FitHalo Calorie Calculations

Author: Jacob Johnston, FitHalo Developer
Last Updated: November 2025

Table of Contents

1. Introduction

FitHalo has a number of unique activity types that aren’t provided natively in watchOS or iOS. This means that Apple has not provided any built-in way to determine the amount of calories burned during the activities. FitHalo, thus, provides its own estimations. These caloric estimations are modeled, as much as possible, based on scientific literature around the specified activity.

This article is for the nerds, the scientifically minded, and the others who may be looking to replicate some of these methodologies in their own applications. In it, I provide the formulas FitHalo uses, reference to the relevant literature, and some of the data used to create the caloric expenditure models used by FitHalo.

I’m always open to adjusting these formulas as new literature becomes available. So, if you’ve noticed a big glaring flaw in my models, have some new publication I should be looking at, or want to simply suggest a feature – drop me a line from the Support section within the FitHalo app.

Disclaimer: These calorie estimates are approximations based on limited studies and modeled data. They’re intended for general guidance, not medical or metabolic diagnosis.

2. Limitations

Flaws Up Front

Let’s start with the elephant in the room: there’s a lot of extrapolation from very small data sets here. If this were ever needed for clinical application, the majority of these studies don’t come anywhere near the sample sizes or statistical power one would need just to avoid being laughed out of the room when presented for peer review or regulatory approval (and that’s before I layer on some of my tenuous assertions for fitness tracking). So - I get it - the data may be weak, but it’s better than just making it up entirely - which I’m sad to say a lot of online calorie calculators and niche fitness tracking apps appear to do. At least I’m transparent about my approach and its origins!

Now let’s talk about the other very large elephant in the room (yes, it’s a crowded room): estimating metabolic burn for activities is a flawed and messy activity even with lots of great data to model from. So, while FitHalo still attempts to do its best at estimating caloric burn, it doesn’t take much digging into scientific literature to see that, unless you personally have a mask strapped to your face to measure oxygen consumption and carbon dioxide production, you’re probably getting a flawed estimation of caloric burn.

Practical Advice: Log Food & Weight, Not Exercise

If you’re looking to get a good estimate of caloric consumption so that you can adjust your diet accordingly, there actually is a good approach you can take - the only caveat is that you need to log all of your food intake and weigh yourself frequently. With just these two pieces of information, however, it’s relatively simple math to work backwards and understand your daily caloric consumption (at least as a weekly or monthly average). My favorite app to do this right now is MacroFactor. FitHalo and its author have no affiliation with MacroFactor, but it’s an absolutely wonderful app backed by a team that appears to care deeply about applying science and research to health.

3. Exercise Types

3.1 Loaded Carriage - Weighted Vests and Rucking

Weighted vest and rucking activities (collectively referred to as “loaded carriage”) have some of the better-studied caloric expenditure estimates. It turns out, militaries around the world have a whole lot of interest in understanding how many calories their soldiers are burning carrying around heavy backpacks all day (so they can, presumably, know how much they need to be feeding them).

Throughout the 1960s-1970s, the U.S. Army Research Institute of Environmental Medicine (USARIEM) conducted a number of military physiology and human performance programs. This was directly funded through the Department of Defense with the goal of providing good, quantitative models for logistics requirements about soldiers (e.g., how much food to provide? how long can marches be? how do weather and terrain impact these things?).

One result of this effort was a publication titled “Predicting energy expenditure with loads while standing or walking very slowly” (Pandolf et al., Journal of Applied Physiology, 1977). It provided this formula for calculating metabolic energy consumption during loaded carriage.

\[ M = 1.5W + 2(W + L) \ \left( \frac{L}{W} \right)^2 + \mu (W + L) \ \left( 1.5V^2 + 0.35VG \right) \]

In this equation:

  • \(M\) = metabolic rate (watts)
  • \(W\) = body weight (kg)
  • \(L\) = load weight (kg)
  • \(µ\) = terrain coefficient (see below)
  • \(V\) = walking speed (m/s)
  • \(G\) = grade/incline percent (e.g., 5% would be 5.0)
Table 1 - Terrain Coefficients Used in the Pandolf Equation for Loaded Carriage
Terrain Type Coefficient
Pavement 1.0
Trail 1.2
Sand 2.0
Snow 3.0

