Rucking Calorie Calculator

The equation, in full

This page does not use a formula of its own. It uses the one published by Pandolf, Givoni and Goldman in the Journal of Applied Physiology in 1977, which has been the standard model for load-carriage planning ever since:

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

• M — metabolic rate, in watts
• W — body mass, kg
• L — external load, kg
• V — walking speed, m/s
• G — grade, per cent
• η — terrain coefficient

Watts become kilocalories per hour by the definition of the calorie: 1 kcal is 4184 J, so kcal/h = M × 3600 ÷ 4184 = M × 0.8604.

A worked example

An 80 kg person carrying 20 kg at 5 km/h (1.389 m/s) on a level dirt road (η = 1.1):

450.8 W × 0.8604 = 388 kcal per hour, of which about 103 kcal/h is the standing term. So the ruck itself is costing roughly 285 kcal per hour net.

Why there are three answers and not one

The 1.5W term is the cost of being upright and alive. It is in the equation because the equation predicts a total metabolic rate, not an increment — and it means that a "calories burned" figure taken straight from M includes energy your body would have spent sitting on the sofa.

So the calculator reports three lines:

• Gross — everything, straight from the equation.
• Standing — the 1.5W term alone, over the same time.
• Net — the difference, which is what the ruck added.

Which one you want depends on what you are doing with it. If you are comparing two rucks, use gross; the standing term is the same in both and cancels. If you are adding this to a daily total that already assumes a basal metabolic rate, use net, or you will count the same energy twice.

What the pack actually costs

The load appears in the equation twice, and the two appearances behave very differently.

It adds to W + L, the mass being moved, which scales the walking and hill terms linearly. And it has a term of its own — 2.0(W + L)(L÷W)² — which grows with the square of the load-to-body-weight ratio. At a light load that squared term is almost nothing; at a heavy one it dominates.

For our 80 kg walker at 5 km/h on a dirt road:

Notice the steps: the first 10 kg buys 9%, the next 10 kg buys another 11, and then the increments keep growing. Doubling the load from 20 to 40 kg does not double the extra cost — it goes from 20% to 50%, two and a half times as much.

Hills are expensive

The grade term is η(W + L) × 0.35VG, and the thing to notice is that it is multiplied by both the total mass and the speed. A hill with a pack is disproportionately costly compared with a hill without one.

Our 80 kg walker with a 20 kg pack at 5 km/h on a dirt road costs 450.8 W on the flat. Put a 10% gradient under them and the grade term alone adds 534.7 W — more than the entire flat-ground cost. The total goes from 388 to 848 kcal/h.

That is why a hilly route is not a slightly harder version of a flat one, and why an average gradient across a rolling route under-reports the real cost: the climbs cost far more than the descents save, and the equation is not even willing to talk about the descents.

Why downhill is refused

Put a negative grade into the equation and the third term goes negative. Make it negative enough and the predicted cost falls below 1.5W — below the cost of standing still — which cannot be right. Walking downhill costs less than walking on the flat, and it does not cost less than standing.

The 1977 model was fitted on level and uphill walking and was never intended to run in reverse. A downhill correction was published separately, and this calculator does not implement it. Implementing half of a model you have not validated produces confident numbers with nothing behind them, which is worse than declining the question.

So the grade field accepts zero and above. If your route is genuinely net-downhill, the honest answer is that this page cannot estimate it.

Terrain coefficients

These are published values from Pandolf and colleagues and from Soule and Goldman, not estimates made here:

The coefficient multiplies the entire movement term, so these are not small adjustments. Loose sand at 2.1 more than doubles the cost of moving compared with tarmac; 35 cm of soft snow quadruples it. Our example ruck goes from 388 kcal/h on a dirt road to 637 in loose sand.

What the equation cannot do

It is a population prediction, and it has documented limits. These are worth knowing before treating any number on this page as yours.

• It under-predicts outside its fitted range. Drain and colleagues (2017) found systematic under-prediction at higher speeds and heavier loads. The calculator flags speeds above 1.9 m/s (about 6.8 km/h) and loads above 70 kg as outside the range it was built on.
• It is a walking model. Not running, not load-carrying in the hands, not stair climbing.
• It does not know about clothing. Bach and colleagues (2016) found it predicts poorly for encapsulating protective clothing, where heat stress changes the picture.
• It does not know about you. Fitness, gait efficiency, how well the pack fits, footwear, temperature, altitude, fatigue — none of these are inputs, and all of them move real energy cost.

What it is genuinely good for is comparison. The difference between 20 and 30 kg, between tarmac and sand, between flat and a 5% grade — those comparisons hold up much better than any single absolute figure, because the individual factors it cannot see are roughly the same on both sides.

METs, and comparing this with other activities

The calculator also reports the figure in METs, which is the unit activity tables use. One MET is the energy cost of sitting quietly — about 1 kcal per kilogram of body weight per hour, or 1.162 W/kg — so a figure in METs is a metabolic rate divided by your own mass, which makes it comparable between people of different sizes.

Our example ruck comes to 4.85 METs; the same walk without the pack is 4.03. That puts a 20 kg ruck at 5 km/h somewhere around brisk walking or easy cycling, and makes the point that rucking is a moderate activity carried on for a long time rather than a hard one.

The other useful comparison the calculator gives is kcal per kilometre, which for the example is about 78. Per-hour figures reward walking faster; per-kilometre figures reward carrying more and reward nothing else, which is a truer picture of what a ruck actually is.

Sources

• 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.
• Soule RG, Goldman RF. Terrain coefficients for energy cost prediction. Journal of Applied Physiology 1972;32(5):706–708.
• Drain JR, Billing DC, Neesham-Smith D, Aisbett B. Predicting physiological capacity of human load carriage — a review. Applied Ergonomics 2017.
• Bach AJE, 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 2016.

Frequently asked questions