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FREE MATH TOOL

Percentage Calculator

Calculate percentages, percentage increase and decrease, reverse percentages, and percentage differences with clear results.

Your details

Find 20% of 250.

Enter any finite decimal values. A zero denominator gives an undefined result instead of an incorrect answer.

Calculation result

Updates as you change the inputs

20% of 25050
Formula used20 × 250 ÷ 100

Quick examples

20% of 250 = 50

80 to 100 = 25% increase

120 after +20% = original 100

CALCULATOR GUIDE

Understand Percentage Calculator

Explore the formula, worked examples and practical explanations behind this calculator.

How to calculate percentages

A percentage means a value per hundred. To calculate a percentage of a number, multiply the number by the percentage and divide by 100.

Example: 20% of 250 = 250 × 20 ÷ 100 = 50.

Find what percentage one value is of another

Divide the part by the whole and multiply by 100.

Example: 30 is what percent of 200? 30 ÷ 200 × 100 = 15%.

If the whole is zero, the ratio is undefined.

Percentage increase and decrease

To find the changed value after an increase, multiply the starting value by (1 + percentage / 100). To apply a decrease, use a negative percentage.

Example: Increase 100 by 15%: 100 × 1.15 = 115. Decrease 100 by 15%: 100 × 0.85 = 85.

Percentage change between two values

Percentage change = (New value − Old value) ÷ |Old value| × 100.

Example: From 80 to 100, the change is (100 − 80) ÷ 80 × 100 = 25%.

A negative answer represents a decrease for a positive starting value. The original value must not be zero.

Reverse percentage calculation

If you know the value after a percentage change, you can calculate the original:

Original = Final ÷ (1 + percentage / 100).

Example: An item costs 120 after a 20% increase. Its original price was 120 ÷ 1.20 = 100.

A change of −100% leaves no unique original value when the final value is zero, so it cannot be reversed by this formula.

Percentage difference between two numbers

A symmetric percentage difference compares the absolute difference with the average of the two numbers’ absolute magnitudes:

Percentage difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100.

Example: For 90 and 110: 20 ÷ 100 × 100 = 20%.

Unlike percentage change, this formula does not identify either number as the starting value.

Common percentage mistakes

  • Confusing percentage points with percent change: going from 10% to 15% is 5 percentage points, but a 50% relative increase.
  • Using the final value as the denominator when calculating percentage change from the starting value.
  • Assuming increasing and then decreasing by the same percentage returns you to the original value.
  • Forgetting that percentages with zero denominators may be undefined.

When is this calculator useful?

Use it to compare prices, analyze discounts, review business growth, understand test scores, estimate changes in measurements, and check everyday percentage questions. The tool shows the expression used so the answer can be verified.

Further reading

For additional examples and a concept-focused explanation, see Percentage Formulas with Real-Life Examples.

COMMON QUESTIONS

Frequently Asked Questions

Clear answers to help you understand your results.

01How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 20% of 250 is 50.
02How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 is 15% of 200.
03How do I calculate a percentage increase?
Subtract the original value from the new value, divide by the absolute original value, and multiply by 100. For example, 80 to 100 is a 25% increase.
04How do I calculate a percentage decrease?
Use the same percentage change formula. A negative answer indicates a decrease. For example, 100 to 80 is a 20% decrease.
05What is a reverse percentage?
Reverse percentage finds the original value when the final value and percentage change are known. Divide the final value by 1 plus the percentage change divided by 100.
06What is the difference between percentage change and percentage difference?
Percentage change uses a starting value as its reference, while percentage difference uses the average absolute magnitude of the two values as its reference.
07Can the calculator use decimal or negative values?
Yes. Decimal and negative inputs are supported; some operations are undefined for particular zero denominators.
08What happens if the whole is zero?
A percentage ratio with a zero denominator is undefined. The calculator displays an undefined result instead of giving a misleading number.
09Is a 50% increase followed by a 50% decrease equal to the starting value?
No. Starting at 100, a 50% increase gives 150, and a 50% decrease of 150 gives 75.
10Is the percentage calculator free?
Yes. The calculator runs in your browser without requiring an account.