In early 2025, GoRuck (a company that produces great rucking gear - again, no affiliation with FitHalo) updated their website with a new calorie estimation calculator and provided conjecture that more-recent scientific literature supported a generally-higher caloric burn rate when rucking. They made reference to, in particular, a paper that was bluntly titled “The Pandolf equation under-predicts the metabolic rate of contemporary military load carriage” (Drain et al., Journal of Science and Medicine in Sport, 2017), which appeared to demonstrate an error rate of 12-33% in the original Pandolf Equation. GoRuck published a modified equation, using the same variables as the Pandolf Equation, that compensates for this error:

\[ M = 1.5W + 2(W + L) \ \left( \frac{L}{W} \right)^2 + \mu (W + L) \ \left( 1.5V^2 + 0.35VG \right) \ 1.1 \ \left( 1 + \frac{\sqrt{0.3V^2}}{7} + 0.25 \left( \frac{VL}{W} \right)^2 \right) \]

FitHalo lets users choose between the Pandolf Equation or the GoRuck equation as its basis for caloric estimates during loaded carriage type exercises.

3.2 Sauna

I have yet to find any big military-funded studies on caloric consumption in the sauna. I guess no big world superpowers get there by having their soldiers spend time relaxing in a sauna all day. What we do have, however, is a nice 2019 paper titled “Correlations between Repeated Use of Dry Sauna for 4 x 10 Minutes, Physiological Parameters, Anthropometric Features, and Body Composition in Young Sedentary and Overweight Men: Health Implications” (Podstawski et al., BioMed Research International, 2019).

In this study, forty-five participants were exposed to a series of four repeated sauna sessions, strapped to the usual array of masks and equipment to measure their metabolic activity. As sauna exposure time went on, heart rate increased, and so did their caloric burn – dramatically. By the last sauna session, the mean caloric consumption was a whopping 10.4 times that of their mean basal metabolic rate. This seems surprising, except that you also observe the participants’ heart rates went as high as 168, and only as low as 135 during this last sauna session. Their hearts were working hard.

It’s not a huge logical leap to reason that the cause for the increased energy expenditure is the amount of extra cardiovascular work that starts to happen. That, in turn, also raises the question of whether we can use standard models for estimating the relationship between heart rate and calorie burn. The paper titled “Prediction of energy expenditure from heart rate monitoring during submaximal exercise” (Keytel et al., Journal of Sports Sciences, 2005) provides a set of regression formulas for that exact estimation and needs only heart rate, sex, age, and weight. This study has actually been used as the basis for caloric consumption estimates by a wide variety of fitness wearables - especially for activities when motion data is unavailable. The regressions are separated for men and women as the following:

\[ M_{\text{men}} = \frac{-55.0969 + (0.6309 \times HR) + (0.1988 \times W) + (0.2017 \times A)}{4.184} \]
\[ M_{\text{women}} = \frac{-20.4022 + (0.4472 \times HR) - (0.1263 \times W) + (0.074 \times A)}{4.184} \]

In these equations:

  • \(M\) = metabolic rate (kcal/min)
  • \(W\) = body weight (kg)
  • \(HR\) = heart rate (bpm)
  • \(A\) = age (years)

Since we have the mean heart rate and age data from the Podstawski et al. sauna study, we can do a head-to-head comparison between the actual observed caloric consumption versus what would have been predicted by following the Keytel et al. model.

Table 2 - Comparison of Measured Sauna Energy Expenditure vs. Keytel Predicted Values
Heart Rate (Mean) Podstawski et al. (2019), Sauna Study (kcal/10-min) Keytel et al. (2005) (kcal/10-min) Formula Percent Difference
98.00 73.04 66.89 -8.41%
109.67 93.82 84.48 -9.95%
121.36 114.91 102.11 -11.14%
133.36 131.40 120.21 -8.52%

When mapped against the data of the 4x10 sauna study, the results came out pretty perfectly. Mean caloric consumption in the sauna study at all data points was between 8.41% and 11.14% of the Keytel study for the mean weight (85.86 kg) and age (20.76 years) of the all-male participants. Note that the sauna study consumption was always slightly higher than the Keytel regression would have predicted.

