About Percentage Calculator
This percentage calculator handles the five questions people actually ask, rather than making you rearrange a formula yourself. Pick a mode and it will find what X% of Y is, tell you what proportion one number is of another, measure the change between a before and after figure, or apply an increase or decrease to a starting value. Every answer comes with the arithmetic written out underneath, so you can copy the working into homework, a spreadsheet note or an email to a colleague who wants to see how you got there.
The three formulas behind the five modes
Everything here reduces to three lines of arithmetic. To find a part, divide the percentage by 100 and multiply by the whole: 25% of 200 is (25 ÷ 100) × 200 = 50. To find what proportion one number is of another, divide the part by the whole and multiply by 100: 47 out of 68 is (47 ÷ 68) × 100 = 69.12%. To measure change, subtract the old value from the new, divide by the absolute value of the old, and multiply by 100: moving from 80 to 92 gives ((92 − 80) ÷ 80) × 100 = 15%. Increase and decrease modes are just shortcuts on the first formula, multiplying by (1 + p/100) or (1 − p/100) respectively. The calculator uses the absolute value of the starting figure when measuring change, which keeps the sign of the result meaningful even when you begin from a negative number such as a loss that shrinks.
Percentage points, and why gains and losses do not cancel
Two traps catch people out repeatedly. The first is confusing a percentage with a percentage point. If an interest rate moves from 4% to 5%, that is a one percentage point rise but a 25% relative increase, and financial reporting uses both phrasings in the same paragraph. When a figure is itself a percentage, always say which you mean. The second trap is assuming a rise and an equal-sized fall bring you home. They do not, because each percentage is applied to a different base. A stock at 100 that rises 50% reaches 150; a subsequent 50% fall takes 50% of 150, leaving 75. To recover from a 50% loss you need a 100% gain. In general, to reverse a fall of p percent you need a gain of p ÷ (100 − p) × 100 percent, which is why deep drawdowns are so hard to climb out of.
How to get your result
- 1
Choose a mode from the 'What do you want to work out?' dropdown — percent of, is what percent of, percentage change, increase or decrease.
- 2
Enter Value X. Depending on the mode this is the percentage, the part, or the starting figure.
- 3
Enter Value Y — the base amount, the whole, the ending figure, or the percentage being applied.
- 4
Read the Answer, the plain-English restatement below it, and the Working panel that shows the full calculation.
Where this helps
Checking a pay rise
Use percentage change to see that a salary moving from 42,000 to 45,500 is a 8.33% rise. Use increase mode to run the reverse and project what a 6% offer would actually pay.
Exam and test marks
Mode 'X is what percent of Y' converts a raw score into a grade percentage. A mark of 47 out of 68 is 69.12%, which is the figure most grade boundaries are set against.
Reading business reports
Percentage change turns two months of revenue into a growth figure, and makes clear whether a fall from 120 to 96 units is a 20% drop rather than a 24% one.
A few pointers
- Percentages commute: 8% of 25 is the same as 25% of 8, which is 2. Flip the numbers when one side is easier to work with mentally.
- To reverse a percentage increase, divide rather than subtract. A price that includes a 20% uplift is recovered by dividing by 1.2, not by taking 20% off.
- Use percentage change with care when the starting value is very small, because tiny bases produce enormous percentages that read as more dramatic than they are.