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Percentage Calculator

Answer three common percentage questions with the equation, denominator, and boundary conditions stated plainly.

Free · Private · Runs in your browser

Three common percentage questions

Choose a question and enter two values

Values stay in your browser. Percentages may be below zero or above 100; percentage change requires a positive original value.

Values
Your result will appear here after you submit valid values.

Formulas and calculation method

A percentage is a number per hundred. To find p% of a value y, this calculator uses (p ÷ 100) × y. For example, 25% of 200 is 0.25 × 200 = 50.

To find what percentage a part x is of a whole y, it uses (x ÷ y) × 100. The whole cannot be zero because division by zero is undefined.

Percentage change from original value o to new value n is ((n − o) ÷ o) × 100. A positive result is an increase; a negative result is a decrease. This mode requires a positive original value so the direction has an ordinary, unambiguous interpretation.

Conventions and boundaries

  • Percent values: values below 0% and above 100% are mathematically valid and accepted.
  • Part-to-whole denominator: the whole may be positive or negative, but cannot be zero.
  • Zero values: zero percent, a zero value, or a zero part produces zero when the denominator is valid. A zero whole or original value is rejected.
  • Percentage-change denominator: the original value must be greater than zero. This calculator does not assign a conventional percent change from zero or a negative starting value.
  • Precision: calculations use JavaScript double-precision numbers. Results display up to eight decimal places and omit unnecessary trailing zeroes.
  • Input bounds: each entry must be a finite number from −1,000,000,000,000,000 through 1,000,000,000,000,000. Empty, nonnumeric, non-finite, and out-of-range entries produce a linked error and focus the invalid field.
  • Fixed versus changing values: all values are entered by the user. The formulas use no live data, customary defaults, jurisdictional tables, or changing external values.

Limitations

A percentage describes a mathematical relationship, not why a value changed or whether two quantities are meaningfully comparable. Check units, time periods, definitions, sampling, and rounding before using a result in a consequential decision. This calculator provides educational information, not financial, legal, tax, medical, or statistical advice.

Worked examples

  • 12.5% of 80 is 10.
  • 45 is 37.5% of 120.
  • A change from 80 to 100 is a 25% increase.

Common questions

Can a percentage be greater than 100?

Yes. NIST defines the percent symbol as the number 0.01, so 125% is the number 1.25. In a percent-of calculation, 125% of 80 is 100.

Why is percentage change unavailable from zero?

The original value is the denominator. Dividing a change by zero is undefined, so the calculator reports an error instead of displaying infinity or a misleading percentage.

Is percentage change the same as percentage-point change?

No. Moving from 20% to 25% is a five-percentage-point change and a 25% relative increase. This calculator’s change mode returns the relative increase or decrease.

Use the Compound Interest Calculator for repeated growth over time, or the Loan Calculator for fixed-rate payment estimates.

Version and verification

Calculation version 1.0.0; formula and deterministic fixtures last verified 2026-08-05. Authority pages were retrieved 2026-08-05. Automated tests cover all three modes, denominator errors, boundaries, metadata, privacy, keyboard, responsive, contrast, and Axe behavior. Manual VoiceOver remains waived and is not claimed as passed.