Percentage Calculator
A percentage is a number expressed as a fraction of 100, so X% of a value equals (X ÷ 100) × that value. This calculator finds what percent one number is of another, percentage increase or decrease, and reverse percentages, showing the working steps for every result.
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
How do you calculate a percentage?
Percentage = (Part / Whole) x 100
Percentage expresses a number as a fraction of 100. To find X% of Y: Result = (X / 100) x Y. To find what percent X is of Y: Percentage = (X / Y) x 100. To compute percentage change between an original and a new value: Change = ((New - Old) / |Old|) x 100. A positive change is an increase; a negative change is a decrease. These three formulas cover the vast majority of real-world percentage problems, from calculating discounts and tax amounts to comparing wages and interpreting grade scores.
How do you work out percentages step by step?
Example 1: Finding a percentage of a number
Problem:What is 15% of 240?
Solution:Multiply 240 × 0.15 (15 ÷ 100 = 0.15)
Result:240 × 0.15 = 36. So 15% of 240 is 36.
Example 2: Percentage change (increase)
Problem:A product's price rose from $80 to $92. What is the percentage increase?
Solution:Percentage change = ((New − Old) ÷ Old) × 100 = ((92 − 80) ÷ 80) × 100
Result:(12 ÷ 80) × 100 = 15% increase
Example 3: Reverse percentage (find the original)
Problem:After a 20% discount, an item costs $64. What was the original price?
Solution:Original = Discounted Price ÷ (1 − discount rate) = 64 ÷ 0.80
Result:64 ÷ 0.80 = $80 was the original price
What else do people ask about percentages?
How do I calculate what X% of a number is?
To find X% of Y, convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, 25% of 200: 25/100 = 0.25, then 0.25 x 200 = 50. The formula is Result = (X / 100) x Y.
How do I find what percentage one number is of another?
To find what percentage X is of Y, divide X by Y and multiply by 100. For example, 45 is what percent of 180? 45 / 180 = 0.25, then 0.25 x 100 = 25%. The formula is Percentage = (Part / Whole) x 100.
How do I calculate percentage change between two numbers?
Percentage change = ((New Value - Old Value) / |Old Value|) x 100. If the result is positive, it is an increase. If the result is negative, it is a decrease.
Why is percentage increase and decrease not symmetrical?
A 50% increase followed by a 50% decrease does not return to the original value because the base changes between the two calculations.
What is the difference between percentage points and percent?
A percentage point is the arithmetic gap between two percentages; a percent change is the relative gap. If an interest rate moves from 4 percent to 5 percent, that is a rise of 1 percentage point, but a relative increase of 25 percent, because 1 divided by 4 is 0.25. Reporting the same move both ways is a common source of confusion in rate, share, and margin figures. Use percentage points when the two numbers are themselves percentages, and percent change only when you want the size of the move relative to the starting rate.
How do you work backwards from a final figure to the original amount?
Divide rather than subtract. If a value has been increased by r percent, the original equals the final amount divided by (1 + r/100); if it was decreased, divide by (1 - r/100). An item costing 64 after a 20 percent discount had an original price of 64 divided by 0.80, which is 80. The common error is to add 20 percent back to 64, which gives 76.80 and is wrong because the 20 percent was taken from the larger original base, not from the discounted price.
What is the difference between percentage change and percentage difference?
Percentage change is directional and uses the original value as the base: from 80 to 92 it is 12 divided by 80, a 15 percent increase. Percentage difference compares two values with no before and after, and uses their average as the base: 12 divided by 86 gives about 13.95 percent. Percentage difference is symmetric, so you get the same answer whichever number you name first, which is why it suits comparisons of two measurements or two competing options rather than change over time.
Can a percentage legitimately exceed 100, and what does that mean?
Yes, whenever the quantity being measured can exceed its reference base. A revenue figure of 150 percent of target simply means one and a half times the target. The trap is percentage increase: growing from 20 to 60 is a 200 percent increase, not 300 percent, because the change of 40 is divided by the original 20 and the starting value already counts as the baseline 100 percent. A decrease, by contrast, cannot exceed 100 percent for a positive quantity, since that would take the value below zero.
How do you convert between percentages, decimals, and fractions?
Percent means per hundred, so divide by 100 to get a decimal and multiply by 100 to go back: 37.5 percent is 0.375, which as a fraction is 375/1000 reduced to 3/8. Working through the decimal form is usually the safest route, since that is exactly what the multiplication step in these calculations uses. Finance adds one more unit: a basis point is one hundredth of a percentage point, so 25 basis points equals 0.25 percent, or 0.0025 as a decimal.
Why must successive percentage changes be multiplied instead of added together?
Each change is applied to the balance left by the one before it, so the effects compound rather than accumulate. Two consecutive rises of 10 percent give a multiplier of 1.10 x 1.10 = 1.21, a total increase of 21 percent, not 20. The same logic explains the increase-then-decrease trap: 1.50 x 0.50 = 0.75, so the value ends 25 percent below where it started. To chain any sequence of changes, convert each to a multiplier of (1 + r/100), multiply them all, then subtract 1 and multiply by 100.
References
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