MATHEMATICAL METHODOLOGY

The Science Behind AdapTDEE

We believe in total transparency. Here is the mathematical framework, thermodynamic equations, and smoothing models that power AdapTDEE.

1. The First Law of Thermodynamics

Human energy expenditure obeys conservation of energy: the energy entering the system (dietary calories consumed) must equal the energy expended plus the rate of change in internal stored energy (body fat and lean mass):

Fundamental Energy Balance Equation:
Change in Stored Energy = Energy Intake - Total Energy Expenditure (TDEE)
Rearranging for TDEE: TDEE = Average Calorie Intake - (Weight Trend Change × Tissue Energy Density)

Where tissue energy density is standardized to 3,500 kcal per pound (~7,700 kcal per kg) of human adipose and lean tissue mixture (Hall KD et al., 2011).

2. Signal Noise Reduction (Weight Trend Smoothing)

Daily scale measurements represent acute water retention, glycogen storage, sodium balance, and gut volume. To isolate the true tissue change signal from daily noise, AdapTDEE applies an Exponential Moving Average (EMA):

Trend Smoothing Formula:
Weight_trend(t) = α × Weight_raw(t) + (1 - α) × Weight_trend(t-1)
Where Weight_trend(t) is the smoothed trend weight for day t, Weight_raw(t) is the raw morning weigh-in, and α = 0.10 is the smoothing coefficient chosen to balance responsiveness with noise dampening.

3. Handling Missing Logging Days

Life happens and users occasionally miss weigh-ins or calorie logs. The algorithm does not penalize missing data or drop abruptly to zero. Missing days are linearly interpolated across the rolling window, dynamically adjusting the algorithm's confidence rating until data density returns.

Experience the Algorithm in Action

AdapTDEE runs these calculations automatically in the background every day—giving you objective, mathematical clarity on your metabolism without spreadsheets.

Academic Citations:

1. Hall KD, et al. Quantification of the effect of energy imbalance on bodyweight. The Lancet. 2011;378(9793):826-837.

2. Mifflin MD, St Jeor ST, et al. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr. 1990;51(2):241-247.

3. Trexler ET, Smith-Ryan AE, Norton LE. Metabolic adaptation to weight loss: implications for the athlete. J Int Soc Sports Nutr. 2014;11(1):7.

4. Levine JA. Non-exercise activity thermogenesis (NEAT). Best Pract Res Clin Endocrinol Metab. 2002;16(4):679-702.