What percent is A of B?
What is X% of B?
Percent change (old → new)
How to use the percentage calculator, and the traps in percentages
Percentages come up constantly, and yet "which number do I divide by?" trips almost everyone up. This tool covers the three cases that account for most of the work — type the numbers and read the answer.
The three patterns
"A is what per cent of B?" for achievement rates and composition (30 is 25% of 120). "What is X% of B?" for sale prices and fees (25% of 120 = 30). Change rate for year-on-year movement and price rises (800 to 1,000 is +25%). When in doubt, remember compared value ÷ base value: the first case is A ÷ B, the third is the change ÷ the original.
Working out "X% off" or "X% more"
For "20% off 1,000", use the second field to get 20% of 1,000 = 200, then 1,000 − 200 = 800. Or enter 1,000 and 800 into the change field to confirm −20%. To get sale prices directly, use the discount calculator.
Trap 1: the same percentage does not undo itself
If 1,000 rises by 20% to 1,200, then taking 20% off 1,200 does not return you to 1,000 — it gives 960. Getting back to 1,000 needs a cut of about 16.7%, because the base has changed. This is the single most common error when chaining percentage changes.
Trap 2: per cent versus percentage points
When approval moves from 40% to 50%, that is a rise of ten percentage points, not ten per cent. Expressed as a percentage it is (50 − 40) ÷ 40 = a 25% increase. Using "points" for changes in a rate itself keeps headline figures honest.
Trap 3: percentages cannot be averaged directly
A 30% success rate over 10 attempts combined with 10% over 90 attempts is not 20%. It is (3 + 9) ÷ 100 = 12%. Rates must be weighted by the size of the group behind them. This bites most often when rolling departmental figures up to a company-wide number.
Ratios, fractions and per cent
A ratio expressed as a decimal is simply the percentage divided by 100: 0.25 is 25%, and 1.25 corresponds to a 25% increase. Keeping one form in mind while reading the other makes the traps above much easier to spot.
Frequently asked questions
How do I find what percent A is of B?+
For example, 30 out of 120 is 30 / 120 × 100 = 25%.
How is percent change calculated?+
Positive is an increase, negative a decrease. It is undefined when the old value is zero.
How do I find a value after X% up or down?+
You can also enter old and new values in the percent-change row to check the rate.
What is the difference between a ratio and a percentage?+
Percentage = ratio × 100.
Are my inputs stored?+
・What percent A is of B = A ÷ B × 100
・X% of B = B × X ÷ 100
・Percent change (%) = (new − old) ÷ old × 100. The base differs between a rise and a fall, so the same percentage does not reverse a change.
・Percentage = ratio × 100 (standard mathematical definition)
・A difference between two rates is conventionally expressed in percentage points, not per cent
・Ratio and percentage: a ratio of 0.25 is 25%, and multiplying by 1.25 corresponds to a 25% increase
・JIS Z 8401, Rules for rounding of numbers: defines Rule A (round half to even) and Rule B (round half up). This tool follows Rule B.
This site does not represent any organization and does not guarantee the accuracy of the results. Rounding may cause slight differences between the displayed and exact values. Use as a guide.