Calculator
Percentage Calculator
Seven calculations covering almost every percentage problem, each written as a plain sentence with the numbers sitting inside it. Type into the sentence and the answer appears underneath, with the working shown.
What do you want to work out?
Find part of a total
What is % of ?
Answer
30
(20 divided by 100) times 150 = 30
Percentage change or percentage points?
They are different, and mixing them up is the most common percentage mistake. A rate moving from 4% to 6% has risen by 2 percentage points, which is a 50% increase. Use percentage points when both numbers are already percentages.
Common percentages
| % | of 100 | of 200 | of 500 | of 1000 |
|---|---|---|---|---|
| 5% | 5 | 10 | 25 | 50 |
| 10% | 10 | 20 | 50 | 100 |
| 15% | 15 | 30 | 75 | 150 |
| 20% | 20 | 40 | 100 | 200 |
| 25% | 25 | 50 | 125 | 250 |
| 30% | 30 | 60 | 150 | 300 |
| 40% | 40 | 80 | 200 | 400 |
| 50% | 50 | 100 | 250 | 500 |
| 75% | 75 | 150 | 375 | 750 |
Four steps
How to calculate a percentage
- 1
Pick the calculation
Choose "of", "is what %", "change" or "reverse" depending on what you know.
- 2
Enter the two numbers
The result appears as you type, no need to press anything.
- 3
Check the working
The formula line shows exactly how the answer was reached.
- 4
Use the reference table
Common percentages of 100, 200, 500 and 1000 are listed underneath.
The seven calculations, and when you need each
| You know | You want | Use |
|---|---|---|
| A rate and a total | The part | X% of Y |
| A part and a total | The rate | X is what % of Y |
| A result and a rate | The original | X is Y% of what |
| A value and a rate | The higher figure | Increase by % |
| A value and a rate | The lower figure | Decrease by % |
| Two values over time | Directional change | % change |
| Two values, no order | How far apart | % difference |
Doing percentages in your head
- 10%: move the decimal one place left. 10% of 240 is 24.
- 5%: half of 10%. So 12.
- 20%: double 10%. So 48.
- 15%: 10% plus 5%. So 36.
- 1%: move the decimal two places left. 2.4.
- The reversal trick: X% of Y always equals Y% of X. 8% of 50 is awkward; 50% of 8 is obviously 4.
Percentage change in practice
The formula is ((new − old) ÷ |old|) × 100. The absolute value on the denominator matters when the starting figure is negative, which is where most spreadsheet formulas quietly go wrong.
Two things worth remembering. First, percentage changes are not symmetric, up 50% then down 50% leaves you at 75% of where you started. Second, a percentage change of a percentage is ambiguous unless you say whether you mean a relative change or percentage points.
Discounts, tax and tips
- Apply a discount: price × (1 − rate). £80 at 25% off = 80 × 0.75 = £60.
- Add tax: price × (1 + rate). £60 plus 20% VAT = 60 × 1.2 = £72.
- Remove tax: price ÷ (1 + rate). £72 including 20% VAT = 72 ÷ 1.2 = £60.
- Stacked discounts: multiply the factors. 20% then 10% off is 0.8 × 0.9 = 0.72, a 28% total reduction, not 30%.
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Answers
Frequently asked questions
(15 ÷ 100) × 200 = 30. The mental shortcut: 10% is the number with the decimal point moved one place left, and you can build most percentages from there, 15% is 10% plus half of 10%.80 ÷ 0.8 = £100. The common mistake is adding 20% back to £80, which gives £96 and is wrong.