The two basic calculations: X% of a number and what percent A is of B
To find X% of a number, divide X by 100 and multiply. 15% of 80 is 0.15 × 80 = 12. 18% of 250 is 0.18 × 250 = 45.
To find what percent A is of B, divide A by B and multiply by 100. If you got 36 of 240 questions right, you scored (36 ÷ 240) × 100 = 15%. Note that the total (240) always goes on the bottom of the division: swapping the numbers is the most common mistake and gives an absurd result, such as 667%.
In the Percentage calculator these are the first two modes: "X% of a number" and "What % is one number of another". You enter the two numbers and the result appears instantly, along with the formula using your values.
Percentage increase and decrease
Percent change compares a starting value with a final one: ((final − starting) ÷ starting) × 100. If something went from 80 to 92, the change is (12 ÷ 80) × 100 = +15%. If it fell from 92 to 80, it is (−12 ÷ 92) × 100 = −13.04%. The same 12-unit move gives different percentages because the base changes: you always divide by the starting value.
To apply an increase or a drop to a value, multiply by (1 + % ÷ 100) or by (1 − % ÷ 100). A price of 100 with a 20% increase becomes 100 × 1.20 = 120; with a 20% discount it becomes 100 × 0.80 = 80.
The Percentage calculator has Percent change, Increase a value and Discount or decrease. There are also dedicated tools: the Discount calculator (final price and savings) and Percent change (positive if it went up, negative if it went down).
The classic mistake: +20% then -20% does not get you back
If a value of 100 rises 20%, it becomes 120. If it then falls 20%, it does not return to 100: the 20% is now taken from 120, which is 24, leaving 96. You lost 4 units. The same happens in reverse and with any percentage, because the second percentage applies to a different base.
Undoing an increase takes a smaller percentage, and undoing a drop takes a larger one. The table shows how much.
| If it rose | To get back, it must fall | If it fell | To get back, it must rise |
|---|---|---|---|
| 10% | 9.09% | 10% | 11.11% |
| 20% | 16.67% | 20% | 25% |
| 25% | 20% | 25% | 33.33% |
| 50% | 33.33% | 50% | 100% |
| 100% | 50% | 75% | 300% |
If you know the final value and the percentage applied and you want the original, do not add or subtract the percentage from the final value: divide. A price of 80 after a 20% discount started at 80 ÷ 0.80 = 100. A price of 150 after a 25% discount started at 150 ÷ 0.75 = 200 (not 150 × 1.25 = 187.5). The Percentage calculator has the modes Value before an increase and Value before a discount for exactly this.
Successive discounts
Two discounts in a row are not added: they are applied one after the other. An item priced at 200 with 30% off becomes 200 × 0.70 = 140; with an extra 20% off, it becomes 140 × 0.80 = 112. The total discount is not 50% but 44% (you saved 88 out of 200). The overall factor is 0.70 × 0.80 = 0.56.
The Discount calculator applies one discount at a time, so for a double discount you use the first result as the starting price for the second.
Adding and removing a tax such as VAT
To add a tax to a net price, multiply by (1 + rate): at a 21% rate, a net of 100 becomes 100 × 1.21 = 121. To remove it from a final price, divide by (1 + rate): 121 ÷ 1.21 = 100.
The typical mistake is subtracting 21% from the total: 121 − 21% of 121 = 121 − 25.41 = 95.59, which is not the net price. It is the same problem as the previous sections: the tax was calculated on the net, not on the total.
In the VAT calculator you choose Add VAT or Remove VAT, enter the amount and pick a country or type the rate yourself. It shows the price without VAT, the VAT, and the price with VAT. The list uses standard rates, which may have changed; check the current one and whether your product has a reduced rate. It does not replace an accountant or an official invoice. In places that use sales tax added at the register, the logic is the same: price × (1 + rate).
Tips and splitting the bill
A tip is a percentage of the bill. On a bill of 84.00 with a 15% tip: 84.00 × 0.15 = 12.60 tip and 96.60 total. Split among 4 people, that is 96.60 ÷ 4 = 24.15 each. At 18%, the tip is 15.12, the total 99.12 and each person pays 24.78.
In the Tip calculator you enter the Bill total, choose the percentage with the common-percentage buttons or by hand, set the Number of people, and that is it. With Round up what each person pays, each share becomes a whole amount. The tool splits evenly and applies the percentage to the total you enter, including taxes if there are any. Which tip percentages are customary depends on the country and the place.
Percentage points, interest and inflation
When a rate moves from 4% to 6%, it rose 2 percentage points, but it rose 50% in relative terms (2 ÷ 4). Both statements are correct and mean different things; mixing them up is very common in headlines.
Percentages that repeat period after period multiply; they do not add. If prices rise 10% two years in a row, the cumulative increase is 1.10 × 1.10 = 1.21, which is 21% and not 20%. Simple interest of 5% a year on 1,000 for 3 years adds 150; if interest builds on the balance (compound), it is 1,000 × 1.05³ = 1,157.63, that is, 157.63. These are arithmetic examples, not financial advice.
Mental-math shortcuts
- 10%: move the decimal point one place left (10% of 64 = 6.4).
- 1%: move it two places (1% of 64 = 0.64).
- 5%: half of 10% (3.2). 15% = 10% + 5% = 6.4 + 3.2 = 9.6.
- 20%: double the 10% (12.8). 25%: a quarter (16). 50%: half (32).
- If the number is awkward, swap them: 8% of 25 is the same as 25% of 8 = 2.
- To check that a result makes sense, round: 19% of 197 is close to 20% of 200 = 40 (the exact value is 37.43).
Frequently asked questions
How do I calculate 20% of an amount?
Multiply the amount by 0.20, or find 10% by moving the decimal point and double it. 20% of 64 is 12.8.
How do I get the price without VAT from the final price?
Divide the final price by (1 + rate). At a 21% rate, a final price of 121 is 121 ÷ 1.21 = 100 before VAT. Subtracting 21% from the total is not enough.
Why don't a 50% increase and a 50% drop cancel out?
Because the second percentage is taken from a different value. From 100 to 150 and then from 150 to 75 leaves you at 75. To get back to the original after a 50% rise, you need a 33.33% drop.
What is the difference between percentage points and percent?
A percentage point is the difference between two percentages: from 4% to 6% is 2 points. In relative terms, the increase is 50%, because 2 is half of 4.
Do two 10% discounts make 20% off?
No, they make 19%. On a price of 100, the first 10% leaves 90 and the second leaves 81, so the total discount is 19.