How to Calculate Percentages: The Complete Guide

What Is a Percentage?

A percentage is a number expressed as a fraction of 100. The symbol % means “per hundred.” So 45% means 45 out of every 100.

Percentages are used everywhere — discounts, tax rates, interest rates, test scores, and nutritional labels all use them.

How to Calculate X% of a Number

To find X percent of a number Y, use the formula:

Result = (X ÷ 100) × Y

Example: What is 20% of 150?
(20 ÷ 100) × 150 = 0.20 × 150 = 30

Use the Percentage Calculator to find this instantly.

How to Find What Percentage X Is of Y

To work out what percentage one number is of another:

Result = (X ÷ Y) × 100

Example: 30 is what percent of 150?
(30 ÷ 150) × 100 = 0.20 × 100 = 20%

How to Calculate Percentage Increase or Decrease

Formula: % Change = ((New Value − Original Value) ÷ |Original Value|) × 100

• Positive result = increase
• Negative result = decrease

Example: A price rises from £80 to £100.
((100 − 80) ÷ 80) × 100 = +25% increase

Example: A price drops from £100 to £80.
((80 − 100) ÷ 100) × 100 = −20% decrease

How to Add or Subtract a Percentage

Add X% to Y: Y × (1 + X/100)
Subtract X% from Y: Y × (1 − X/100)

Example: Add 15% to $200.
200 × 1.15 = $230

Example: Subtract 15% from $200.
200 × 0.85 = $170

Common Percentage Mistakes

1. Confusing % increase with the final value. A 20% increase on 100 gives 120, not 20.
2. Reversing the order in % change. Always divide by the original, not the new value.
3. Percentage points vs percentages. Going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase.

Quick Reference

Try our free Percentage Calculator to solve any of these in seconds.