20% off a $150 item
$150 x (1 - 0.20) = $120
The discount is $30 and the sale price is $120.
Everyday math· Five percentage problems, one tool
Percentage Calculator
Find a percentage, compare two values, apply a change, or recover the original number. The formula and substituted numbers update with every input.
Enter values
What is X% of Y?
Answer
15% of 80
15% represents 12 out of a total value of 80.
(percentage / 100) x number
(15 / 100) x 80 = 12
Quick reference
Percentage formulas
Choose the formula by identifying the part, whole, original value, and final value first.
Percent of a number
(percentage / 100) x number
15% of 80 = 12
What percentage?
(part / whole) x 100
25 of 200 = 12.5%
Percentage change
((new - original) / original) x 100
50 to 60 = +20%
Adjusted value
original x (1 +/- percentage/100)
100 increased 20% = 120
Reverse percentage
final / (1 +/- percentage/100)
80 after -20% came from 100
Worked examples
Where percentage math changes a decision
Salary rises from $60k to $66k
($66k - $60k) / $60k x 100 = 10%
The raise is $6,000, or a 10% increase.
18 correct answers out of 24
18 / 24 x 100 = 75%
The score is 75%. The whole is the 24 possible answers.
$96 after a 20% increase
$96 / 1.20 = $80
The original value was $80, not $76.80.
Method notes
Use the correct base value
Most percentage errors come from choosing the wrong denominator. In “25 is what percent of 200,” the whole is 200. In percentage change, the original value is the denominator because the question measures change relative to the starting point.
An increase and an equal decrease do not cancel. Increasing 100 by 20% gives 120, while decreasing 120 by 20% gives 96. Reverse percentage calculations divide by the applied factor, which is why the original value before a 20% increase is final / 1.20.
Percentage points answer a different question. A rate moving from 20% to 30% rises by 10 percentage points, but the relative increase is (30 - 20) / 20 = 50%. State which measure you mean when comparing rates, margins, survey shares, or conversion rates.
Choose the operation
How to choose the right percentage calculation
Start by writing the question in words before entering numbers. The same two values can produce very different answers depending on whether one is the part, the whole, the original value, or the final value. These five patterns cover the most common percentage tasks.
Use “Percent of” to find a portion
Choose this when you know a rate and a base amount. Discounts, tips, commissions, tax estimates, and test-score weighting often use this pattern. For 18% of 250, the rate is 18 and the number is 250.
Use “What percent?” to compare a part with a whole
Choose this when you know the portion and the total. A student answering 42 of 50 questions correctly, a team completing 16 of 20 tasks, or a business reaching 75,000 of a 100,000 target all use part divided by whole.
Use “Change” when there is a clear starting value
Choose this for growth or decline over time. The original value is the reference and belongs in the denominator. A move from 80 to 100 is a 25% increase because the 20-point gain is measured against the original 80.
Use “Adjust value” to apply a known increase or decrease
Choose this when a price, salary, budget, population, or measurement changes by a stated percentage. Select the direction instead of entering a negative percentage; this keeps the question explicit and reduces sign mistakes.
Use “Reverse” when you know the final value
Choose this to recover an original price, pre-tax amount, or value before a rise or fall. Reverse calculations divide by the factor that was applied. A final value of 120 after a 20% increase means the original was 120 / 1.20 = 100.
Accuracy notes
Rounding, negative values, and edge cases
Keep the unrounded result through the full calculation and round only the displayed answer. Currency usually uses two decimal places, while rates may need one to four. Rounding each intermediate step can create a visible error when the numbers are large or the percentage is small.
A zero whole makes “what percent?” undefined, and a zero original makes ordinary percentage change undefined. The absolute difference can still be reported, but there is no finite percentage relative to a zero starting value. The calculator shows an error instead of presenting a misleading zero.
Negative inputs can be mathematically valid, but their interpretation depends on context. Moving from a loss to a profit, comparing temperatures below zero, or decreasing a value by more than 100% may require a domain-specific explanation. Treat the numeric result as math, not automatic business advice.
FAQ · Common questions
Frequently Asked Questions
How do you calculate a percentage of a number?
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Divide the percentage by 100, then multiply by the number. For example, 25% of 80 is (25 / 100) x 80 = 20.
How do you calculate what percentage one number is of another?
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Divide the part by the whole and multiply by 100. For example, 25 is 12.5% of 200 because (25 / 200) x 100 = 12.5%.
What is the formula for percentage change?
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Percentage change is ((new value - original value) / original value) x 100. The original value is the denominator and cannot be zero.
How do you reverse a percentage increase or decrease?
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For an increase, divide the final value by 1 + percentage/100. For a decrease, divide the final value by 1 - percentage/100. For example, $80 after a 20% decrease came from $100.
What is the difference between percentage and percentage points?
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Percentage points are the direct difference between two percentage values. A move from 20% to 30% is 10 percentage points, but it is a 50% relative increase from the original 20%.
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