Solve common percentage questions, compare values, calculate increases and decreases, or reverse a percentage change.
Choose a calculation, enter your numbers, and see the formula with your values filled in. Calculations run in your browser.
Use the mode that matches your question, whether you need a proportion, a change from a baseline, or a symmetric comparison.
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Start with “What is X% of Y?” or switch to one of the other percentage calculations.
A percentage calculator works out proportions and relative changes from the numbers you provide. This one covers percentage amounts, part-to-whole questions, increases, decreases, reverse calculations, and symmetric differences.
Result = Number × Percentage ÷ 100
20% of 500 = 500 × 20 ÷ 100 = 100
Percentage = (Part ÷ Whole) × 100
50 out of 200 = 50 ÷ 200 × 100 = 25%
((New − Original) ÷ |Original|) × 100
100 to 120 = ((120 − 100) ÷ 100) × 100 = 20% increase
|A − B| ÷ ((|A| + |B|) ÷ 2) × 100
100 and 120 have a 18.181818% difference
Write the part as a fraction of the whole, then multiply by 100. The denominator should represent the full amount being compared.
Percentage = (Part ÷ Whole) × 100
For example, if 18 of 24 questions are correct, calculate 18 ÷ 24 × 100 = 75%. A useful check is that the part and whole use the same units.
The right comparison depends on whether one value is a baseline.
Use an original value and a new value when describing movement over time or after an event. The original is the baseline, so the answer has a direction: increase, decrease, or no change.
((New − Original) ÷ |Original|) × 100
Use this when comparing two values without choosing either as the baseline. It uses the average of their absolute values, so switching the order gives the same answer.
|A − B| ÷ ((|A| + |B|) ÷ 2) × 100
A percentage change is based on the value at that step. Increasing 100 by 20% gives 120. Decreasing 120 by 20% gives 96, not 100, because 20% is now taken from 120.
To reverse the increase: 120 ÷ 1.20 = 100
For an increase, divide the final amount by 1 plus the rate as a decimal. For a decrease, divide by 1 minus the rate. At a 100% decrease the final amount is zero, so the original cannot be recovered from it.
Subtract the original from the new value, divide that difference by the absolute original value, and multiply by 100. A positive answer means an increase; a negative answer means a decrease. If the original is zero, the percentage change is undefined.
((New − Original) ÷ |Original|) × 100
For example, moving from 120 to 100 gives about −16.666667%, a decrease. The absolute denominator keeps the direction meaningful even when the original value is negative.
Percentages appear in everyday comparisons. Confirm the relevant base and rules before using a result for a real-world decision.
Find the amount taken off a marked price, then subtract it to estimate the sale price.
Apply a stated rate to a taxable amount to understand a mathematical total; rules vary by location.
Work out a gratuity from a bill amount and chosen percentage.
Divide earned marks by possible marks to express a score as a percentage.
Compare a new pay amount with the original to describe the size of a change.
Compare two periods with a clear baseline to describe relative growth or decline.
Measure how much a price moved relative to its earlier value.
Express profit as a proportion of revenue, while checking which margin definition applies.
Compare proportions or relative changes while keeping the denominator and baseline clear.
A percentage is a way to express a number as a part of 100. For example, 25% means 25 out of every 100, or one quarter.
Convert the percentage to a decimal by dividing it by 100, then multiply by the number. For example, 20% of 500 is 500 × 20 ÷ 100 = 100.
Divide the part by the total and multiply by 100. For example, 50 ÷ 200 × 100 = 25%, so 50 is 25% of 200.
Subtract the original value from the new value, divide by the absolute original value, then multiply by 100. A positive result is an increase.
Use the same percentage-change formula: (new value − original value) ÷ |original value| × 100. When the new value is lower, the result is negative and indicates a decrease.
Percentage change uses an original value as its baseline and shows direction. Percentage difference compares two values symmetrically using their average absolute size; neither value is the baseline. They should not be used interchangeably.
Yes. A percentage can be greater than 100% when the part is larger than the whole or when a change exceeds the starting value. A decrease above 100% produces a negative final value.
Yes. A negative percentage can represent a decrease or a reversed operation. This calculator accepts negative percentages when the selected formula allows them.
Percentage change divides by the absolute original value. If that original value is zero, the formula has a zero denominator, so no finite percentage change is defined.
Divide the discounted final value by one minus the discount rate as a decimal. For example, 80 after a 20% discount means 80 ÷ 0.80 = 100 before the discount.
The second percentage applies to the increased value, which is a different base. Increasing 100 by 20% gives 120; decreasing 120 by 20% gives 96. To reverse the increase, divide 120 by 1.20 to get 100.
The calculator keeps full JavaScript number precision during each calculation and rounds only for display, showing up to six decimal places by default without unnecessary trailing zeros.
Calculator disclaimer
This tool performs general mathematical calculations using the values you enter. It does not determine tax treatment, investment outcomes, pricing rules, or financial decisions. Check the relevant definitions and rules for your situation.