Percentage Calculator
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Six questions in one place: what a percentage of a number is, what one number is as a percentage of another, how much something changed, what a discount leaves you paying, and VAT in both directions. The last of those is the one people get wrong most often, because taking the tax back out of a total is not the same sum as putting it in.
The six sums, and when to use each
| Choose this | You want to know | Example | Answer |
|---|---|---|---|
| What is X% of Y? | A tip, a commission, a deposit, VAT on its own | 15% of 2,400 | 360 |
| X is what percent of Y? | A share of a total: how much of the budget one line took | 18 out of 60 | 30% |
| Percentage change from X to Y | Growth or a drop between two figures | 50 to 60 | 20% increase |
| Price after a discount | What you actually pay in a sale | 1,200 less 25% | 900 |
| Add VAT to a price | Quoting a price with tax included | 100 plus 7% | 107 |
| Remove VAT from a total | Splitting a receipt into price and tax | 107 including 7% | 100, tax 7 |
The two fields change their labels when you change the question, so you never have to remember which number goes on which side.
The arithmetic, so you can check it by hand
| Sum | How it is worked out |
|---|---|
| X% of Y | Y × X ÷ 100 |
| X as a percent of Y | X ÷ Y × 100 |
| Change from X to Y | (Y − X) ÷ X × 100 |
| Price after a discount | Price × (100 − discount) ÷ 100 |
| Add VAT | Price × (100 + rate) ÷ 100 |
| Remove VAT | Total ÷ (100 + rate) × 100 |
Every one of these is a single line of arithmetic. The reason a calculator is worth opening is not that the sums are hard, it is that the last two look like each other and are not, which is where the money goes missing.
Taking tax off is not the reverse of putting it on
Add 7% to 100 and you get 107. Now take 7% off 107 and you get 99.51, not 100. Nothing went wrong: the 7% you added was 7% of the price, and the 7% you subtracted was 7% of the larger total.
To get back to the price you divide by 1.07. On 107 that gives 100, with 7 of tax. Use Remove VAT from a total for anything where the figure in front of you already includes the tax, such as a receipt or a card statement. Use Add VAT to a price when you are quoting.
The rate is a field, so the same two work for 10%, 20%, or any other rate.
A rise and a fall of the same size do not cancel out
A percentage change is always measured against the number it started from, and that number moves.
- 100 rising by 25% is 125.
- 125 falling by 25% is 93.75, because that 25% is a quarter of 125, not of 100.
- To get from 125 back to 100 you need a fall of 20%.
This is why a stock that halves needs to double to recover, and why a 30% discount followed by a further 20% is 44% off rather than 50%. When you want the change between two figures rather than a percentage of one, Percentage change from X to Y is the one to pick: it reports the direction as well as the number, so a fall is never read as a rise.
Frequently asked questions
Why does removing VAT not use the same sum as adding it?
Because the tax was a percentage of the price, not of the total. Adding 7% to 100 gives 107. Taking 7% off 107 gives 99.51, not 100, because the 7% is now being measured against a bigger number. To get back to the price you divide by 1.07, which is what this tool does.
Why is a 25% rise not cancelled by a 25% fall?
A percentage change is always measured against the number it started from. 100 rising by 25% is 125; 125 falling by 25% is 93.75, because that 25% is a quarter of 125 rather than of 100. To get back to 100 from 125 you need a fall of 20%.
What VAT rate should I use?
The tool starts at 7%, which is the standard rate in Thailand, and the rate is a field you can change. Any country works: put in your own rate and both directions still hold.
Is anything I type sent anywhere?
No. The arithmetic runs in your browser. The site’s security policy sets connect-src ‘none’, so the browser blocks network requests from these pages, meaning nothing could be sent even if the code tried.