Percentage Calculator

Calculate percentages, proportions and percentage changes — fast and free.

What is X% of Y?

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of

X is what percent of Y?

is ?% of

Percentage change from X to Y

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What Is a Percentage Calculator?

A percentage calculator helps you quickly solve common percentage problems: calculate a percentage value, determine the proportion of a number, or find the percentage change between two values. Percentage calculations are used constantly in everyday life — shopping (discounts), school, financial calculations and statistics.

Percentage Formulas

X% of Y = (X / 100) × Y  |  X is what % of Y = (X / Y) × 100  |  Percentage change = ((New − Old) / |Old|) × 100. These three basic formulas cover virtually all percentage problems.

Examples

  • 20% of 150 = (20 / 100) × 150 = 30 — e.g. a 20% discount on a $150 item saves $30.
  • 30 is what % of 200? = (30 / 200) × 100 = 15% — e.g. scoring 30 out of 200 points on a test equals 15%.
  • From 80 to 100 = ((100 − 80) / 80) × 100 = 25% increase — e.g. a stock price rising from $80 to $100.

Percentages from the ground up

The word "percent" comes from Latin per centum — "per hundred". So a percentage is a fraction with a fixed denominator of 100: 25% = 25/100 = 0.25 = one quarter. This convention makes it possible to compare shares of differently sized totals without having to find a common denominator first. In spreadsheets, accounting, and everyday life it provides a uniform language: a 20% discount is immediately comparable with a 3.5% inflation rate or a 19% tax rate. The crucial distinction is between a relative share (percent of a base value) and an absolute value (e.g. euros). 5% of €80 is €4 — one is a fraction, the other a concrete number with a unit.

Percentage change is where things get interesting — and error-prone. "Revenue rose from 200 to 240" is a 20% increase (relative to the base of 200). If revenue then falls back to 200, that is not a 20% drop — it is a 16.67% drop, because 240 is now the reference. This asymmetry causes endless confusion in statistics: 100 → 200 is +100%, 200 → 100 is only −50%. Chaining multiple changes means multiplying factors: +20% followed by −10% is 1.20 × 0.90 = 1.08, i.e. a net +8% — not +10%.

An important distinction in finance and politics news: percent vs. percentage points. If a central bank raises its rate from 4% to 4.5%, that is 0.5 percentage points higher, but at the same time a 12.5% relative increase (0.5 / 4 × 100). Election results, market shares, and inflation rates are almost always compared in percentage points to avoid this ambiguity. German VAT is a good worked example: 19% VAT on a net price of €100 produces €19 of tax, i.e. a €119 gross price. To back out the VAT from a gross price, divide by 1.19 — not by 1.21.

Formulas at a glance

Three basic formulas cover almost every practical case. X% of Y: (X / 100) × Y. Example: 20% of 80 = 0.20 × 80 = 16. X is what % of Y: (X / Y) × 100. Example: 12 of 80 = (12 / 80) × 100 = 15%. Change from old to new: ((new − old) / |old|) × 100. Example: 80 → 100 = ((100 − 80) / 80) × 100 = +25%. From a percentage markup back to gross: gross = net × (1 + p/100) and net = gross / (1 + p/100). For multi-stage operations multiply the factors: "first +10%, then −5%" = 1.10 × 0.95 = 1.045 → +4.5%.

Practical examples

Real numbers from tax, savings, and shopping:

  • 20% of 80 = 16 — classic discount example: a €80 sweater with 20% off costs €64 at checkout.
  • 19% VAT on €100 net = €19 → gross price €119. Reverse: €119 gross / 1.19 = €100 net.
  • Stock €80 → €100: +25% return. The following year falling back to €80 equals −20%. Over two years the net is 0%, but the annualised average is not 2.5%.
  • Restaurant tip: 18% on a $47.50 check = $8.55 tip → $56.05 total. Quick rule of thumb: 10% plus half of it = 15%.
  • Compound interest: 5% p.a. on €10,000 after 10 years is 10,000 × 1.05^10 = €16,288.95 — a 62.89% gain, even though the rate is "only" 5% per year.

Common mistakes and limits

Three pitfalls show up over and over again. First, confusing percent with percentage points — a drop from 8% to 6% is 2 percentage points, or 25% in relative terms. Second, asymmetric comparisons: a 50% rise followed by a 50% fall does not return to the original — it gives 100 × 1.5 × 0.5 = 75. Third, floating-point effects: many percentage operations in JavaScript yield results like 0.1 + 0.2 = 0.30000000000000004 instead of 0.3 — for monetary values always round to two decimals (cent precision) or compute in integer cents. Also note: a percentage of 100% equals the base value itself (factor 1), 200% is twice as much. "Giving 110%" is fine as a figure of speech, but mathematically it would be a doubling of the base plus 10%.

Frequently asked questions

What's the difference between percent and percentage points?
Percentage points are absolute differences between two percentages; percent describes a relative change. A move from 5% to 7% is +2 percentage points = +40% relative.
How do I back out VAT?
Divide the gross price by (1 + tax rate / 100). At 19% VAT: €119 / 1.19 = €100 net. Tax = gross − net = €19. For 7%, divide by 1.07.
How do I combine multiple discounts?
Multiply the factors. "20% off then an extra 10% customer discount" is 0.80 × 0.90 = 0.72, so a total discount of 28% — not 30%.
Can the result be negative?
Yes — in "change" mode a decrease produces a negative sign. In the other modes the sign follows from the signs of the input and the base value, using ordinary fraction rules.
How precise are the results?
The display rounds to up to 4 decimals; internally we use IEEE 754 double precision (~15 significant digits). For monetary values you should round the final result to the cent manually.
Are my inputs stored?
No. The calculation runs entirely in your browser — no input leaves your device. Reload the page and all fields are empty again.

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