How to use the percentage calculator
The page has four small calculators, each answering one kind of question. Find the one that matches yours and type your numbers into it. Results update as you type, and the line under each result shows the formula with your numbers filled in, so you can check the working or copy it into your own notes.
- What is X% of Y? – a share of an amount, such as a tip or a deposit.
- X is what percent of Y? – a part compared with the whole, such as a test score.
- Percentage change – how much a value went up or down, compared with where it started.
- Add or subtract a percentage – a price with tax added or a discount taken off.
The three kinds of percentage questions
Every basic percentage problem links three quantities: the part, the whole and the percentage. They are connected by one formula, part = whole × percentage ÷ 100, so if you know any two you can find the third.
- Find the part: what is 20% of 150? 20 ÷ 100 × 150 = 30. Use the first calculator.
- Find the percentage: 30 is what percent of 120? 30 ÷ 120 × 100 = 25%. Use the second calculator.
- Find the whole: 30 is 25% of what? 30 ÷ 25 × 100 = 120. There is no separate box for this, but the Calculator does it in one step:
30 ÷ 25%= 120.
Working out which number is the whole is usually the hard part. The whole is the reference amount the question compares with: the original price, the total number of questions, last year’s figure.
Percentage change
Percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase and a negative one a decrease. The old value is always the base, so the direction matters: going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease. The starting value can’t be zero, because a change from nothing can’t be expressed as a percentage of it.
If the old value is negative, the calculator divides by its size, so a move upwards always shows as an increase: going from −50 to −25 is +50%.
Adding or subtracting a percentage
Adding X% multiplies the number by (1 + X ÷ 100); subtracting multiplies by (1 − X ÷ 100). The explanation line shows both steps, for example “50 − 15% of 50 (7.5) = 42.5”.
Worked examples
- Test score: 42 correct answers out of 50 is 42 ÷ 50 × 100 = 84%.
- Tip: 18% of a 64.00 bill is 11.52.
- Sales tax or VAT: 120 plus 20% VAT is 120 × 1.2 = 144.
- Discount: 50 with 15% off is 42.50.
- Rent increase: rent going from 1,200 to 1,290 is a 7.5% increase.
- Falling sales: from 250 units to 180 units is a 28% decrease.
Common mistakes
- Percentages in a row don’t simply add up. 100 + 50% = 150, but 150 − 50% = 75, not 100, because the second percentage is taken of a larger number. Two discounts of 30% and then 20% take 100 down to 70 and then 56 – a total of 44% off, not 50%.
- Removing a percentage is not the same as subtracting it. If 144 already includes 20% tax, the price before tax is 144 ÷ 1.2 = 120, not 144 − 20% = 115.20.
- The base changes when you turn a comparison around. 125 is 25% more than 100, but 100 is only 20% less than 125.
- Percent and percentage points are different. When an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, but by 25 percent, because 1 is a quarter of 4.
FAQ
How do I find the original price before a discount?
Divide the sale price by what is left after the discount. If something costs 42.50 after 15% off, the original price was 42.50 ÷ 0.85 = 50. The Discount Calculator also works out savings and tax.
Can a percentage be more than 100%?
Yes. 300 is 250% of 120, and a rise from 40 to 100 is an increase of 150%. For amounts that can’t go below zero, such as prices, a decrease can’t go beyond −100%, which would mean the value has fallen to zero.
How many decimal places are shown?
Percentages are rounded to at most 4 decimal places and other results to at most 6, so 1 out of 3 shows as 33.3333%. Round the result yourself to whatever precision you need.
What does “%” actually mean?
“Per cent” means “per hundred”: 25% is 25 out of every 100, the same as the fraction 1/4 or the decimal 0.25. Converting between the three forms is just a matter of multiplying or dividing by 100.