So - what does FitHalo do? Well, it just uses the Keytel formula with a 10% increase in caloric consumption to account for the differences observed in direct sauna studies:

\[ M = M_{\text{Keytel}} \times 1.1 \]
Table 3 - Accuracy of the FitHalo Sauna Formula Relative to Measured Energy Expenditure
Heart Rate (Mean) Podstawski et al. (2019), Sauna Study (kcal/10-min) FitHalo Formula Percent Difference
98.00 73.04 73.59 +0.75%
109.67 93.82 92.95 -0.93%
121.36 114.91 112.35 -2.28%
133.36 131.40 132.25 +0.65%
Sauna validation plot comparing measured energy expenditure with the Keytel prediction and FitHalo’s adjusted formula.
Comparison of measured caloric expenditure from Podstawski et al. (2019) against both the Keytel et al. (2005) prediction and the FitHalo-adjusted formula. The measured values come from 4×10-minute dry sauna sessions in young men, showing that the standard Keytel regression slightly underestimates energy expenditure while the FitHalo model closely tracks the empirical data.

As you can see, this maps really well – at least for the small, male-only data set that is available to us. Hopefully some university somewhere, soon, will replicate or expand upon this experiment with a more diverse set of demographics as I would love FitHalo to be able to validate (or refine) its formula against a second data set.

3.3 Cold Plunge

Creating a model for cold plunge has been a bit more challenging than other activity types because cold plunge does not appear to have the same correlation to elevated heart rate as sauna or movement-based activities. Yet, there does seem to be an elevation in metabolic rate when measuring VO₂.

The most direct study I have seen showing the metabolic effects of immersion is titled “Human physiological responses to immersion into water of different temperatures” (Srámek et al., European Journal of Applied Physiology, 2000). In this study, 10 participants were recorded in 1-hour immersions of water at various temperatures, in a random order, with a week between sessions. The water temperatures were 32 °C (89.6 °F), 20 °C (68 °F), and 14°C (57.2°F). The results showed modest changes in heart rate, but significant changes in VO₂.

Table 4 - Metabolic and Heart-Rate Responses to Water Immersion at Different Temperatures (Srámek et al., 2000)
Water Temperature Δ Metabolic Rate Δ Heart Rate
32 °C / 89.6 °F Similar -9 BPM
20 °C / 68 °F +93% VO₂ Similar
14 °C / 57.2 °F +350% VO₂ +3 BPM

The publication then goes on to describe lots of really interesting things about how/why our bodies behave the way they do when exposed to different water temperatures (including measures of temperature, blood pressure, and some notable hormone changes). It’s definitely worth a read if you’re into cold plunge! The results are all interesting, but they DO create a fitness tracking conundrum. Often, we rely heavily on heart rate measurements for caloric estimates (e.g., the Keytel formulas), but this doesn't work well here.

So - where does that leave FitHalo? In absence of direct biometric data that FitHalo can use to map to metabolic consumption for cold plunge, it instead uses the cold plunge temperature the user specifies. Temperature is converted to a multiplier for base metabolic rate (extrapolated from the multiplier that applied to VO₂ in the data set). Fitting the logarithmic nature of this curve to the data we have available, while also not allowing a runaway caloric multiplier for even colder temperatures, we get a curve using the following formula:

\[ M(T) = M_{\text{BMR}} \times \left( 1 + \frac{5.5}{1 + e^{\,0.36\,(T - 15.57)}} \right) \]

In this equation:

  • \(M(T)\) = metabolic rate for a temperature
  • \(M_{\text{BMR}}\) = basal metabolic rate
  • \(T\) = temperature (degrees Celsius)

Any power units for metabolic rate may be used so long as \(M(T)\) and \(M_{\text{BMR}}\) match. This formula produces the following metabolic rate mapping.

Table 5 - FitHalo Predicted Metabolic Multipliers for Cold-Water Immersion by Temperature
Water Temperature Δ Metabolic Rate
32 °C / 89.6 °F +1%
30 °C / 86 °F +3%
25 °C / 77 °F +17%
20 °C / 68 °F +93%
15 °C / 59 °F +303%
10 °C / 50 °F +484%
5 °C / 41 °F +538%
Cold plunge validation plot showing FitHalo’s curve vs Srámek VO₂ data.
FitHalo’s temperature-based metabolic multiplier curve plotted against the three available VO₂ data points from Srámek et al. (2000). Because the study only tested water immersion at 32°C, 20°C, and 14°C, values for colder temperatures represent extrapolation, not measured data.

3.4 Stroller Walks & Runs

There have been a handful of studies that provide data on the metabolic costs for pushing a stroller around. FitHalo bases its model on data from two papers.

