equation, and that is exactly why the two numbers can never disagree about where the line between them falls.

This page recommends no load at all. The ruck weight calculator does that, and it is the page to use if the question is what you should be carrying rather than what a carry costs. The only load opinion here is a warning, and it fires when the weight you entered is heavier than 50 percent of your body weight, which is the heaviest share this site will program for anyone.

See what you should be carrying

Published terrain factors, for the surface underfoot

These are the published surface coefficients, and this calculator does not apply any of them. It holds the factor at one, which is the blacktop value. To correct by hand, multiply the movement term of the equation, the third one, by the factor for your surface. It multiplies that term and never the two standing terms.

These coefficients are conventions rather than precision constants. They were fitted to the earlier Givoni and Goldman equation rather than to the one on this page, and a later USARIEM review by Richmond, Potter and Santee, cited in full below, back calculated them from the raw data of Soule and Goldman through the Pandolf equation and arrived at materially different numbers: loose sand came out somewhere between 2.8 and 6.5 against the 2.1 tabulated here. Treat any factor in this table as a rough correction rather than as a measurement.

Calories per mile at a glance

Gross kilocalories per mile at 15 minutes a mile on flat ground. These are total figures, so they include the metabolism you would have spent standing still. Pick your row, then your column.

Common questions