Percentage Formulas: How to Calculate Any Percentage
Every percentage formula you need — finding X% of a number, percentage change, reverse percentages, percentage difference, and the distinction between percentages and percentage points.
What Is a Percentage?
A percentage is a ratio expressed as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." A percentage of 25% means 25 out of every 100, or equivalently 0.25 as a decimal or 1/4 as a fraction.
Percentages appear in everyday life: discounts, tax rates, interest rates, exam grades, polling data, nutritional labels, and more. Despite their ubiquity, percentage calculations trip people up — particularly percentage change and the distinction between percentage points and percentages.
The Three Core Percentage Formulas
Almost every percentage problem is a variation of one of three questions. Each has its own formula:
= 0.15 × 200 = 30
= (30 ÷ 200) × 100 = 15%
= 30 ÷ 0.15 = 200
The third formula — "X is P% of what?" — is called a reverse percentage. It lets you work back to the original value when you know a percentage and the resulting amount. This is useful for finding pre-discount prices, pre-tax amounts, and original values before any percentage change was applied.
Percentage Change Formula
Percentage change measures how much a value has grown or shrunk relative to its starting point. It is always calculated using the original (old) value as the denominator.
Change = 100 − 80 = 20
Percentage change = (20 ÷ 80) × 100 = +25%
A £20 rise on an £80 base is a 25% increase — not a 20% increase.
Change = 80 − 100 = −20
Percentage change = (−20 ÷ 100) × 100 = −20%
A £20 fall on a £100 base is a 20% decrease — not the same as the 25% rise that got there.
Percentage Increase and Decrease
To apply a known percentage change to a starting value, use a multiplier:
New price = £120 × (1 + 20/100) = £120 × 1.20 = £144
Removing VAT (reverse): £144 ÷ 1.20 = £120
The multiplier method is faster and less error-prone than calculating X% then adding or subtracting it separately.
Percentage Difference
When comparing two values and neither is the clear "original" or "base," use percentage difference. It takes the average of both values as the denominator, making the result symmetric.
|90 − 110| = 20
Average = (90 + 110) ÷ 2 = 100
Percentage difference = (20 ÷ 100) × 100 = 20% — the same whether you go from £90 to £110 or £110 to £90.
Percentage Points vs Percentages
One of the most common errors in interpreting data is confusing a change in percentage points with a change in percentage. These are not the same thing.
If a central bank raises the base rate from 2% to 3%:
- The change is 1 percentage point (absolute arithmetic difference)
- The rate has increased by 50% relative to its previous level (percentage change = (1 ÷ 2) × 100)
Headlines that say "mortgage rates rose by 1%" when they mean 1 percentage point are technically incorrect — the actual percentage increase is much larger. The distinction matters when comparing rates, grades, poll results, or any data expressed as percentages.
Quick-Reference Percentage Table
| Calculation | Formula | Example |
|---|---|---|
| Find X% of Y | (X ÷ 100) × Y | 20% of £350 = £70 |
| What % is X of Y? | (X ÷ Y) × 100 | £70 of £350 = 20% |
| Find the original (before increase) | Known ÷ (1 + P/100) | £120 after 20% rise → £120 ÷ 1.20 = £100 |
| Find the original (before decrease) | Known ÷ (1 − P/100) | £75 after 25% off → £75 ÷ 0.75 = £100 |
| Tip at 15% | Bill × 0.15 | £48 bill → £7.20 tip |
| Tip at 20% | Bill × 0.20 (or Bill ÷ 5) | £48 bill → £9.60 tip |
| Percentage change | ((New − Old) ÷ Old) × 100 | £40 → £52: +30% |
| Percentage of a percentage | (A% × B%) ÷ 100 | 30% of 40% = 12% |
Use the free percent calculator — solve all four percentage question types instantly, including percentage change and reverse percentage.
Open Percent Calculator →Frequently Asked Questions
How do I calculate a percentage increase?
Formula: ((New − Old) ÷ Old) × 100. If a salary rises from £30,000 to £33,000: ((33,000 − 30,000) ÷ 30,000) × 100 = (3,000 ÷ 30,000) × 100 = 10% increase. Alternatively: New = Old × (1 + P/100), so £30,000 × 1.10 = £33,000.
What is the difference between percentage and percentage points?
A percentage point is an absolute difference between two percentages: going from 4% to 5% is a rise of 1 percentage point. The percentage change in the rate itself is (1 ÷ 4) × 100 = 25%. Misusing these terms is common in news reporting — always check which one is being used when reading financial or statistical data.
How do I reverse a percentage?
Divide by the multiplier. To undo a 20% increase: divide by 1.20. To undo a 25% decrease: divide by 0.75. Never subtract or add the percentage of the final value — that gives the wrong answer because the percentage should be applied to the original, not the result.
How do I calculate a percentage of a percentage?
Multiply the two percentages and divide by 100. For example, 30% of 40% = (30 × 40) ÷ 100 = 12%. In decimal form: 0.30 × 0.40 = 0.12 = 12%. This comes up in probability (independent events) and in compound discounts — a 20% discount followed by a further 10% is not a 30% discount but 20% + (10% of 80%) = 28%.
Evidence & Methodology
How This Page Is Grounded
Method
Explains part/whole percentage, percentage change, reverse percentage and percentage difference with worked examples.
Important limitation: The correct formula depends on which value is the baseline; percentage change and percentage-point change are different.
Primary Sources
- Understanding percent OpenStax
Quality Checks
Each worked example is recalculated and checked in reverse.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.