How to use the percentage calculator
The calculator answers the four percentage questions people ask most often. Each box works on its own and updates as you type:
- What is X% of Y? — for example, a 15% tip on a 200 bill.
- X is what percent of Y? — for example, scoring 45 out of 60 in an exam.
- Percentage change from X to Y — for example, a price that rose from 80 to 100.
- Increase or decrease Y by X% — for example, adding 20% VAT or taking 20% off.
Underneath each answer you will see the exact formula used, so you can follow the working or copy it into homework.
Percentage formulas explained
“Percent” means “per hundred”, so 15% is the same as 15 ÷ 100 = 0.15. Every percentage calculation is built on that idea.
1. Finding a percentage of a number
Result = (X ÷ 100) × Y
15% of 200 = 0.15 × 200 = 30.
2. Finding what percent one number is of another
Percent = (X ÷ Y) × 100
45 out of 60 = 45 ÷ 60 × 100 = 75%. This is how exam marks are turned into percentages.
3. Percentage change (increase or decrease)
% change = (New − Old) ÷ |Old| × 100
From 80 to 100: (100 − 80) ÷ 80 × 100 = +25%. A negative answer means a decrease. Always divide by the original (old) value — this is the most common mistake.
4. Increasing or decreasing by a percentage
Increase: Y × (1 + X ÷ 100) Decrease: Y × (1 − X ÷ 100)
250 increased by 20% = 250 × 1.2 = 300. 250 decreased by 20% = 250 × 0.8 = 200.
A common trap: percentages don’t cancel out
If a price goes up by 20% and then down by 20%, you do not end up where you started. 100 + 20% = 120, but 120 − 20% = 96. The second change is calculated on a bigger number. The same applies to investments: a 50% loss needs a 100% gain to recover.
Percentage points vs. percent
If an interest rate rises from 5% to 6%, it has risen by 1 percentage point, but by 20 percent (because 1 is 20% of 5). News reports and bank offers often mix these up, so it is worth knowing the difference.
Quick mental-maths shortcuts
- 10%: move the decimal point one place left (10% of 340 = 34).
- 5%: half of 10% (5% of 340 = 17).
- 1%: move the decimal point two places left (1% of 340 = 3.4).
- Swap trick: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8 = 4.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 200 is 0.15 × 200 = 30.
How do I work out my exam percentage?
Divide the marks you scored by the total marks and multiply by 100. 45 out of 60 is 45 ÷ 60 × 100 = 75%. Use the second box in the calculator.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is a 25% increase.
Can a percentage be more than 100%?
Yes. If a value more than doubles, the increase is over 100%. For example, going from 50 to 150 is a 200% increase.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages (5% to 6% is 1 point). Percent change measures that difference relative to the starting value (5% to 6% is a 20% increase).