How percentage calculation works
A percentage is a way of expressing a number as a fraction of 100. "25%" means 25 out of every 100 — or equivalently, 25 ÷ 100 = 0.25 as a decimal. All three calculation modes on this page are different arrangements of the same core relationship between a part, a whole, and a percentage.
Finding X% of a number
The most common percentage question. Divide the percentage by 100 to convert it to a decimal, then multiply by the whole.
Result = (X ÷ 100) × Y Example: What is 25% of 200? → (25 ÷ 100) × 200 = 50 Finding what percentage one number is of another
Divide the part by the whole, then multiply by 100. This tells you what share the part represents out of the total.
Result = (X ÷ Y) × 100 Example: 50 is what % of 200? → (50 ÷ 200) × 100 = 25% Finding the whole from a part and a percentage
If you know a part and the percentage it represents, divide to recover the original whole.
Result = (X × 100) ÷ Y Example: 50 is 25% of what? → (50 × 100) ÷ 25 = 200 Converting between percentages, decimals, and fractions
The same value can be written three ways, and converting between them uses simple, fixed rules:
Percentage → Decimal: divide by 100 (60% → 0.60) Decimal → Percentage: multiply by 100 (0.6 → 60%) Fraction → Percentage: divide, then multiply by 100 (3⁄8 → 0.375 → 37.5%) Common percentage reference
| Percentage | Decimal | Fraction | Of 200 |
|---|---|---|---|
| 1% | 0.01 | 1/100 | 2 |
| 2% | 0.02 | 1/50 | 4 |
| 5% | 0.05 | 1/20 | 10 |
| 10% | 0.10 | 1/10 | 20 |
| 15% | 0.15 | 3/20 | 30 |
| 20% | 0.20 | 1/5 | 40 |
| 25% | 0.25 | 1/4 | 50 |
| 30% | 0.30 | 3/10 | 60 |
| 33.33% | 0.333… | 1/3 | 66.67 |
| 40% | 0.40 | 2/5 | 80 |
| 50% | 0.50 | 1/2 | 100 |
| 60% | 0.60 | 3/5 | 120 |
| 66.67% | 0.667… | 2/3 | 133.33 |
| 75% | 0.75 | 3/4 | 150 |
| 80% | 0.80 | 4/5 | 160 |
| 90% | 0.90 | 9/10 | 180 |
| 100% | 1.00 | 1/1 | 200 |
| 125% | 1.25 | 5/4 | 250 |
| 150% | 1.50 | 3/2 | 300 |
Where percentages show up in everyday life
The three modes on this page are the building blocks behind a lot of everyday math:
- Shopping — working out what a sale price actually saves you. See the Discount Calculator for stacked discounts.
- Dining out — figuring a tip on the bill. See the Tip Calculator.
- Business and sales — commission on a sale, or the markup between cost and sale price. See the Commission Calculator and Markup Calculator.
- Investing — how much a return actually gained or lost relative to what you put in. See the ROI Calculator.
- Test scores and stats — converting a raw score like 42/50 into a percentage grade.
Frequently asked questions
What is the difference between percentage and percentage points?
A percentage point is an absolute difference between two percentages. If a tax rate rises from 10% to 15%, it increased by 5 percentage points — but by 50% in relative terms (because 5 is 50% of 10). The two are often confused in news reporting and financial documents.
How do I calculate a percentage tip or discount in my head?
For 10%, shift the decimal point one place left — 10% of £85 is £8.50. For 20%, double that. For 15%, take 10% and add half of it. For 5%, take 10% and halve it. These shortcuts work for any amount.
Can a percentage be greater than 100%?
Yes. A percentage greater than 100% simply means the part is larger than the whole used as a reference. "Sales grew 150%" means sales are now 2.5 times their original value. "200% of 50" is 100. There's no mathematical ceiling.
Why can't I divide by zero in the "find the whole" tab?
If the percentage is 0%, the formula requires dividing by zero, which has no defined result — mathematically, there is no number of which 0% equals any non-zero value. The calculator blocks this input and shows an error.
Does this calculator support scientific notation?
Yes. All number fields accept standard scientific notation. You can type 1e3 instead of 1000, 2.5e6 instead of 2500000, or 5e-2 instead of 0.05. This is useful when working with very large or very small values. Results are always displayed in standard decimal form.
Does this calculator store my inputs?
No. All calculations run in your browser. Nothing is sent to a server or saved anywhere.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For 3/8: 3 ÷ 8 = 0.375, so 3/8 = 37.5%.
How do I calculate the percentage change between two numbers?
Subtract the old value from the new value, divide by the old value, then multiply by 100. This calculator's three modes don't cover signed percentage change directly — use the Percentage Increase or Percentage Decrease calculator for that, depending on the direction.
Can a percentage be negative?
Yes — a negative percentage typically represents a decrease, such as "sales fell 12%" meaning a change of −12%. It follows the same math as a positive percentage, just with a negative sign carried through.
Does the calculator handle decimal inputs, not just whole numbers?
Yes — both the percentage and the numbers you enter can include decimals. Results like 33.33% are calculated and displayed precisely, as shown in the reference table above.