How we verify accuracy
Standard web calculators make subtle rounding mistakes caused by binary floating-point representation. Here is how our 40-digit decimal engine and automated test suites guarantee 100% mathematical accuracy.
The binary floating-point problem
Almost all online calculators and spreadsheet applications rely on native binary floating-point arithmetic (IEEE 754). In a binary system, common decimal values like tenths (0.1) and hundredths (0.01) cannot be represented finitely, similar to how 1/3 cannot be written finitely in decimal form (0.3333...).
Native binary rounding drops the fractional half, producing 1.00 instead of the true rounded figure 1.01.
Calculates exact intermediate value 1.005 and applies mathematical round-half-up to reach the correct 1.01.
Our 40-digit decimal architecture
Every calculator on this site runs on a custom decimal arithmetic engine that adheres to four strict principles:
Raw string ingestion
Numbers are parsed directly from keystrokes into exact Decimal objects without ever passing through parseFloat() or native binary conversion.
40 internal significant digits
Intermediate calculations maintain 40 digits of internal precision to prevent cumulative truncation errors across multi-step formulas.
Standard round-half-up rules
Rounding occurs only at the final display output according to standard academic and commercial round-half-up conventions.
Repeating decimal analysis
Denominators are factored for non-terminating expansions, properly handling recurring fractions such as 1/3 or 1/6.
Automated property-based testing
Before any update is committed, our continuous testing suite verifies mathematical properties across thousands of randomized decimal values:
- ✓reverse(percentOf(P, X), P) === X (Exact Inverse Theorem)
- ✓isWhatPercent(percentOf(P, X), X) === P (Exact Identity Theorem)
- ✓split(Total, Ratios).sum === Total (Hare-Niemeyer penny balancing)