Methodology

1. Two ways to estimate the starting energy baseline

Apple Health–informed mode

The preferred path asks for a recent typical daily Resting Energy, Active Energy, and Steps value from Apple's Health app. The website does not request HealthKit permission or read those values automatically.

starting expenditure estimate ≈ Resting Energy + Active Energy

The sum anchors the starting daily energy state. Active Energy is also normalized by current body weight to initialize the physical-activity coefficient used by the dynamic model. This mapping is a HealthPro calibration choice; it is not an Apple or NIH formula. Entries are bounded to broad adult product ranges and unusual values trigger a warning rather than silent correction.

Use a representative recent average, not an unusually active or inactive day. Apple Health and Apple Watch calorie values are device-derived estimates, not direct calorimetry.

Manual-estimate mode

If Apple Health values are unavailable, resting energy is estimated with Mifflin–St Jeor and multiplied by a documented physical activity level (PAL):

male RMR   = 10 × weight + 6.25 × height − 5 × age + 5
female RMR = 10 × weight + 6.25 × height − 5 × age − 161

PAL: sedentary 1.40 · light 1.60 · active 1.75 · very active 2.05
starting expenditure estimate = RMR × PAL

For the Hall model's baseline physical-activity coefficient, the manual path uses equation 8 from the 2011 web appendix, including baseline thermic effect of feeding.

2. Dynamic body-weight model

The NIH/NIDDK Body Weight Planner is based on work by Kevin Hall and colleagues published in The Lancet in 2011. The full model includes early changes in glycogen, fluid, carbohydrate intake, sodium, and adaptive thermogenesis. HealthPro Tools V3 intentionally does not ask users for carbohydrate or sodium inputs, so it uses the peer-reviewed long-term linearized phase from equations 10–15 of the published web appendix.

In that model, after the early transient phase:

ρ · dBW/dt = ΔEI − ε · (BW − BW₀)

β = βAT + βTEF = 0.14 + 0.10 = 0.24
α = C / F₀, where C = 10.4 kg

ρ = [ηF + ρF + α(ηL + ρL)] / [(1 − β)(1 + α)]
ε = [(γF + αγL)/(1 + α) + δ] / (1 − β)

The implementation uses the paper's published tissue-energy, synthesis-cost, and resting-expenditure coefficients, converted from kJ to kcal. Starting body fat is estimated from the appendix's sex-specific Jackson regression when it is not directly measured.

Changes in physical activity

The appendix's equation 17 explicitly allows the physical-activity parameter δ to change. HealthPro Tools uses the same relationship when planned exercise is added, so new activity changes both the immediate energy imbalance and the body-weight-dependent expenditure response.

for each simulated day:
  Δδ = planned additional activity coefficient for that day
  total δ = baseline δ + Δδ

  expenditure response =
    [BW₀ × Δδ + (γmix + total δ) × (BW − BW₀)] / (1 − β)

  dBW = (ΔEI − expenditure response) / ρ

The solver advances the model one day at a time and uses binary search to find the daily intake that reaches the requested target weight on the requested target date. This replaces the old fixed 7,700-kcal/kg linear rule.

3. Apple Health calibration and no double counting

The Apple Health baseline already represents the user's recent routine. New exercise is therefore modeled only as an increment above that baseline. Existing steps and workouts are not credited a second time.

If the user chooses brisk walking as the new activity, the interface may show an approximate number of steps per planned walking session for context. Those steps are explicitly described as overlapping the walking total. They are not converted into a second calorie credit.

4. Planned activity energy

Activity energy uses MET values from the 2024 Adult Compendium of Physical Activities. For a planned session, HealthPro Tools credits only energy above rest:

net additional kcal/session ≈ (MET − 1) × weight(kg) × duration(hours)

MET estimates describe typical energy cost and can differ substantially from an individual's real cost. The generic moderate/vigorous entries are deliberately labeled representative values rather than exact measurements.

5. Activity ramp-up changes the forecast

The selected activity routine is not assumed to begin at full volume on day one. The planner constructs a session-frequency ramp over the selected number of weeks and feeds the resulting day-by-day activity coefficient into the weight simulation.

example: target 5 sessions/week over 4 weeks
start at 2/week → build through 3/week and 4/week → reach 5/week

This is a HealthPro planning heuristic, not an official medical progression schedule. A slower ramp means less activity energy early in the plan and therefore changes the food target needed for the same goal and date.

6. Same goal and date, three strategy choices

All strategy cards use the same target weight and target date:

• Less diet change: use the maximum new activity frequency the visitor said they are willing to do.
• Balanced: use up to 3 new sessions/week, bounded by the visitor's stated maximum.
• Less activity: credit no additional exercise and rely more on food change.

The calorie target is solved separately for each schedule. Because the model includes the actual ramp, the three numbers are not fixed percentage splits.

7. Walking reference

The planner keeps approximately 7,000 steps/day as a practical general-health reference. If the current average is below 7,000, it suggests a gradual ramp; if the visitor already exceeds the reference, it keeps approximately the current level rather than prescribing a decrease.

The step number is not used as a formula for kilograms lost. Step-health evidence is population research, while the weight forecast is calculated from the energy/body-weight model.

8. Goal-weight maintenance

Maintenance is recalculated at the target weight using the same dynamic equation and the full new activity schedule the visitor expects to continue:

set dBW/dt = 0 at target weight
solve the same model for maintenance intake
include continued planned activity

This is more informative than simply reusing today's maintenance estimate, but it is still a model result. Real maintenance should be recalculated from actual weight and activity when the goal is reached.

9. Safety boundaries

• Supported age range: 18–79.
• Current weight must be above target weight.
• Current and target BMI screening values must remain at or above 18.5.
• Target date must be at least 14 days away and within the supported 5-year simulation range.
• The model never proposes less than 1,000 kcal/day. When the requested date would require less, it says the goal is too aggressive and searches for a later modeled feasible date instead.
• The planner is not intended for pregnancy, breastfeeding, eating-disorder treatment, or individualized medical care.

BMI is used only as a conservative product screening boundary. It is not a diagnosis or a statement that weight loss is appropriate for a particular individual.

10. Validation approach and limitations

Automated tests cover baseline calibration, stable no-change simulations, target-solving, activity ramps, strategy ordering, the 1,000-kcal floor, maintenance with continued activity, and no double counting of planned walking. Representative numerical fixtures are recorded in the repository's V3 validation note.

The implementation is deliberately described as Hall long-term model v3.0, not “the NIH calculator.” The full NIDDK tool contains additional early-phase physiology and implementation choices, so close numerical agreement should be demonstrated across a formal validation grid before stronger equivalence language is used.

Sources

1. NIDDK — Research Behind the Body Weight Planner
2. Hall et al. (2011) — Quantification of the effect of energy imbalance on bodyweight
3. Hall et al. — Dynamic Mathematical Model of Body Weight Change in Adults (web appendix)
4. Mifflin et al. (1990) — predictive equation for resting energy expenditure
5. 2024 Adult Compendium of Physical Activities
6. Ding et al. (2025) — daily steps and health outcomes
7. NIDDK — Body Weight Planner

Method version: hall-long-term-v3.0. Source review date: September 6, 2026.