Tool guide
How to use the Percentage Calculator
A percentage is a ratio expressed per hundred. This calculator handles five different questions that are often confused with one another: finding a percentage of a number, finding what percentage one value represents of another, measuring percentage change, comparing two values with percentage difference, and reversing a percentage increase or decrease to recover the original value. Each mode uses a different denominator, so choosing the correct question matters as much as entering the correct numbers.
People also use this tool for
People also use this percentage calculator to check sale prices, calculate tips, compare grade percentages, estimate tax, work out invoice changes, find percentage increase or decrease, compare old and new prices, and answer quick questions like “what percent is 25 of 200?” or “what is 20% off $80?”
What this tool is useful for
- Calculate a percentage of any number for discounts, tax, tips, commissions, interest, grades, budgets, recipes, and measurements.
- Measure percentage increase or decrease between an original value and a new value while also seeing the absolute change.
- Compare two values with percentage difference or reverse a percentage change to find the original amount.
Practical example
Suppose a price rises from $80 to $100. The absolute change is $20, and percentage increase uses the original $80 as its denominator: ($100 − $80) ÷ $80 × 100 = 25%. Percentage difference answers a different question and divides the $20 gap by the average of $80 and $100, producing 22.22%. Neither result is interchangeable with simply saying that $20 is 20% of $100.
Helpful tips
- Choose percentage change when one value is clearly the starting point; choose percentage difference when neither value is the baseline.
- Percentage change from an original value of zero is undefined because the standard formula divides by the original value.
- A decrease of 20% followed by an increase of 20% does not return to the starting value because the second percentage uses a smaller base.
Related tools and next steps
Discount Calculator, Tip Calculator, Sales Tax Calculator, Grade Percentage Calculator, Margin Calculator, Calculators
Common questions this tool can help answer
Common questions this calculator can help answer
- What percent is one number of another?
- What is 20% of 80?
- How do I calculate percentage increase?
- How do I calculate percentage decrease?
- How much is 20% off a sale price?
- What percentage grade did I get?
Frequently asked questions
What formulas does the percentage calculator use?
To find P% of N, use P ÷ 100 × N. To find what percent A is of B, use A ÷ B × 100. Percentage change uses (new − original) ÷ |original| × 100. Percentage difference uses |A − B| divided by the average magnitude of A and B, multiplied by 100.
Why are percentage change and percentage difference different?
Percentage change treats the original value as the baseline. Percentage difference treats both values equally and compares their gap with their average magnitude. They answer different questions and usually produce different results.
Can I calculate a percentage when the total or original value is zero?
You can calculate a percentage of zero, but you cannot express a part as a percentage of a zero total or calculate standard percentage change from an original value of zero because both formulas would divide by zero.
How do I reverse a percentage increase?
Divide the final value by 1 plus the percentage rate written as a decimal. For example, 120 after a 20% increase came from 120 ÷ 1.20 = 100.
Why does decreasing and then increasing by the same percentage not cancel out?
The two changes use different base values. Reducing 100 by 20% gives 80; increasing 80 by 20% adds only 16, producing 96 rather than 100.
Can percentages be greater than 100% or negative?
Yes. A part can exceed 100% of a smaller total, and percentage change can be negative when a value decreases. The meaning depends on the quantities and the formula selected.
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