Percentage Calculator
Three ways to calculate percentages — pick the one you need.
What is X% of Y?
X is what % of Y?
Percentage change
Understanding the units
Per cent
The word comes from the Latin per centum — "by the hundred." A percentage is simply a ratio expressed as a fraction of 100. Rather than saying "3 in every 20," you say 15%, which is easier to compare across different totals.
Percentages became the dominant notation for proportions in European commerce during the 16th and 17th centuries, when cross-border trade made a universal scale essential. Today the % sign appears on everything from tax forms to nutrition labels.
Percentage vs. percentage points
These two are frequently confused. If a savings rate rises from 3% to 4%, it has increased by 1 percentage point — but by 33% in relative terms. Mixing them up is one of the most common errors in financial reporting.
Basis points
In finance, interest rates and fees are often quoted in basis points (bps), where 1 basis point = 0.01%. A rate moving from 5.00% to 5.25% is a rise of 25 basis points. This precision matters when small fractions represent large sums.
When do you need this?
- Shopping discounts: A coat is 30% off its £120 price — how much do you actually pay?
- Tax and VAT: Calculating the VAT portion of an invoice, or the pre-tax price from a gross total.
- Restaurant tips: Working out 15% or 20% of a bill quickly, especially when splitting.
- Salary changes: You got a 4% pay rise — how much extra is that per month?
- Test scores: You scored 47 out of 60 — what percentage did you get?
- Interest and savings: How much will 3.5% interest earn on £5,000 over a year?
Quick reference
- X% of Y → Y × (X ÷ 100) · e.g. 20% of 150 = 30
- X is what % of Y? → (X ÷ Y) × 100 · e.g. 30 ÷ 150 × 100 = 20%
- Percentage change → ((new − old) ÷ old) × 100 · e.g. 80→100 = +25%
- Add VAT at 20% → multiply by 1.20 · e.g. £50 × 1.20 = £60
- Remove VAT at 20% → divide by 1.20 · e.g. £60 ÷ 1.20 = £50
- 10% shortcut → move the decimal one place left · 10% of 85 = 8.5
Common real-world percentages
| Scenario | Rate |
|---|---|
| UK VAT (standard rate) | 20% |
| EU average VAT | ~21% |
| US sales tax (varies by state) | ~7–10% |
| Restaurant tip — US | 15–20% |
| Restaurant tip — UK | 10–12.5% |
| Credit card cashback | 1–2% |
| Savings account interest (typical) | 3–5% |
Common mistakes
- Confusing percentage points with percent: A rate rising from 4% to 5% is a 1 percentage-point increase, but a 25% relative increase. These are very different statements.
- Reversing percentage change: A 50% increase followed by a 50% decrease does not return to the original — it leaves you 25% below it.
- Applying a discount twice: "20% off, then an extra 10% off" is not 30% off — it's 28% off total (you apply 10% to the already-reduced price).
- Adding VAT to a VAT-inclusive price: If a price already includes VAT, you need to back-calculate — not add VAT on top again.
- Rounding too early: When chaining percentage calculations, rounding intermediate results can compound into a visible error in the final figure.
Which should you use?
Finding a percentage of a number (e.g. calculating a tip, a discount, or interest earned): use What is X% of Y?
Expressing one number relative to another (e.g. a test score, a market share): use X is what % of Y?
Comparing two values over time (e.g. a price rise, salary change, or stock movement): use Percentage change. Always put the original value in the "from" field.
Frequently asked questions
How do I calculate what percent one number is of another?
Divide the part by the whole, then multiply by 100. For example, 30 is what percent of 150? 30 ÷ 150 = 0.2, then 0.2 × 100 = 20%. So 30 is 20% of 150.
How do I calculate a percentage of a number?
Multiply the number by the percentage divided by 100. For example, 20% of 150 = 150 × (20 ÷ 100) = 150 × 0.2 = 30.
How do I calculate percentage change between two numbers?
Subtract the original value from the new value, divide by the original value, then multiply by 100. For example, from 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase.
What is the difference between percentage increase and percentage decrease?
If the new value is higher than the original, it's a percentage increase. If it's lower, it's a percentage decrease. The formula is the same — a negative result means a decrease.
How do I work out a tip as a percentage?
Multiply the bill amount by the tip percentage divided by 100. For a 15% tip on a $60 bill: 60 × 0.15 = $9. In the UK a 10% tip is standard; in the US 15–20% is typical. A quick mental trick: find 10% first (move the decimal), then adjust up or down.
How do I calculate VAT from a price?
To find the VAT amount inside a VAT-inclusive price, divide by 1 plus the rate. For UK VAT at 20%: divide the total by 1.20 to get the pre-VAT price, then subtract to find the VAT portion. For example, £72 ÷ 1.20 = £60 pre-VAT, so the VAT is £12.
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