Percentage Calculator — friendly & detailed

A complete set of percentage tools that update automatically as you type. Each tool below shows the inputs, the result, the exact formula used, and a short example.

1. % of = 0
Formula: P% of X = (P / 100) × X — Example: 20% of 500 = (20/100)×500 = 100.
2. is what percent of = 0%
Formula: Percent = (X ÷ Y) × 100 — Example: 50 is (50 ÷ 200) × 100 = 25%.
3. From to = 0%
Formula: Percent change = ((new − old) ÷ old) × 100 — Example: (120−100)÷100×100 = 20% increase. For decreases, result is negative.
4. Percent difference between and = 0%
Formula: Percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100 — Example: |40−60|÷((40+60)/2)×100 = 40%.
5. is after a % → Original = 0
Formula: If final = original × (1 + r) → original = final ÷ (1 + r) (for increase)
If final = original × (1 − r) → original = final ÷ (1 − r) (for decrease) — Example: 120 after 20% increase → original = 120 ÷ 1.20 = 100.
6. % = 0
Formula: Add: result = base × (1 + r)   Subtract: result = base × (1 − r) — Example: Add 10% to 200 → 200 × 1.10 = 220.
7. / = 0%
Formula: Percent = (numerator ÷ denominator) × 100 — Example: 1/4 = 0.25 × 100 = 25%.
8. = 75%
Formula: Percent = decimal × 100 — Example: 0.75 × 100 = 75%.

How percentage calculations work — formulas & quick guide

Percentages express a number as a fraction of 100. This page provides the exact formulas used for each calculation and quick examples so you can check your answers manually if you like.

Common percentage formulas (quick reference)

  • P% of X = (P ÷ 100) × X
  • X is what % of Y = (X ÷ Y) × 100
  • Percent change = ((new − old) ÷ old) × 100
  • Percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100
  • Reverse percent (original) = final ÷ (1 ± r)
  • Add/Subtract % = base × (1 ± r)
  • Fraction → % = (numerator ÷ denominator) × 100
  • Decimal → % = decimal × 100

Practical uses

Percentage calculations are widely used in finance (discounts, interest rates), commerce (tax, VAT), data analysis, statistics, and everyday life (tips, grade calculations).

Accuracy & rounding

Results are shown with up to four decimal places for precision. For display or monetary use you may round to 2 decimal places (e.g., cents) where appropriate.

Input rules & limits

  • Percent inputs: typically 0 – 100 (but this tool accepts beyond 100 for cases like growth >100%).
  • Values (base, old, new, etc.): should be finite numbers. Avoid zero in denominators (the calculator handles this and shows 0 where division by zero would occur).
  • Fraction denominator must be non-zero for a valid fraction to percent conversion.

Frequently Asked Questions

A percentage is a number or ratio expressed as a fraction of 100. For example, 25% means 25 out of every 100, or 0.25 in decimal form.
Use the formula ((new − old) ÷ old) × 100. If the result is positive it is an increase; if negative it is a decrease.
If you know the final price and the percent change, use reverse percentage: original = final ÷ (1 ± r).
Percent difference compares two values relative to their average to give a symmetric measure that doesn't depend on which value is chosen as the reference.