How the percentage calculator works
Percentages appear in prices, grades, statistics, recipes and pay rises, but the same word covers several different questions. This calculator handles the five most common ones. Pick the question from the menu and the two input boxes relabel themselves, so it is clear which number goes where. The answer updates instantly and the result card repeats the question in words so you can confirm you set it up correctly.
A percentage is just a fraction with a denominator of 100. So 15% means 15 out of every 100, or 0.15. Every percentage problem is a way of moving between the part, the whole and the percentage, given any two of them. Once you see the pattern, you can solve these on paper too.
One subtle point is the difference between percentage change and percentage points. If an interest rate moves from 4% to 5%, it has risen by one percentage point, but the percentage change is 25%. The calculator’s change mode gives the latter.
The five formulas
A% of B = B × A / 100
A is what % of B = A / B × 100
Change from A to B = (B − A) / |A| × 100
Increase B by A% = B × (1 + A/100)
Decrease B by A% = B × (1 − A/100)
The change formula divides by the starting value, so it cannot be calculated when the starting value is zero. The what-percent formula divides by the whole, so the whole cannot be zero.
Worked examples
15% of 240: 240 × 15 / 100 = 36. 45 is what percent of 360: 45 / 360 = 0.125, so 12.5%.
Percentage change from 80 to 100: (100 − 80) / 80 = 0.25, an increase of 25%. Reverse it: going from 100 back to 80 is a drop of 20 out of 100, which is a 20% decrease. The two are not the same, because the base is different. This asymmetry is why a stock that falls 50% needs a 100% gain to recover.
Increase 200 by 15%: 200 × 1.15 = 230. Decreasing 200 by 15% gives 200 × 0.85 = 170.
Tips and common mistakes
- Check the base. Most percentage errors come from using the wrong number as the starting point.
- Do not add successive percentages. A 20% rise followed by a 20% fall leaves you 4% below where you began.
- Mental shortcut: 10% is the number divided by 10; 5% is half of that; 1% is the number divided by 100.
- Percentage points are not percent. Say which one you mean in reports.
- Round at the end, not in the middle of a multi-step calculation.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For 15% of 240, multiply 240 by 15 to get 3,600, then divide by 100 to get 36. Choose the "What is A% of B?" option.
How do I find percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. A price that goes from 80 to 100 has risen by 25%. The calculator’s change mode does this automatically.
Why is a 50% drop followed by a 50% rise not back to the start?
Because the second percentage applies to a smaller base. A 100 item that falls 50% is worth 50. A rise of 50% on 50 gives 75, not 100.
What is the difference between percent and percentage points?
Percentage points are the simple arithmetic difference between two percentages. Percent change compares them relative to the starting value. A move from 10% to 12% is 2 percentage points but a 20% relative increase.
Can the result be over 100%?
Yes. If the part is larger than the whole, such as 150 is what percent of 100, the answer is 150%. Percentage increases can also exceed 100% when a value more than doubles.