Study 1: Stroller Weights Compared

The first study, described in the publication “Physiologic Responses to Running with a Jogging Stroller” (Gregory et al., International Journal of Sports Medicine, 2012), had participants run without a stroller, with a jogging stroller loaded to 25 lbs (11.36 kg), and with a jogging stroller loaded to 50 lbs (22.72 kg). Some trials were done on an indoor track, and others were done on an outdoor greenway. Trials were also split between self-paced versus a controlled pace. All tests were done with strollers specifically designed for jogging (i.e., the kind that offer minimal resistance during exercise).

On a flat, smooth indoor track - strollers of either weight did not seem to significantly alter VO₂ or heart rate. The trials on the less-flat and less-smooth greenway, however, showed increased VO₂ consumption with higher perceived exertion levels from participants (though, interestingly, heart rate remained largely unchanged - I speculate because participants were likely already near max heart rates).

Study 2: Strollers on an Incline

The second study, described in the publication “Energetic Cost and Kinematics of Pushing a Stroller on Flat and Uphill Terrain” (Sandbakk et al., Frontiers in Physiology, 2020), specifically looked at the metabolic costs associated with walking and running on different incline levels (1% grade vs 10% grade) with, and without, a stroller. Participants were placed on a big ol’ treadmill and asked to push at various paces (from brisk walking to pretty intense running).

The results are what most people would expect (and also mostly in line with the Gregory et al. study). The difference between stroller and no stroller was minimal on a flat surface and much more profound on an incline.

Putting it Together

So, with these two studies providing some useful data, let’s try to model how FitHalo should be handling caloric consumption. As a starting point, I always like to see how the Keytel formula (described above) would predict energy expenditure and compare it to the actual empirical data from the studies.

First, we convert the VO₂ reported in the studies (mL·kg−1·min−1) to kilocalories per minute (i.e., what the Keytel formula reports) using:

\[ M(\text{kcal} \ \text{min}^{-1}) \;=\; \frac{\dot V\!O_2 \;(\mathrm{mL \ kg^{-1} \ min^{-1}})\;\times\;m\;(\mathrm{kg})}{1000}\;\times\;5 \]

Both studies provided mean ages and body masses of participants, but did not divide their data sets between men and women. Since the Keytel formulas are split between men and women, each of these conversions was done using both formulas and then weighted based on the makeup of their respective studies. Gregory et al. was 60% women and 40% men, and Sandbakk et al. was 53% women and 47% men.

Table 6 - Comparison of Keytel Predictions vs. Measured VO₂-Derived Caloric Expenditure (Gregory et al., 2012)
Trial Heart Rate (Mean) VO₂ -> kcal/min Keytel Estimate (kcal/min) Δ (%) VO₂ vs Keytel
Indoor Track (Controlled Pace)
No stroller 148 10.6 10.1 -5%
25 lb stroller 149 10.6 10.2 -4%
50 lb stroller 154 10.6 10.6 0%
Indoor Track (Self-Paced)
No stroller 163 12.2 11.7 -4%
25 lb stroller 166 12.7 12.1 -5%
50 lb stroller 166 12.5 12.1 -3%
Outdoor Greenway (Controlled Pace)
No stroller 160 14.1 13.8 -2%
25 lb stroller 164 15.1 14.4 -5%
50 lb stroller 164 15.1 14.4 -5%
Outdoor Greenway (Self-Paced)
No stroller 168 15.4 14.7 -5%
25 lb stroller 170 16.3 15.1 -7%
50 lb stroller 172 16.8 15.5 -8%
Table 7 - Keytel Prediction Accuracy Across Stroller Trials on Flat and Incline Surfaces (Sandbakk et al., 2020)
Trial Heart Rate (Mean) VO₂ -> kcal/min Keytel Estimate (kcal/min) Δ (%) VO₂ vs Keytel
Flat (1% Incline) - Walking (6 km/h)
No stroller 103 6.0 5.8 -3%
24 kg stroller 106 6.4 6.0 -6%
Flat (1% Incline) - Medium Run (8-9 km/h)
No stroller 132 11.0 10.3 -6%
24 kg stroller 140 11.9 11.1 -7%
Flat (1% Incline) - Fast Run (11-12 km/h)
No stroller 157 14.3 13.5 -6%
24 kg stroller 164 15.4 14.5 -6%
Uphill (10% Incline) - Walking (5 km/h)
No stroller 119 9.1 8.6 -5%
24 kg stroller 132 11.2 9.9 -12%
Uphill (10% Incline) - Medium Run (6.5-7.5 km/h)
No stroller 150 14.4 13.2 -8%
24 kg stroller 168 17.3 15.5 -10%
Uphill (10% Incline) - Fast Run (7.5-8.5 km/h)
No stroller 163 16.2 14.3 -12%
24 kg stroller 180 19.2 16.8 -13%

