How to Calculate Percentages: Formulas and Real Examples

Percentages show up everywhere: discounts, tips, taxes, exam scores, and interest rates. Yet many people freeze when they need to work one out quickly. Once you understand the core formula, every percentage problem becomes simple arithmetic.

The Basic Percentage Formula

A percentage is just a fraction out of 100. To find what percentage one number is of another, divide the part by the whole and multiply by 100:

percentage = (part / whole) x 100

Example: What percent is 45 of 180?
(45 / 180) x 100 = 25%

To find a percentage of a number (for example, 20% of 250), convert the percentage to a decimal and multiply: 0.20 x 250 = 50.

Percentage Increase and Decrease

To calculate how much a value has changed in percentage terms, use the difference divided by the original value:

change = ((new - old) / old) x 100

Example: A price rises from $80 to $100
((100 - 80) / 80) x 100 = 25% increase

• A positive result means an increase.
• A negative result means a decrease.
• Always divide by the original (old) value, not the new one, this is the most common mistake.

Reverse Percentages

Sometimes you know the final amount and need the original. If a price is $120 after a 20% increase, divide by 1.20 to find the original: 120 / 1.20 = $100. For a discount, divide by (1 minus the decimal): a $75 price after 25% off was originally 75 / 0.75 = $100.

When speed and accuracy matter, a dedicated percentage calculator removes the risk of a misplaced decimal, especially with reverse percentages and multi-step problems.