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Calculates

Percentage Calculator

Calculate percentages, increases, decreases and differences instantly.

Calculated & verified for mathematical accuracy·Reviewed by the Calculates Editorial Team

What is X% of Y?

Result

100

Working

20% × 500 = 100

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About this calculator

Percentages express one number as a proportion of another. This calculator covers the five calculations people actually need: finding a percentage of a value, expressing one number as a percentage of another, and measuring increase, decrease or the difference between two values. Each mode shows its working so you can check the result.

How to use this calculator

  1. Pick the calculation you need

    The five tabs are distinct calculations, not variations of one. Choose the one that matches the question you are asking.

  2. Enter your two numbers

    Labels change with the mode so it is always clear which value goes where. For increase and decrease, order matters: the first field is the original value.

  3. Read the working

    Every result shows the substituted formula, so you can verify the arithmetic or reproduce it by hand.

  4. Mind the denominator

    Increase and decrease are measured against the original value. Percentage difference is measured against the average of both values, which is why it gives a different answer.

Formula

1. X% of Y = (X / 100) × Y 2. X is what % of Y = (X / Y) × 100 3. Percentage increase = ((New − Original) / |Original|) × 100 4. Percentage decrease = ((Original − New) / |Original|) × 100 5. Percentage difference = (|A − B| / ((|A| + |B|) / 2)) × 100
  • Modes 3 and 4 use the original value as the denominator, so the answer depends on which number you start from.
  • Mode 5 uses the average of both values as the denominator, making it symmetric — swapping the inputs gives the same answer.
  • A negative result in mode 3 means the value fell rather than rose; a negative result in mode 4 means it rose.
  • Percentage change from zero is undefined: there is no base to measure against, so the calculator reports this rather than returning a misleading number.

Worked example

Inputs

  • Original value: 120
  • New value: 100

Calculation

Percentage decrease: ((120 − 100) / 120) × 100 = (20 / 120) × 100 = 16.67% Percentage difference (same pair): average = (120 + 100) / 2 = 110 (|120 − 100| / 110) × 100 = (20 / 110) × 100 = 18.18%

Going from 120 to 100 is a 16.67% decrease, but the percentage difference between 120 and 100 is 18.18%. The two answers differ because they divide by different denominators — 120 versus the average of 110.

What the result means

  • A percentage of a value (mode 1) returns a plain number in the same units as the input — 20% of ₹500 is ₹100.
  • A percentage share (mode 2) tells you how big one figure is relative to a total. Above 100% means the part exceeds the whole.
  • Increase and decrease describe a change over time or between two states, and the direction is meaningful.
  • Percentage difference describes how far apart two independent values are, with no implication that one came before the other. Use it when neither value is the natural baseline.

Related calculations

  • A 50% increase followed by a 50% decrease does not return you to the start: 100 → 150 → 75. Try it in the increase and decrease modes.
  • Use mode 2 to convert marks or scores into a percentage of the maximum.
  • Use mode 1 to work out a discount amount, then subtract it from the original price to get the sale price.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For example, 20% of 500 is (20 ÷ 100) × 500 = 100. A quick shortcut is to find 10% by moving the decimal point one place left, then scale it: 10% of 500 is 50, so 20% is 100.

What is the difference between percentage change and percentage difference?

Percentage change (increase or decrease) divides by the original value, so it measures movement from a known starting point and the order of the numbers matters. Percentage difference divides by the average of the two values, so it measures how far apart two comparable figures are and gives the same answer whichever order you enter them.

How do I calculate a percentage increase?

Subtract the original value from the new value, divide by the original value, then multiply by 100. Going from 100 to 120 gives ((120 − 100) ÷ 100) × 100 = 20%. If the result is negative, the value decreased rather than increased.

Why can I not calculate a percentage change from zero?

Percentage change is measured relative to the starting value, and dividing by zero is undefined. Any increase from zero is infinitely large in percentage terms, so the calculation carries no meaning. Report the absolute change instead — for example, "rose from 0 to 50".

Does a 50% increase cancel out a 50% decrease?

No. The two percentages are applied to different bases. Starting at 100, a 50% increase gives 150; a subsequent 50% decrease takes 50% off 150, leaving 75. To reverse a 50% increase you need a decrease of 33.33%.

How do I work out the original price before a discount?

Divide the discounted price by (1 − discount/100). If an item costs ₹800 after a 20% discount, the original price was 800 ÷ 0.8 = ₹1,000. Subtracting 20% from ₹800 would give the wrong answer because the discount was calculated on the higher original price.

What do percentage points mean?

A percentage point is the arithmetic difference between two percentages, while a percentage change compares them proportionally. A rate moving from 5% to 7% is a rise of 2 percentage points, but a 40% increase in relative terms. Financial and statistical reporting uses the distinction to avoid ambiguity.

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