Sources & References
The authoritative sources behind every formula we use — organized by calculator category.
Last Updated: July 4, 2026
How We Use Sources
Every formula on FreebieCalculator.com is traced back to a primary authoritative source. We prioritize government agencies, peer-reviewed research, and recognized professional standards. Where a formula has multiple accepted versions (such as BMR equations), we document which version we use and why.
If you notice a discrepancy between our calculation and a source you believe is authoritative, please contact us at bugs@freebiecalculator.com with the reference link. We review all reports carefully.
Financial Calculators
| Calculator | Formula / Method | Primary Source |
|---|---|---|
| Mortgage Calculator | Standard amortization formula M = P[r(1+r)^n]/[(1+r)^n−1] | Consumer Financial Protection Bureau (CFPB) |
| Compound Interest | A = P(1 + r/n)^(nt) | U.S. Securities and Exchange Commission (SEC) — Investor.gov |
| Simple Interest | I = P × r × t | Standard financial mathematics (CFPB) |
| Amortization Schedule | Monthly interest = remaining balance × monthly rate | Federal Reserve consumer guides |
| Car Loan Calculator | Standard installment loan formula | Consumer Financial Protection Bureau (CFPB) |
| EMI Calculator | EMI = P × r × (1+r)^n / [(1+r)^n−1] | Reserve Bank of India (RBI) financial education |
| Retirement Calculator | Future value with periodic contributions | Department of Labor, IRS Publication 590-A |
| Investment ROI | ROI = (Gain − Cost) / Cost × 100 | CFA Institute — Investment Foundations |
| CAGR Calculator | CAGR = (End/Start)^(1/years) − 1 | SEC Investor Education Office |
| Inflation Calculator | CPI-based purchasing power adjustment | U.S. Bureau of Labor Statistics (BLS) — CPI data |
| Income Tax Calculator | 2024 Federal Tax Brackets (progressive) | IRS Revenue Procedure 2023-34; IRS Publication 505 |
| Paycheck Calculator | FICA: SS 6.2% (wage base $168,600), Medicare 1.45% | IRS Publication 15 (Circular E), SSA fact sheets |
| Salary After Tax | Federal progressive brackets + estimated state rates | IRS Tax Tables; Tax Foundation state data |
| Debt-to-Income | DTI = Monthly Debt Payments / Gross Monthly Income | CFPB "Debt-to-income calculator" guidelines |
| Net Worth Calculator | Net Worth = Total Assets − Total Liabilities | Federal Reserve Financial Accounts of the United States |
| Canadian GST/HST | Province-specific combined tax rates 2024 | Canada Revenue Agency (CRA) GST/HST rates table |
| US Sales Tax | State sales tax rates 2024 | Tax Foundation State Sales Tax Rates; Sales Tax Institute |
Health & Fitness Calculators
| Calculator | Formula / Method | Primary Source |
|---|---|---|
| BMI Calculator | BMI = weight(kg) / height(m)² | World Health Organization (WHO); CDC Adult BMI Calculator |
| BMR Calculator | Mifflin-St Jeor Equation (1990) | Mifflin MD et al., J Am Diet Assoc. 1990;90(3):375–381 |
| Calorie Calculator | Mifflin-St Jeor BMR × Activity Multiplier (Harris 1919, revised) | Academy of Nutrition and Dietetics; NIH Dietary Guidelines |
| Body Fat Calculator | US Navy circumference method | Hodgdon JA & Beckett MB, 1984, Naval Health Research Center Report |
| Ideal Weight | Devine (1974), Robinson (1983), Miller (1983) formulas | Devine BJ, Drug Intell Clin Pharm. 1974;8:650–655 |
| Water Intake | General recommendation: 35ml/kg body weight/day, adjusted for activity | National Academies of Sciences — Dietary Reference Intakes for Water (2004) |
| Macro Calculator | Mifflin-St Jeor BMR + TDEE activity multipliers + macro split ratios | International Society of Sports Nutrition (ISSN) Position Stands |
| Sleep Calculator | 90-minute sleep cycle model, 15-minute sleep onset | National Sleep Foundation — Sleep Duration Recommendations (2015) |
| Due Date Calculator | Naegele's Rule: LMP + 280 days | ACOG Practice Bulletin No. 700 — Methods for Estimating Due Date |
| Ovulation Calculator | Ogino-Knaus method: ovulation = LMP + (cycle length − 14 days) | American College of Obstetricians and Gynecologists (ACOG) |
| Pregnancy Calculator | Gestational age from LMP; trimester boundaries per ACOG | ACOG; WHO ICD-10 pregnancy stage definitions |
| Running Pace | Pace = Time / Distance; VO2max estimate (optional) | Jack Daniels' Running Formula; USA Track & Field (USATF) |
Math & Education Calculators
| Calculator | Formula / Method | Source |
|---|---|---|
| Percentage Calculator | P = (Part / Whole) × 100; standard arithmetic | Standard mathematical definition |
| GPA Calculator | Weighted average of grade points by credit hours; 4.0 scale | College Board; NACAC GPA definitions |
| Grade Calculator | Weighted average of assignment scores | Standard academic grading methodology |
| Standard Deviation | Population SD: σ = √(Σ(x−μ)²/N); Sample SD: s = √(Σ(x−x̄)²/(N−1)) | NIST/SEMATECH e-Handbook of Statistical Methods |
| Fraction Calculator | Standard fraction arithmetic with LCM for addition/subtraction | Standard mathematical definitions |
| Average Calculator | Mean = Σx / n; Median = middle value; Mode = most frequent | Standard statistical definitions |
| Triangle Calculator | Law of Cosines, Law of Sines, Heron's Formula | Standard Euclidean geometry |
| Binary Converter | Positional notation base conversion | IEEE 754 standard; standard computer science definitions |
| Subnet Calculator | CIDR notation; binary subnet mask operations | RFC 1918 (IANA); RFC 4632 (CIDR) |
Reporting a Source Error
If you believe we have misapplied a formula or cited an incorrect source, please email bugs@freebiecalculator.com with:
- The calculator name and URL
- The specific formula or value you believe is incorrect
- A link to the authoritative source that supports your correction
We take source accuracy seriously and will respond within 5 business days.
For more on how we maintain accuracy, see our Calculator Accuracy Policy.