EXPLAINING THE EQUATION - INPUTS

Estimating caloric expenditure is an inexact science because everyone has a unique BMR - Basic Metabolic Rate, which is NOT factored in here, and the conditions have a lot of variables. But a guesstimate is better than nothing, and the Pandolf Equation satisfies that intent. First published by Army researchers in the 1970s and updated a number of times over the years, it is the most frequently used method by scientists to estimate the metabolic cost of load carriage (what they call rucking).

The basic Pandolf Equation looks like this:

MC is the metabolic rate, given in Watts. W stands for body weight, L for the load carried. V is speed and G is the grade or slope of the terrain. The character μ is the terrain factor, including pavement, brush, snow, and sand.

The basic Pandolf equation contains three parts. The first estimates the metabolic cost of standing (or in other words, most of the work your body is doing at any given time), the second adds the weight carried, and the third estimates the additional cost of actually walking with that weight. In the last 50+ plus years, a significant number of studies have shown the basic Pandolf Equation to under-represent the caloric burn of load carriage, especially with increases in weight carried and speed (to date, militaries have had the greatest incentive to study load carriage). One of the most frequently cited, conducted by the Australian military in 2017, measured the underestimation at 12-17% at around 2.8 mph and 21-33% at 4 mph when subjects carried 22.7kg (50lbs). Other studies (including one from the same Army lab that produced the original Pandolf study) have reached similar conclusions under a variety of conditions.

An updated equation looks like this:

This updated equation serves to bring the estimate in line with the modern studies on caloric expenditure. This version places an important emphasis on the ratio of load to body weight. Two differently-sized people both carrying 20% of their respective body weights, for example, will see the same percentage difference between our formula’s estimate and the Pandolf’s (though their actual estimates will differ). For fitness inspired ruckers, we recommend a maximum carry weight of ⅓ of your bodyweight. At this limit, 33% body weight at 4 mph, this adjustment works out to a 27% higher final estimate, in line with the regression analysis from the Australian and other studies. That number–the difference between the two estimates as a percentage–will be lower for anyone carrying a smaller percentage of their body weight. The goal of this adjustment is simply to reconcile the Pandolf equation with the regression analyses that subsequent studies have found in a way that scales with the load/body weight ratio.

Here are a few examples of what it looks like in action:

This is where we see the value of adding weight to your walks. It’s not exactly rocket science to say that making things harder by adding weight will burn more calories, but we can get an idea of how effective it is. In this example, we’re looking at a 180lb rucker on flat pavement, so there’s no terrain factor or slope to consider. Each line represents a different amount of weight carried, in pounds. We can see the greater weight/speed combinations doubling the energy expenditure of an unweighted walk.

If you’re going faster than 4mph, or a 15 minute mile pace, it’s probably worth upping the weight for more of a challenge.

By playing around with the equation some more, we can see the effects of carrying weight at different speeds:

Each line represents a different weight carried at various speeds for 3 miles. This is just another way of visualizing the effect of adding weight and speed, but for a set distance (again on flat pavement). Keep in mind that in this scenario, the rate of caloric burn will increase with speed, but the time will go down, flattening the line somewhat. An increase in weight will usually be accompanied by a decrease in speed. But if we compare two adjacent lines, we can see how our caloric expenditure may stay the same with more weight (having the same y-axis value on this graph), but the upside is greater as you get used to the weight and your pace starts going back up. But there are more variables at play than weight, speed, and distance.

This chart shows what a 180lb rucker carrying 45lbs across different terrains would look like. We’re leaving slope out of it for now, so picture all this on level ground (a Florida ruck, if you will). Here we can see just how important terrain is in terms of energy expenditure. While there are legitimate reasons a person might want to ruck on pavement (it’s still a great workout), there’s so much to gain from branching out. Go hit the beach or a hiking trail, enjoy nature while burning more calories than you would rucking around the neighborhood. Hiking trails also tend to add verticality to your ruck for an even greater gain. It’s worth keeping in mind that 5 miles per hour is almost impossibly fast in difficult terrain, especially with weight, but once again the equation gives us an idea of how changing an aspect of your ruck (in this case terrain) can give you more bang for your buck, so to speak.

This graph displays energy as a function of weight, rather than by time. It’ll help to show the relationship between weight carried and calories burned on different terrains. The takeaway from all these graphs is that a person can tinker with different combinations of weight, speed, distance, and terrain to achieve their fitness goals (or just for the sake of variety). Change in each variable will feel different, but you can find the right way to ruck for you.

This one’s for the real masochists. It shows the caloric burn over different terrains at different grades. We’ve dropped the pace to 3mph, because to trudge through snow at a 15% grade your speed will decline, but it gives you an idea how much that last variable–slope–can level up your ruck. If you have a treadmill, you can see here how much extra burn you can get out of a few degrees (most max out around 15%). And if you’ve got a mountain to climb, give it a go. And let us know how it goes, we love a good story..

It is important to remember that this equation can only give an estimate of energy expenditure. Really, there are an uncountably large number of variables that will determine how many calories you actually burn. But with this equation we can at least get an idea of the metabolic value of additional weight, as well as all the other dials a person can tinker with to find what works for them. You can play around with this for yourself using our calorie calculator tool. And don’t forget that rucking isn’t just about burning calories, even if it excels at that. You’re also getting stronger, physically and mentally. The Pandolf equation doesn’t express it, but you will see an impact not just in the reduction of fat but in muscle growth. And when you embrace the suck each step is towards a better, stronger, more resilient version of yourself.