Methodology
Last reviewed: June 22, 2026
A calculator is only worth using if you can trust its answers. This page explains how Numvella's 37 calculators work, the formulas behind them, how we keep results accurate, and why your numbers never leave your device.
How our calculators work
Every calculation runs in a single, framework-free calculation engine — pure functions with no UI, no network, and no surprises. The same engine powers the live tool and our automated tests, so what you see is exactly what we verify. Each tool also shows the formula it used and a worked example, so you can check any result by hand. Nothing is a black box.
Accuracy & rounding
Computers represent decimals in binary (IEEE-754), which means naïve arithmetic can produce artifacts like 0.1 + 0.2 = 0.30000000000000004. We round results to an appropriate number of places for display while keeping full precision during the calculation, so totals add up and money shows to the cent.
Every engine function is covered by unit tests, including the awkward edge cases: zero, negative numbers, division by zero (which returns a friendly message, never NaN or Infinity), very large and very small magnitudes, and calendar quirks like leap years. Inputs are validated before any math runs.
Formulas & sources
We use standard, widely accepted definitions from mathematics, accounting, finance, and public health. Each tool's page documents its own formula; here is the full reference:
| Calculator | Formula | Basis |
|---|---|---|
| Percentage of a number | (percent ÷ 100) × value | Definition of percent (per hundred). |
| What percent of | (part ÷ whole) × 100 | Definition of percent. |
| Percentage change | ((new − old) ÷ old) × 100 | Relative change vs. the original value. |
| Discount / Sales Tax / VAT | amount × (rate ÷ 100); reverse: ÷ (1 + rate ÷ 100) | Standard percentage arithmetic. |
| Tip | bill × (tip% ÷ 100), split by people | Standard percentage arithmetic. |
| Profit margin / markup | margin = profit ÷ revenue; markup = profit ÷ cost | Standard accounting definitions. |
| Average (mean / median) | mean = sum ÷ count; median = middle of sorted values | Descriptive statistics. |
| GPA | Σ(grade points × credits) ÷ Σ(credits) | US unweighted 4.0 scale (A = 4.0 … F = 0.0). |
| Fraction → decimal | numerator ÷ denominator | A fraction is a division; terminates when the reduced denominator's only prime factors are 2 and 5. |
| Ratio | divide both terms by their GCD; a : b = c : x → x = b·c ÷ a | Greatest common divisor; cross-multiplication. |
| BMI | weight (kg) ÷ height (m)² (×703 for lb/in) | WHO body mass index; adult categories 18.5 / 25 / 30. |
| Compound interest | A = P(1 + r/n)^(nt) + contributions | Standard compound-interest formula; Rule of 72 for doubling time. |
| Hours between times | (end − start) in minutes ÷ 60 | Minute arithmetic; overnight shifts wrap past midnight. |
| Date difference / add | whole days between dates; start date ± days | Calendar-correct, leap-year aware, local time. |
| Commission | sale × (rate ÷ 100) + base pay | Standard percentage arithmetic. |
| Percent error | (|measured − actual| ÷ |actual|) × 100 | Magnitude of deviation from an accepted true value. |
| Standard deviation | σ = √(Σ(x − mean)² ÷ N); sample s uses N − 1 | Descriptive statistics; Bessel's correction for samples. |
| TDEE / BMR | BMR = 10·kg + 6.25·cm − 5·age + s; TDEE = BMR × activity | Mifflin–St Jeor equation (s = +5 male, −161 female); activity factor 1.2–1.9. |
| Mortgage / Loan payment | M = P·r(1+r)^n / ((1+r)^n − 1) | Standard fixed-rate amortization; r = annual rate ÷ 12, n = months. 0% → P ÷ n. |
| PMI drop-off | loan balance ≤ 80% × home price | Conventional-loan standard; PMI applies when the down payment is under 20%. |
| Home affordability (28/36) | PITI ≤ 28% income; PITI + debts ≤ 36% income | Lender debt-to-income ratios; max home price back-solved from the binding limit. |
Finance calculators
Our mortgage, loan, auto-loan, and amortization tools share one tested engine built on the standard fixed-rate amortization formula:
M = P · r(1 + r)^n / ((1 + r)^n − 1)
where M is the monthly payment, P is the loan principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. At a 0% rate the payment is simply P ÷ n. Each month, interest is charged on the outstanding balance and the remainder reduces principal; the final payment is adjusted to the cent so the balance reaches exactly zero. Extra payments are applied entirely to principal, ending the schedule early.
PMI drop-off: Private Mortgage Insurance applies when the down payment is under 20% of the home price, and is removed once the loan balance reaches 80% of the original home value (the conventional-loan standard). Home affordability uses the lender 28/36 debt-to-income rule: housing costs (PITI) are capped at 28% of gross monthly income (front-end ratio) and total debt including housing at 36% (back-end ratio); the maximum home price is back-solved from whichever limit binds first.
All calculations use IEEE 754 double-precision arithmetic, with figures rounded to the cent for display. These tools are estimates for educational use and are not financial advice — see each tool's disclaimer.
Privacy by design
All computation happens in your browser. The numbers you enter are never uploaded, logged, or stored on a server. Some calculators remember your last inputs in your browser's local storage so you can pick up where you left off, and your inputs can be encoded into a shareable link — both stay on your device until you choose to share a link. See our Privacy Policy for details.
Important: estimates, not advice
Numvella is built for general and educational use, and its results are estimates. It is not financial, tax, accounting, medical, or legal advice. BMI in particular is a screening number, not a diagnosis. For decisions that matter, verify critical figures independently or consult a qualified professional. See our Terms of Use.
Found a mistake?
Accuracy is a moving commitment, not a one-time claim. If a result looks wrong, please tell us the inputs and what you expected at hello@numvella.com — we investigate every report. You can also browse all our tools on the calculators page.