What Energy Expenditure Means
Energy expenditure (EE) is the energy the body uses, normally reported in kilocalories (kcal). Total Daily Energy Expenditure (TDEE) is composed of Basal Metabolic Rate (BMR), or resting energy used to maintain basic body functions; the Thermic Effect of Food (TEF), or energy used to digest and process food; Exercise Activity Thermogenesis (EAT), or energy expended during structured exercise; and Non-Exercise Activity Thermogenesis (NEAT), or energy expended while active but not related to structured exercise. For an app, it is important to distinguish between resting/base calories, active calories, and total daily calories because they are not the same measurement.
How Mobile Apps Estimate Calories
A phone app does not directly measure energy expenditure. It estimates it from user information and sensor data. Apps commonly combine age, sex, height, weight, and sometimes an activity-level setting with accelerometer motion, step count, speed, distance, GPS, elevation/barometer data, and heart rate. The software first estimates activity type or intensity. It then converts that estimate into calorie burn. Apps may use regression equations, MET-based calculations, or machine-learning models. Some systems use only motion data, while others combine several signals. For example, adding elevation or barometer information can help distinguish level walking from stair climbing or uphill movement, which may have similar step counts but different energy costs. Commercial formulas are often proprietary, so researchers can test the output but cannot examine the internal calculations. Below is a discussion of a variety of studies on the subject.
Johnson et al. (2016): Samsung S Health (1)
Twenty-nine healthy young adults carried Samsung Galaxy S4 phones in their hands and pockets during 15 minutes of self-paced track walking and 15 minutes of treadmill running at 2.24 m/s. S Health used sex, birth date, height, weight, and a selected activity level, but Samsung did not disclose its calorie equation. Compared with indirect calorimetry, walking estimates were close to the criterion (about 69.5-69.9 vs. 68.6 kcal). Running estimates were much too high (about 189.6-194.5 vs. 144.0 kcal, roughly 32%-35% over). The study therefore supports reasonable accuracy only for walking conditions, not across all activities or speeds. In addition, phone placement affected results, especially during running.
Manohar et al. (2011) (2)
Smartphone Accelerometer Validation: Participants walked at controlled speeds while a smartphone triaxial accelerometer was compared with indirect calorimetry. Accelerometer output increased with walking speed and measured energy expenditure, with strong relationships (r² > 0.9). Phone placement affected the accelerometer signal. The results support using smartphone motion data to estimate EE. Developers should consider phone placement when developing or validating the calculation.
Nolan et al. (2014) (3)
iPhone/iPod Activity Classification and MET Prediction: Researchers developed an accelerometer-based iPhone/iPod model that classified walking versus running and then estimated speed and energy expenditure in METs. The model classified walking versus running with approximately 99% accuracy. Average EE bias was 0.35 MET during walking and -0.43 MET during running. The study suggests that identifying the activity first and then estimating its intensity may be more useful than applying one calculation to all movement. This was a research model, not Apple’s commercial calorie formula.
Pande et al. (2015) (4)
Accelerometer and Barometer Model: Researchers combined smartphone accelerometer and barometer data with age, sex, height, weight, and BMI to estimate energy expenditure. The barometer added information about changes in elevation, such as stair climbing, that accelerometer movement alone may not capture. Bagged regression trees performed best, with correlations of up to approximately 96% with indirect calorimetry. The results suggest that combining motion, elevation, and personal information may improve calorie estimates compared with using step count alone.
Faria et al. (2019) (5)
Google Fit in Adults With Chronic Stroke: Google Fit and an ActiGraph accelerometer were compared with indirect calorimetry during over-ground walking in adults with chronic stroke. Google Fit did not provide valid energy-expenditure estimates during fast walking in this population. The findings showed that EE accuracy depended on population and movement patterns and supported validation across users rather than assuming that a single algorithm performs equally well for everyone.
Shcherbina et al. (2017) (6)
Commercial Wearable Devices: Seven commercial wrist devices, including Apple Watch, Fitbit Surge, Microsoft Band, and Samsung Gear S2, were tested across activities of different intensities. Heart-rate estimates were generally more accurate than energy-expenditure estimates, and no wrist device achieved EE error below the study’s 20% threshold across conditions. Because the commercial algorithms were proprietary, researchers could not determine the exact cause of over- or underestimation. The study shows that accurate sensor measurements do not necessarily produce an accurate final calorie estimate.
Murakami et al. (2019) (7)
Laboratory and Free-Living Wearable Validation: Twelve wearable devices were tested in a metabolic chamber over 15 standardized days of normal living using doubly labeled water as the reference. Devices sometimes ranked participants from low to high EE, but absolute calorie estimates varied substantially across devices and from the reference measurements. The findings show that correlation alone does not establish calorie accuracy. Validation should also measure absolute error and bias under both controlled and real-world conditions.
Energy Expenditure Formulas Reported in the Studies
MET Calorie Equation (3)
kcal/min = MET × 3.5 × body weight (kg) / 200
MET means metabolic equivalent; 1 MET approximates resting intensity. The equation converts an activity’s MET intensity into estimated calories per minute. Multiplying by exercise duration gives estimated total activity calories. Nolan et al. reported activity intensity in METs, but this conversion is a standard exercise equation rather than Samsung, Apple, or Google Fit’s proprietary formula. Read Calculating Activity Burn Using METS: The Old Versus New Formula for a deeper dive into this equation
Indirect-Calorimetry Equation (4)
EE (kcal/min) = [3.815 + 1.232 × RER] × VO₂
EE means energy expenditure in kilocalories per minute. VO₂ is liters of oxygen consumed per minute. RER equals VCO₂/VO₂, or carbon dioxide produced divided by oxygen consumed. The formula converts respiratory-gas measurements from the COSMED calorimeter into calories burned per minute. To find total calories, multiply the kcal/min result by the number of minutes. This was the study’s criterion measurement, not the phone app’s internal formula.
