Percentage maths, finally painless
PercentBase answers the percentage questions that come up in shops, classrooms, invoices and spreadsheets — and shows every step of the working so the method sticks.
- Eleven calculators covering discounts, tips, tax, markup, grades and more.
- Every answer comes with the formula and a step-by-step solution.
- Runs entirely in your browser — your numbers never leave your device.
Percentage calculator
Pick the question you need to answer, type your numbers, and see the full working.
What is a given percentage of a number?
Turn a part and a whole into a percentage.
Work backwards from a part to the whole.
How much did a value rise or fall, in percentage terms?
Recent calculations
Every calculator on PercentBase
Each one is a full page with its own formula, worked example and common mistakes — not just a box that spits out a number.
Percentage Calculator
The three classic questions: percent of a number, part as a percent, and working back to the whole.
Open calculator →Percentage Increase
Find the percentage a value went up by, or add a percentage on top of a starting number.
Open calculator →Percentage Decrease
Measure a drop between two values, or take a percentage off a starting number.
Open calculator →Percentage Change
One tool for rises and falls, with the direction of the change stated clearly.
Open calculator →Percentage Difference
Compare two values that have no natural before and after, using their average.
Open calculator →Discount Calculator
See the sale price and the money saved, or work out what discount a price tag represents.
Open calculator →Tip Calculator
Add a tip to a bill and split the total evenly between any number of people.
Open calculator →Markup Calculator
Set a selling price from your cost, and see the profit margin that results.
Open calculator →Tax Calculator
Add a tax rate to a price, or strip an included tax back out of a total.
Open calculator →Grade Percentage
Convert marks into a percentage, and find the score you need in a final exam.
Open calculator →Reverse Percentage
Recover the original number when you only know the value after a change.
Open calculator →What a percentage actually is
A percentage is simply a fraction with 100 on the bottom. The word comes from the Latin per centum, meaning "by the hundred", and the % sign is a worn-down way of writing /100. So 45% is another way of writing 45/100, or 0.45 in decimal form.
That single idea is what makes percentages useful. Fractions with different denominators are awkward to compare — is 17/40 bigger than 3/7? Convert both to percentages, 42.5% against 42.86%, and the answer is obvious. Putting everything over the same denominator turns comparison into a glance.
Moving between percentages, decimals and fractions
| Percentage | Decimal | Fraction | Often seen in |
|---|---|---|---|
| 5% | 0.05 | 1/20 | Small service charges |
| 12.5% | 0.125 | 1/8 | Bulk discounts |
| 25% | 0.25 | 1/4 | Sale prices |
| 33.33% | 0.3333 | 1/3 | Three-way splits |
| 75% | 0.75 | 3/4 | Exam scores |
| 150% | 1.5 | 3/2 | Growth over time |
To go from a percentage to a decimal, divide by 100 — or just move the decimal point two places to the left. To go the other way, multiply by 100. Everything else on this site is built on top of that one move.
The three questions that cover almost everything
Nearly every percentage problem is one of three shapes. Once you can spot which shape you are looking at, the arithmetic takes seconds.
1. What is X% of Y?
This is the shape you need when a percentage is applied to something: a 15% tip on a bill, 8% tax on a price, 30% off a jacket. Turn the percentage into a decimal and multiply.
2. X is what percentage of Y?
Use this when you have two real numbers and want to express one as a share of the other: 34 marks out of 40, 12 defective units out of 500, 1,800 spent from a 6,000 budget.
3. X is Y% of what number?
This one works backwards. You know a part and the percentage it represents, and you want the total. If a 15% deposit came to 4,500, the full price was 4,500 ÷ 0.15 = 30,000.
Worked examples from everyday life
Shopping: a jacket reduced from 2,400 to 1,680
- Find the money saved: 2,400 − 1,680 = 720
- Divide by the original price: 720 ÷ 2,400 = 0.3
- Multiply by 100: 0.3 × 100 = 30% off
School: 57 marks out of a possible 75
- Divide the score by the total: 57 ÷ 75 = 0.76
- Multiply by 100: 0.76 × 100 = 76%
Work: a salary rising from 42,000 to 46,200
- Find the rise: 46,200 − 42,000 = 4,200
- Divide by the original salary: 4,200 ÷ 42,000 = 0.1
- Multiply by 100: a 10% increase
Three mistakes worth avoiding
Adding percentages of different totals. A 10% rise followed by a 10% fall does not return you to where you started. Start at 100, rise to 110, then fall by 10% of 110 — that is 11, not 10 — and you land on 99. Each percentage is taken from whatever the value is at that moment.
Confusing percentage points with percentages. If an interest rate moves from 4% to 6%, that is a rise of two percentage points, but a 50% increase in the rate itself. Both statements are true, and they describe very different things.
Taking a discount off the wrong number. When a price already includes tax, applying a discount to the pre-tax figure gives a different answer than applying it to the total. Decide which number the percentage belongs to before you start.
Popular right now
The four tools people reach for most often.
Working out a sale price
Enter the ticket price and the discount to see exactly what you will pay and what you save.
Discount calculator →Splitting a restaurant bill
Add the tip, divide between everyone at the table, and settle up without any arguments.
Tip calculator →Adding or removing tax
Go from a pre-tax price to a total, or pull an included tax back out of a final amount.
Tax calculator →Measuring growth
Turn a rise in sales, salary, rent or followers into a percentage you can quote.
Increase calculator →