Percentage Calculator

The formula is `result = (X / 100) × Y`, where X is the percentage and Y is the base. Worked example: 25% of 80 = (25/100) × 80 = 0.25 × 80 = 20. The inverse — finding what percent A is of B — uses `percent = (A / B) × 100`. Worked example: 20 is what percent of 80 → (20/80) × 100 = 25%. Both formulas derive from the ISO 80000-1:2022 definition of percentage as the dimensionless ratio 0.01 (so "1%" literally means 0.01); the BIPM SI Brochure 9th edition (2019) permits the % symbol alongside SI units. The two forms are inverses of each other: knowing the percent + base gives the part; knowing the part + base gives the percent.

Stacked discounts compose multiplicatively, not additively. A 30% discount followed by an additional 20% off the discounted price = original × 0.70 × 0.80 = original × 0.56, equivalent to 44% off, NOT 50% off. The intuition: each percentage applies to the running price, not the original. Common retail patterns: "40% off + extra 20% with code" → 0.60 × 0.80 = 0.48 = 52% effective off; "50% off + extra 30% clearance" → 0.50 × 0.70 = 0.35 = 65% effective off. The FTC Guides Against Deceptive Pricing (16 CFR Part 233, enforced under FTC Act § 5) require retailers to disclose stacking math accurately when the cumulative claim could mislead. To compute the effective rate from N stacked discounts, multiply (1 − rate_i) for each, then subtract from 1.

A percentage-point is an absolute difference between two percentages; a percent is a relative difference. If an interest rate moves from 5% to 6%, that's an increase of 1 percentage point (absolute) but a 20% relative increase (1 / 5 × 100). Financial reporting often confuses the two — a Fed rate cut from 5.50% to 5.25% is "25 basis points" or "0.25 percentage points" (absolute), NOT "0.25%" (which would be a tiny relative cut). Bank for International Settlements (BIS) reporting standards use basis points (1 bp = 1/100 of 1% = 0.01%) for sub-percent moves to avoid this confusion. Quick rule: when comparing two percentages directly, use percentage-points (or basis points); when expressing one number as a fraction of another, use percent.

Percentages scale proportionally with the bill, which matches how these charges are conceptually justified: tips proportional to service value (US convention 15-20% pre-tax, UK service charge 12.5-15% often included on the bill (12.5% historical, drifting to 15% in London restaurants 2025-2026), EU varies by country with optional rounding), sales tax / VAT proportional to the taxable value (EU VAT: Spain 21%, Germany 19%, UK 20%, Norway 25%; US sales tax state-by-state 0% Oregon to ~10% with local add-ons), commissions proportional to deal size (real estate 5-6% in US, 1-3% in EU). The percentage-of-base computation is identical across these contexts; only the conventional rate and pre-tax-vs-post-tax base differ. Always check whether tip is computed on the pre-tax or post-tax total in your jurisdiction.

Decimals are accepted in both the percentage and the base inputs — useful for sales tax rates that aren't whole numbers (8.5% California, 7.25% baseline), commission splits (12.75% on a deal), or precision financial numbers. The calculation uses IEEE-754 double-precision floats (the JavaScript Number type), which gives 15-17 significant decimals — well beyond any practical financial or measurement precision. Negative inputs are mathematically valid: a negative percentage (e.g. -10%) returns a negative fraction of the base; a negative base returns a negative result. Sign is preserved consistently. The display rounds to a configurable number of decimal places for readability, but the underlying calculation retains full precision so that round-tripping the result through the calculator returns the same value.