The basic percentage formula
A percentage expresses one number as a fraction of another, scaled to 100. The word literally means "per hundred" (from Latin per centum).
The core formula:
Percentage = (Part / Whole) × 100
Or rearranged to find the part:
Part = (Percentage / 100) × Whole
Finding a percentage of a number
Question: What is 15% of 200?
Part = (15 / 100) × 200
Part = 0.15 × 200
Part = 30
15% of 200 is 30.
Another way to think about it: 10% of 200 is 20, and 5% is half of that (10), so 15% = 20 + 10 = 30.
Mental shortcuts like this are handy for rough estimates without a calculator.
Percentage increase
Use this when a value has grown and you want to know by what percentage.
Percentage increase = ((New Value − Old Value) / Old Value) × 100
Example: A product cost £40 last year and costs £52 this year.
Increase = ((52 − 40) / 40) × 100
Increase = (12 / 40) × 100
Increase = 0.30 × 100
Increase = 30%
The price increased by 30%.
Percentage decrease
The same structure applies when a value has fallen.
Percentage decrease = ((Old Value − New Value) / Old Value) × 100
Example: A stock was worth 250 and dropped to 200.
Decrease = ((250 − 200) / 250) × 100
Decrease = (50 / 250) × 100
Decrease = 20%
The stock decreased by 20%.
Percentage difference
When you want to compare two values without treating either as the "original", use percentage difference:
Percentage difference = (|Value A − Value B| / Average of A and B) × 100
The denominator is the average of the two values, which avoids the ambiguity of which is the reference point.
Example: Comparing two salary offers of 70,000 and 80,000.
Difference = 10,000 / ((70,000 + 80,000) / 2) × 100
Difference = 10,000 / 75,000 × 100
Difference ≈ 13.3%
The salaries differ by approximately 13.3%.
Working backwards from a changed value
Sometimes you know the result of a percentage change and need the original.
Example: After a 20% increase, a price is 120. What was the original price?
Original = New Value / (1 + Percentage / 100)
Original = 120 / 1.20
Original = 100
For a decrease — if after a 20% decrease a price is 80:
Original = 80 / (1 − 0.20)
Original = 80 / 0.80
Original = 100
Common percentage mental shortcuts
| To find... | Shortcut |
|---|---|
| 10% | Divide by 10 |
| 5% | Divide by 20 (or take half of 10%) |
| 25% | Divide by 4 |
| 50% | Divide by 2 |
| 1% | Divide by 100 |
| 20% | Divide by 5 |
These building blocks let you estimate most percentages quickly. For example, 35% = 25% + 10%.
Practical examples
VAT at 20%: A product costs 85 before tax. Tax = 0.20 × 85 = 17. Total = 102.
Exam score: You got 47 out of 60 correct. Score = (47 / 60) × 100 ≈ 78.3%.
Population growth: A city grew from 820,000 to 890,000. Increase = ((890,000 − 820,000) / 820,000) × 100 ≈ 8.5%.
Use the Percentage Calculator for any of these scenarios without having to recall the formula. For discount calculations specifically, see the How to Calculate a Discount guide.