Taking a look at this data, a few things are notable:

  • The Keytel formula actually does a commendable job all by itself, never being more than 13% off from the empirical data. FitHalo could probably use the Keytel formula alone and be accurate enough for most people’s tastes.
  • Introducing incline or challenging surfaces causes the Keytel formula to drift off. There are a few plausible reasons why this might be happening:
    • The linear relationship between heart rate and VO₂ works at sub-maximal heart rates, and the average heart rates of participants reached near-maximal levels in the more-intense trials.
    • Keytel was modeled on steady-state exercise types. The greenway terrain, in particular, could have had varied intensities in traversal.

However, we do have another model that incorporates an added term for incline: the formulas we use for loaded carriage - Pandolf Equation and the GoRuck equation. So, as an experiment, I just added that term to the Keytel equation (and adjusted the multiplier to convert from watts to kcal/min) and de-emphasized the value of weight - after all - pushing a stroller is a lot easier from carrying its full weight on your back. Yeah, I know, this is a "creative" (read: admittedly scientifically and mathematically invalid) method fitted to a very specific data set, but it will be the heuristic FitHalo uses until a more validatable source comes through.

Thus, FitHalo’s formula ends up being:

\[ M = M_\text{Keytel} + .295 \times (W + L) \times \left( 0.0049 G \right) \]

In this equation:

  • \(M_\text{Keytel}\) = the metabolic rate predicted by the Keytel formula (kcal/min)
  • \(W\) = body weight (kg)
  • \(L\) = weight of the stroller and its contents (kg)

When this formula is used against the empirical data from the Sandbakk et al. study - we get:

Table 8 - FitHalo Stroller Formula Performance vs. Observed Energy Expenditure (Sandbakk et al., 2020)
Trial Heart Rate (Mean) VO₂ -> kcal/min FitHalo Estimate (kcal/min) Δ (%) VO₂ vs FitHalo
Flat (1% Incline) - Walking (6 km/h)
No stroller 103 6.0 5.9 -2%
24 kg stroller 106 6.4 6.1 -5%
Flat (1% Incline) - Medium Run (8-9 km/h)
No stroller 132 11.0 10.4 -5%
24 kg stroller 140 11.9 11.2 -6%
Flat (1% Incline) - Fast Run (11-12 km/h)
No stroller 157 14.3 13.6 -5%
24 kg stroller 164 15.4 14.6 -5%
Uphill (10% Incline) - Walking (5 km/h)
No stroller 119 9.1 9.6 +5%
24 kg stroller 132 11.2 11.2 0%
Uphill (10% Incline) - Medium Run (6.5-7.5 km/h)
No stroller 150 14.4 14.2 -1%
24 kg stroller 168 17.3 16.8 -3%
Uphill (10% Incline) - Fast Run (7.5-8.5 km/h)
No stroller 163 16.2 15.3 -6%
24 kg stroller 180 19.2 18.1 -6%
Stroller running validation plot comparing measured VO₂, Keytel, and FitHalo estimates.
Measured energy expenditure (VO₂-derived kcal/min) from Sandbakk et al. (2020) compared with both the Keytel heart-rate regression and FitHalo’s stroller-adjusted model. The scatter plot illustrates how the FitHalo adjustment improves prediction accuracy particularly during incline and high-effort trials.

This gave FitHalo a closer match on every point (and bonus calories for users doing those steep hill-climb workouts).

4. Closing Thoughts

Again, I want to acknowledge the premise that I very likely overfitted some of these models to very limited data sets. Yet, I also want to emphasize that this should still perform significantly better than most online calculators out there, as well as simply choosing to log an “Other” workout type on the Apple Watch. Likewise, none of FitHalo’s custom workout types will be using the Walk, Run, or Hike underlying workout types that make an outright assumption you are not carrying or pushing any sort of load (at the time of this writing) - and have the consequence of really punishing your Cardio Fitness score in Apple Health.

If you see some smart ways I could improve these even further, find new studies, or just have something you want to share with me - please reach out to me.