Every number on FitMathHub comes from a published formula or reference value. This page lists them all, says how the calculators are tested, and what none of them can tell you.
The formulas
| Calculator | What it calculates | From |
|---|---|---|
| BMR | Mifflin-St Jeor: 10 × kg + 6.25 × cm − 5 × age + 5 (men) or − 161 (women). Harris-Benedict as revised by Roza and Shizgal shown alongside. With a body fat %: Katch-McArdle 370 + 21.6 × lean kg and Cunningham 500 + 22 × lean kg. | Mifflin et al. 1990; Roza & Shizgal 1984; Cunningham 1980 |
| TDEE | BMR (Mifflin-St Jeor) × an activity multiplier of 1.2, 1.375, 1.55, 1.725 or 1.9. | Widely used rounded multipliers, compared on the page with the FAO/WHO/UNU 2004 physical activity levels |
| Calorie table | TDEE × (1 + change ÷ 100) for −20% to +15%; rows below the estimated BMR are marked. | Arithmetic on the TDEE result |
| Macros | Grams = calories × share ÷ 4 (protein, carbs) or ÷ 9 (fat); the other way, kcal = 4 × protein + 4 × carbs + 9 × fat. | Atwater energy factors (FAO); adult AMDR ranges (US National Academies) |
| Protein | 0.8 g per kg (RDA) and 1.4–2.0 g per kg (ISSN range for people who exercise). | US Dietary Reference Intakes; ISSN position stand 2017 |
| Water | Adequate intakes of total water: 2.5 L men / 2.0 L women (EFSA) and 3.7 L / 2.7 L (US/Canada); per-kg rules of thumb shown for comparison. | EFSA 2010; US/Canada DRI 2004; NICE CG174 (hospital IV fluids) |
| Sweat rate | [weight before − (weight after − fluid drunk + urine)] ÷ hours; 1 kg ≈ 1 L. | Baker 2017 (Sports Medicine); ACSM 2007 position stand |
| BMI | kg ÷ m² (US: 703 × lb ÷ in²), with the WHO adult classes; BMI Prime = BMI ÷ 25; ponderal index = kg ÷ m³. NICE's lower thresholds shown as a reference table. | WHO; CDC; WHO expert consultation 2004; NICE NG246 |
| Body fat | U.S. Navy circumference equations for body density, then Siri: % fat = 495 ÷ density − 450. Compared with Deurenberg: 1.20 × BMI + 0.23 × age − 10.8 × sex − 5.4. | Hodgdon & Beckett 1984 (Naval Health Research Center reports 84-11 and 84-29); Deurenberg et al. 1991 |
| Waist-to-height ratio | Waist ÷ height (same units), with the NICE adult classes 0.4–0.49, 0.5–0.59 and 0.6 or more. | NICE guideline NG246 |
| Heart rate zones | Max heart rate 208 − 0.7 × age (Tanaka), 220 − age or 206 − 0.88 × age (Gulati, women); Zone 2 = 60–70%; zones by heart-rate reserve (Karvonen) or % of max. | Tanaka, Monahan & Seals 2001; Gulati et al. 2010; Karvonen et al. 1957 |
| Running pace | Pace = time ÷ distance; treadmill pace = 60 ÷ speed; race estimates T2 = T1 × (D2 ÷ D1)^1.06. | Riegel's endurance model (the 1.06 version used for race conversion); checked against world records on this page |
| One rep max | Epley: weight × (1 + reps ÷ 30); Brzycki: weight × 36 ÷ (37 − reps); the result is their average. Lander, Lombardi, Mayhew, O’Conner and Wathen shown for comparison. | Epley 1985; Brzycki 1993; coefficients as in Ribeiro et al. 2024 |
| Sleep | Bedtime = wake-up − time to fall asleep (15 min by default) − cycles × 90 min (editable); hours slept; nap alarms at 10 and 20 min. | NINDS Brain Basics; Brooks & Lack 2006; sleep-cycle and sleep-latency sources on the page |
Each calculator page links its sources (papers, official reports and position stands) under the text, with the date they were last checked. When a source states a range of uncertainty or a group the formula wasn't built for, the page repeats it.
The formulas side by side
Four data pages run the formulas against each other, with tables computed by the same code as the calculators: max heart rate by age, BMR formulas compared, one rep max formulas compared and race predictions vs world records.
How the results are tested
- All formulas live in one small code file. Automated tests run them on the worked examples printed on the pages, for example the 80 kg, 180 cm, 30-year-old man whose Mifflin-St Jeor BMR is 1,780 kcal a day, or the 07:00 wake-up that gives bedtimes of 21:45, 23:15 and 00:45.
- Metric and US inputs are converted with exact factors (1 lb = 0.45359237 kg, 1 in = 2.54 cm, 1 mile = 1.609344 km) and tested both ways.
- If a page and its calculator ever disagree, the tests fail and the site isn't published.
Rounding
Calculations use full precision. Results are rounded only for display: calories to whole numbers, BMI and body fat to one decimal, times to the second or minute. That's why a hand calculation with rounded steps can differ by one.
What no formula can tell you
- Formulas describe groups. A prediction equation can be off by a few hundred calories for one person, and BMI can't tell muscle from fat.
- They were fitted on healthy adults, so they aren't made for children, pregnancy or medical conditions.
- They give numbers, not advice. For decisions about your health, diet or training, talk to a qualified professional. See the Health disclaimer.
Editorial and corrections policy
These are the rules every page on FitMathHub follows.
How a formula gets on the site
- It must be published: in a peer-reviewed paper, an official report (for example FAO/WHO, EFSA, NICE or the US National Academies) or a position stand.
- Where several formulas are in common use, the page shows them side by side and says which one the main result uses, instead of picking one silently.
- The page states the groups a formula was built on and its known error, when the source gives them.
The sources rule
- Every fact and number in a page's text comes from a source that was opened and read while writing it. The sources are listed under the page with the date they were last checked.
- Pages written by companies (for example app makers) are used only for what they say about their own method or view, and are labeled as such.
- No invented statistics, no made-up examples presented as real people, no unsourced claims from forums or social media.
How pages are checked
- The worked examples printed on the pages are run against the calculators by automated tests, so text and calculator can't drift apart.
- When a page changes, its numbers and sources are checked again and its "last checked" date is updated.
How AI is used
AI tools help write the code and first drafts of the texts. Formulas, numbers and source links are checked against the original sources before a page goes up, and the worked examples are covered by the tests above.
Who runs the site
FitMathHub is run by one independent developer in the EU, without a name or photo on purpose. There is no named expert reviewer and none is implied: the site doesn't claim credentials it doesn't have. Trust has to come from the formulas, the sources and the tests, which you can all check. More on the About page.
Not medical advice
The calculators show what published formulas give for the numbers you type. They don't give diet plans, weight-loss targets or diagnoses. See the Health disclaimer.
Corrections
Found a mistake? Use the contact form and choose "Mistake or bug". Every report is checked against the source; confirmed errors are fixed and the page's "last checked" date is updated.