Percentages come up everywhere — discounts, tax, exam scores, salary increases, statistics, tips. Yet most people rely on a calculator without really understanding what is happening. Once you know the handful of core formulas, you can work out almost any percentage problem quickly, and catch errors when numbers don't feel right.
What a percentage actually means
The word percent comes from the Latin per centum, meaning "out of one hundred." A percentage is simply a fraction with 100 as the denominator. So 35% means 35 out of 100, or 0.35 as a decimal. That decimal form is what makes percentage arithmetic straightforward.
To convert a decimal to a percentage: multiply by 100.
Formula 1: What is X% of Y?
This is the most common percentage question — finding a portion of a total. The formula is:
Example: What is 15% of 240?
(15 ÷ 100) × 240 = 0.15 × 240 = 36
A quick mental shortcut: to find 10%, move the decimal point one place left. Then halve it for 5%, double it for 20%, and combine as needed.
Formula 2: X is what percentage of Y?
Here you know both numbers and want to express the relationship as a percentage.
Example: 45 is what percentage of 180?
(45 ÷ 180) × 100 = 0.25 × 100 = 25%
Formula 3: Percentage change
This tells you how much something has grown or shrunk relative to its starting value. It is used for price changes, growth rates, test score improvements and much more.
Example: A price goes from £80 to £96.
((96 − 80) ÷ 80) × 100 = (16 ÷ 80) × 100 = +20% increase
If the result is positive it is an increase. If negative it is a decrease. Always divide by the original value, not the new one — a common mistake that gives the wrong answer.
Formula 4 & 5: Adding or subtracting a percentage
Adding VAT, a tip, a markup, or a discount all use the same logic:
Subtract X%: Result = Number × (1 − X÷100)
Example — adding 20% VAT to £250:
250 × 1.20 = £300
Example — applying a 30% discount to £120:
120 × 0.70 = £84
Formula 6: Score as a percentage
Converting a raw score to a percentage is just a division:
Example: You scored 68 out of 85.
(68 ÷ 85) × 100 = 80%
Quick reference
| Question | Formula |
|---|---|
| What is X% of Y? | (X ÷ 100) × Y |
| X is what % of Y? | (X ÷ Y) × 100 |
| % change from A to B | ((B − A) ÷ |A|) × 100 |
| Add X% to a number | Number × (1 + X÷100) |
| Subtract X% from a number | Number × (1 − X÷100) |
| Score out of total | (Score ÷ Total) × 100 |
Calculate any percentage instantly
All six formulas in one tool — just enter your numbers and get the answer.
Open Percentage Calculator