ActiGraph Equations (5)
WET: kcal/min = 0.0000191 × counts/min × body mass (kg)
Freedson: kcal/min = 0.00094 × counts/min + 0.1346 × body mass (kg) – 7.37418
The combined method used WET at 1,952 counts/min or below and Freedson above 1,952 counts/min. Counts/min is the amount of movement recorded by the accelerometer, and body mass is entered in kilograms. These equations convert recorded movement into estimated calories per minute. Multiplying kcal/min by activity duration estimates total calories. These were ActiGraph equations used for comparison, not Google Fit’s formula.
Physical Activity Energy Expenditure Equation (7)
PAEE = TEE – BMR – (0.1 × TEE)
PAEE means physical activity energy expenditure, TEE means total energy expenditure, and BMR means basal metabolic rate. The researchers treated 10% of TEE as diet-induced thermogenesis and subtracted both BMR and that 10% from TEE to isolate the calories associated with physical activity. They also calculated physical activity level as PAL = TEE / BMR. These equations help separate total daily calories from active calories. The researchers used these equations in the study; they are not the proprietary equations used in commercial devices.
What the Energy Expenditure Formulas Show
The published equations fall into different categories. The Pande equation calculates energy from respiratory gases. Researchers use it as a reference measurement. The ActiGraph equations estimate calories directly from accelerometer movement and body mass. The MET equation converts an estimated activity intensity into calories. The Murakami equation separates active calories from total daily calories. Commercial apps may combine several of these ideas with additional sensor data and machine- learning models, but the complete commercial formulas are usually not published. This is why a high-quality validation study must compare the final app output with an accepted reference method rather than assuming the internal formula is correct.
Reference Methods Used to Check Accuracy
For short laboratory activities, researchers commonly use indirect calorimetry as the criterion measurement. It measures oxygen consumption and carbon dioxide production and then converts these respiratory gases into energy expenditure. For longer periods of normal daily life, doubly labeled water can estimate total energy expenditure over multiple days without requiring the person to remain connected to a metabolic cart. A metabolic chamber can also measure energy expenditure over an entire standardized day. These methods are useful because an app that performs well in a single treadmill test may not perform equally well in daily living.
Energy ExpenditureImplications for The Difference
The app should clearly separate resting/base calories from active calories and total daily calories, state which inputs and sensors are used, and label calorie results as estimates rather than exact measurements. A stronger model than one that relies only on step count may combine personal information with several independent signals, including accelerometer data, activity type, speed, distance, elevation or barometer data, and heart rate. It may also be better to use different calculations or models for different activities because walking, running, cycling, resistance exercise, stair climbing, and daily-living movement do not have the same relationship between sensor motion and energy cost.
Validation
The Towards Intelligent Health and Well-Being Network of Physical Activity Assessment (INTERLIVE), a joint European initiative of six universities and one industrial partner founded in 2019, recommended a detailed framework for validation of wearables and apps (8). They state that validation should compare The Difference with indirect calorimetry across walking, running, cycling, strength exercise, daily living, different phone placements, and a diverse sample. If longer-term TDEE, EAT, or NEAT is being tested, metabolic chamber or doubly labeled water methods can provide stronger reference measurements. Results should include bias, mean absolute error or percentage error, and Bland-Altman limits of agreement, not correlation alone. The app version and algorithm version should also be recorded because accuracy can change between software updates.
References
(1) “Validity of the Samsung Phone S Health application for assessing steps and energy expenditure during walking and running: Does phone placement matter?”, National Library of Medicine, Johnson et al., 2016.
(2) “Evaluation of the Accuracy of a Triaxial Accelerometer Embedded into a Cell Phone Platform for Measuring Physical Activity”, National Library of Medicine, Manohar et al., 2011.
(3) “Validity of the Apple iPhone®/iPod Touch® as an Accelerometer-Based Physical Activity Monitor: A Proof-of-Concept Study”, Human Kinetics Journals, Nolan et al., 2014.
(4) “Using Smartphone Sensors for Improving Energy Expenditure Estimation”, National Library of Medicine, Pande et al., 2015.
(5) “Validity of the accelerometer and smartphone application in estimating energy expenditure in individuals with chronic stroke”, National Library of Medicine, Faria et al., 2019.
(6) “Accuracy in Wrist-Worn, Sensor-Based Measurements of Heart Rate and Energy Expenditure in a Diverse Cohort”, National Library of Medicine, Shcherbina et al., 2017.
(7) “Accuracy of 12 Wearable Devices for Estimating Physical Activity Energy Expenditure Using a Metabolic Chamber and the Doubly Labeled Water Method: Validation Study”, JMIR Publications, Murakami et al., 2019.
(8) “Recommendations for Determining the Validity of Consumer Wearables and Smartphones for the Estimation of Energy Expenditure: Expert Statement and Checklist of the INTERLIVE Network”, Springer Nature, Argent et al., 2022.
