What Even Is a Percentage?
A percentage is just a way of saying "out of 100." The word comes from Latin — "per centum" means "for each hundred."
So 50% means 50 out of 100. 25% means 25 out of 100. Simple.
But percentages come up in three very different situations, and each one needs a slightly different approach.
Type 1: What Is X% of a Number?
The question: "What is 20% of 500?"
The formula: (Percentage ÷ 100) × Number
Example: 20 ÷ 100 = 0.2. Then 0.2 × 500 = 100.
Real life: A shirt costs £80. There is a 15% discount. How much do you save?
15 ÷ 100 × 80 = £12 discount. You pay £68.
Type 2: What Percentage Is X of Y?
The question: "30 is what percent of 150?"
The formula: (X ÷ Y) × 100
Example: 30 ÷ 150 = 0.2. Then 0.2 × 100 = 20%.
Real life: You scored 72 out of 90 on a test. What is your percentage?
72 ÷ 90 × 100 = 80%. Good job!
Type 3: Percentage Change (Increase or Decrease)
The question: "A phone cost £600 last year. Now it costs £750. What is the percentage increase?"
The formula: ((New − Old) ÷ Old) × 100
Example: (750 − 600) ÷ 600 × 100 = 150 ÷ 600 × 100 = 25% increase.
If the number goes down, you get a negative result — that is a percentage decrease.
Real life: Your salary was £2,000. It went up to £2,300. That is a 15% raise.
Common Percentage Situations in Daily Life
| Situation | Type to Use |
|---|---|
| Shopping discount | Type 1 — what is X% of price? |
| Exam score | Type 2 — what % did I get? |
| Price increase | Type 3 — what % did it change? |
| Tip at a restaurant | Type 1 — what is 15% of the bill? |
| Weight loss progress | Type 3 — what % did I lose? |
| Tax on a purchase | Type 1 — what is 20% of the price? |
Skip the Maths — Use a Free Calculator
If you do not want to calculate by hand, just use our Percentage Calculator. It handles all three types above. Type in two numbers, choose the question you are asking, and get the answer instantly.
It also works great for: