Case 1
- Your body weight
- 75kg
- Pack weight
- 20kg
- Pace
- 5km/h
- Grade
- 0%
- How long?
- 60min
- Surface
- Paved road
345kcal
Open with these valuesRucking Calorie Calculator
345kcal
Result: 345 kcalAn hour under a 20 kg pack at 5 km/h costs a 75 kg walker about 345 kcal on a paved road and 605 kcal on loose sand. The Pandolf equation splits that into a resting cost, a load penalty and the cost of moving. It is an estimate with a wide spread, not a measurement.
The numbers at a glance
Held fixed: Your body weight 75.0 kg, Pack weight 20.0 kg, Pace 5.0 km/h, Grade 0 %, Surface Paved road.
| How long? (min) | Result (kcal) |
|---|---|
| 20 | 115 |
| 40 | 230 |
| 60Your value | 345 |
| 80 | 460 |
| 100 | 575 |
| 120 | 690 |
Worked examples
Case 2
- Your body weight
- 75kg
- Pack weight
- 20kg
- Pace
- 5km/h
- Grade
- 10%
- How long?
- 60min
- Surface
- Paved road
742kcal
Open with these valuesCase 3
- Your body weight
- 75kg
- Pack weight
- 20kg
- Pace
- 5km/h
- Grade
- 0%
- How long?
- 60min
- Surface
- Loose sand
605kcal
Open with these valuesHow it's calculated
M = 1.5·W + 2·(W+L)·(L/W)² + η·(W+L)·(1.5·V² + 0.35·V·G)
- StepEnter your own weight and the pack weight separately — they do different work in the equation.
- StepSet the pace and the average grade of the route; downhill is not modelled.
- StepPick the surface — it multiplies the whole movement term.
- ResultEnter the time under load; the result scales straight with it.
What this number means
The number comes from the Pandolf equation, published in 1977 to predict the metabolic cost of walking under load. It adds three parts. The first is what standing still costs, 1.5 watts per kilogram of body mass. The second is a penalty for the load itself, and it grows with the square of the load-to-body-weight ratio — which is why a heavy pack on a light person costs more than the same pack on a heavy one. The third is the cost of moving: it scales with the square of your speed, adds a term for the grade, and is multiplied by a terrain factor running from 1.0 on a paved road to 2.1 in loose sand. The result is watts, converted here with 4184 joules per kilocalorie and the time you spend under load. Two things follow from the shape of it. Pace matters more than it feels like: the speed term is squared, so walking 20 percent faster costs about 44 percent more in that term. And surface matters as much as weight: the same hour costs 345 kcal on tarmac and 605 kcal in sand. Treat the figure as an estimate with a wide spread. Validation work finds the equation under-predicts measured metabolic rate by 12 to 33 percent at the heavy loads carried today, and individual fitness, gait and heat shift the real number further. It is not nutrition or training advice.
The equation is published, the precision is not
Pandolf, Givoni and Goldman published this in 1977 for level and uphill walking under load. Validation studies since find it under-predicts measured rates by 12 to 33 percent at modern military load weights.
Downhill is not modelled
The grade term only ever adds energy, so the equation cannot describe a descent, where the muscular cost falls but never to zero. The field therefore starts at zero percent, and a route with real descent will read too low.
The load penalty is not linear
The second term grows with the square of the load-to-body-weight ratio. Twenty kilograms on a 60 kg walker costs nearly twice the load penalty of the same pack on an 85 kg one.
An estimate, not a measurement
This is a population model, not your metabolism, and it is not nutrition or training advice. Build pack weight and grade up gradually rather than to a target number on a screen.
Commonly misread
Rucking burns roughly three times what walking burns.
Not on a road: 20 kg on a 75 kg walker at 5 km/h adds about 13 watts of load penalty to roughly 388 watts of walking. The big multipliers here are speed and surface, not the pack.
A downhill stretch cancels out the uphill one.
The equation has no negative grade term and the field starts at zero. Descending costs less than climbing but far more than standing still, so a hilly route reads low.
The pack weight is what makes rucking hard on sand.
The terrain factor multiplies the whole movement term, body weight included. Loose sand turns 345 kcal into 605 kcal for the same hour and the same pack.
Reference table
| Surface | Terrain factor η | Watts | 1 h at 75 kg + 20 kg, 5 km/h |
|---|---|---|---|
| Paved road | 1.0 | 401 W | 345 kcal |
| Dirt road | 1.1 | 428 W | 369 kcal |
| Light brush | 1.2 | 456 W | 392 kcal |
| Heavy brush | 1.5 | 538 W | 463 kcal |
| Swampy bog | 1.8 | 621 W | 534 kcal |
| Loose sand | 2.1 | 703 W | 605 kcal |
Questions
What is the Pandolf equation?
It is an empirical formula published in 1977 by Pandolf, Givoni and Goldman for the metabolic cost of standing or walking with an external load. It returns a metabolic rate in watts from body mass, load, speed, grade and a terrain factor. It became the standard military model for load carriage.
How accurate is the estimate?
Treat it as a wide bracket rather than a figure. Validation work finds it under-predicts measured metabolic rate by 12 to 33 percent at the heavy loads carried today, and individual fitness, gait, footwear and heat move the real value further.
Why can I not enter a downhill grade?
The grade term in the published equation only adds energy, so a negative value would produce a number the model was never fitted for. Descending does cost less than climbing, but the equation cannot say how much less.
Does the terrain factor really change that much?
Yes, because it multiplies the entire movement term, not just the pack. The same hour at 75 kg with a 20 kg pack comes to 345 kcal on a paved road, 463 kcal in heavy brush and 605 kcal in loose sand.
Should I eat back the calories the calculator shows?
This page cannot answer that, and it is not nutrition advice. The figure is a population estimate with a wide spread, and it is gross energy, which includes the resting metabolism you would have spent anyway.
Sources and last check
Information, not medical advice.