Calculation Methodology
Understand exactly how Tooler computes every result — the formulas we use, the assumptions we make, and the limits of what our calculators can tell you.
Core principles
Every Tooler calculator follows these rules:
- Inputs are required unless marked optional. Missing required fields return a clear error explaining what is needed.
- Results are rounded for readability but computed with double-precision floating-point arithmetic. Display precision is chosen to match real-world usage (e.g., currency to 2 decimal places, BMI to 1 decimal).
- Displayed values are estimates unless explicitly stated as formula-exact. Our health calculators produce screening numbers, not medical diagnoses. Our financial calculators show mathematical payments, not binding loan offers.
- No data is stored. Calculator inputs are processed in memory and discarded immediately. We do not log, save, or share your numbers.
Formula reference
BMI (Body Mass Index)
BMI = weight_kg ÷ (height_m)²
Weight in kilograms, height converted from centimeters to meters. Classification follows WHO thresholds: Underweight < 18.5, Normal 18.5–24.9, Overweight 25–29.9, Obese ≥ 30.
EMI (Loan Payment)
EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
Where P = principal, r = monthly interest rate (annual rate ÷ 12 ÷ 100), n = total months. Uses the standard reducing-balance method applied by banks worldwide.
GST / Tax (Add & Remove)
Add tax: tax = amount × rate%, total = amount + tax
Remove tax: net = total ÷ (1 + rate%), tax = total − net
Calories (BMR & TDEE)
Uses the Mifflin–St Jeor equation, the most accurate predictive formula for the general population:
Men: BMR = (10 × kg) + (6.25 × cm) − (5 × age) + 5
Women: BMR = (10 × kg) + (6.25 × cm) − (5 × age) − 161
TDEE = BMR × activity factor (1.2 sedentary through 1.9 extra active).
Age & Date Differences
Age is computed using strict calendar arithmetic — counting completed years, remaining months, and remaining days from birth date to reference date. February 29 birthdays advance on March 1 in non-leap years. Date differences count absolute calendar days between any two dates, correctly handling month boundaries and leap years.
Unit Converters
All unit conversions use internationally defined conversion factors. Length uses 1 inch = 2.54 cm (exact). Weight uses 1 lb = 0.45359237 kg (exact). Temperature uses standard linear formulas. Currency uses indicative rates for estimation only — always verify live rates with your payment provider before transactions.
Validation behavior
Invalid input returns explicit error messages rather than silent fallbacks. Common validation rules:
- Negative values are rejected for real-world measurements (weight, height, age, loan amounts).
- Division by zero is caught and reported — entering zero for height in BMI, for example, returns a clear message.
- Unreasonable values (age > 150, weight > 500 kg) produce a warning rather than silently computing absurd results.
- Text-to-ASCII enforces character and line limits (120 chars, 8 lines, 24 chars per line) to keep output usable.
- File processing tools validate MIME types and file sizes before processing. Invalid files are rejected with a specific error.
Precision and rounding
Tooler uses double-precision (64-bit) floating-point arithmetic for all calculations. Final results are rounded for display:
- Currency (EMI, GST, currency converter): 2 decimal places
- BMI: 1 decimal place
- Calories: nearest whole number
- Percentages: 2 decimal places
- Age (months/days): exact integers
- Unit conversions: up to 6 significant digits
Rounding follows standard "round half up" convention. Cumulative rounding errors are negligible for the precision levels we display.
Important disclaimer
Our calculators are educational and estimation tools. BMI is a screening metric, not a medical diagnosis. EMI calculations show mathematical payments excluding bank-specific fees, insurance, or rounding policies. GST rates should be verified against official government schedules for your product category. Always consult qualified professionals for financial, medical, or legal decisions.