Percentage Calculator — every percentage question, worked out
X% of a number, what percentage one number is of another, percentage increase and decrease, adding or removing VAT, discounts, tips, grades, markup and margin, fractions and successive changes. Each answer shows the formula with your numbers and a picture of what it means. Free, instant, nothing to install.
1What is X% of Y?
2X is what percent of Y?
3Percentage increase or decrease
4Add or subtract a percentage
5Find the original (reverse percentage)
6Discount — percent off a price
7Tip and split the bill
8Test score and grade percentage
9Markup and margin
10Fraction, decimal and percentage
11Successive percentage changes
Guide — find the right percentage calculator
"What is 15% of 200?", "37 is what percent of 45?", "how much did it go up?" — the wording tells you which card to use.
Each card reads like the question. Replace the example numbers with yours; decimals and negative numbers work.
The big number is the answer. Underneath you see it in a sentence and the formula with your numbers.
The donut, bar or stack shows the size of the result, so a misplaced decimal stands out at once.
copy puts the sentence on your clipboard. The address bar always holds your numbers, so the link reopens the same calculation.
Which card for which question
- X% of Y
- 15% of 200, a 6% commission, 20% of a budget
- what %
- 37 out of 45, a share of a total, a completion rate
- % change
- prices, salaries, followers, stock prices
- add / remove
- add VAT, add a raise, take off a reduction
- original
- price before VAT, value before a rise or a sale
- successive
- several changes in a row
- discount
- percent off, including stacked discounts
- tip
- tip and split the bill per person
- markup
- set a price from cost, or check a margin
- grade
- score as a percentage, letter grade, out of 10 and 20
- fraction
- 3/8 to 37.5% and back to a fraction
How to calculate a percentage
A percentage is a number out of 100: 15% means 15 per 100, or 0.15. Almost every percentage question uses one of three forms of the same relation, part = percentage ÷ 100 × whole:
- The part:
part = p ÷ 100 × whole. 15% of 200 = 0.15 × 200 = 30. - The percentage:
p = part ÷ whole × 100. 37 is 37 ÷ 45 × 100 = 82.2% of 45. - The whole:
whole = part ÷ p × 100. If 30 is 15% of something, that something is 30 ÷ 15 × 100 = 200.
A quick mental trick: x% of y equals y% of x. 8% of 50 is hard, 50% of 8 is 4 — and the answers are the same.
Percentage increase and decrease
change = (new − old) ÷ old × 100. From 80 to 100 is (100 − 80) ÷ 80 = +25%. From 100 back to 80 is (80 − 100) ÷ 100 = −20%. The two are not the same because the starting point is different, and that is why a 25% rise followed by a 20% fall brings you back exactly where you started.
Do not confuse percentage change with percentage points. An interest rate going from 2% to 3% rose by 1 percentage point, but by 50% in relative terms. News reports mix these up all the time.
Adding and removing a percentage, such as VAT
To add a percentage, multiply by 1 plus the percentage: €100 + 21% VAT = 100 × 1.21 = €121. To take a percentage off, multiply by 1 minus it: €100 − 30% = 100 × 0.70 = €70.
To go back to the original, divide instead. A price of €121 including 21% VAT was €121 ÷ 1.21 = €100 before VAT. Taking 21% off €121 gives €95.59, which is wrong — the 21% was calculated on the smaller amount. This is also how to find the price before a sale (divide by 1 − discount) or a salary before a raise (divide by 1 + raise). The Find the original card does it for you.
Discounts and stacked discounts
The sale price is price × (1 − discount). Two discounts in a row multiply, they do not add: 30% off and then an extra 20% off is 0.70 × 0.80 = 0.56, a total discount of 44%, not 50%. The discount card shows the combined percentage.
Tips and splitting a bill
The tip is bill × tip% ÷ 100; the total is the bill plus the tip, divided by the number of people. Tipping customs differ widely: in the United States 15–20% is standard in restaurants, while in Belgium, the Netherlands and much of Europe service is included and people round up or leave 5–10% for good service.
Grade percentage
grade = score ÷ maximum × 100. 37 out of 45 is 82.2%. To convert to a score out of 20, as in Belgium and France, multiply the percentage by 0.2: 82.2% is 16.4/20. Out of 10, multiply by 0.1. The card also shows the usual US letter grade (A from 90%, B from 80%, C from 70%, D from 60%) and the UK degree classification (first from 70%, upper second from 60%, lower second from 50%, third from 40%). Your own school or university may use different boundaries.
Markup and margin
Both describe the same profit, divided by something different. Markup is profit as a percentage of the cost; margin is profit as a percentage of the selling price. An item that costs €50 and sells for €70 has a profit of €20: a markup of 20 ÷ 50 = 40%, and a margin of 20 ÷ 70 = 28.6%. To reach a target margin, divide the cost by 1 minus the margin: a 40% margin on €50 needs a price of 50 ÷ 0.60 = €83.33. The conversions are margin = markup ÷ (1 + markup) and markup = margin ÷ (1 − margin).
Fractions, decimals and percentages
A fraction becomes a percentage by dividing and multiplying by 100: 3/8 = 0.375 = 37.5%. Back from a percentage to a fraction: write it over 100 and simplify — 62.5% = 62.5/100 = 625/1000 = 5/8. Common ones worth knowing: 1/2 = 50%, 1/3 ≈ 33.3%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 3/4 = 75%.
Successive percentage changes
Changes in a row multiply: each one works on the result of the one before. A price that rises 10% and then falls 10% ends at 1.10 × 0.90 = 0.99, a 1% loss. Lose 50% and gain 50% and you are at 75%. Five rises of 5% are not 25% but 1.05⁵ − 1 = 27.6% — that is compound growth. The average change per step is the geometric mean: (total factor)^(1/n) − 1.
Rounding
The calculators keep full precision and show up to four decimals. Percentages of money are rounded to cents only in the final amount, so rounding errors do not pile up across steps.
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