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Choose a percentage type, enter two values, and calculate the answer instantly.
What Is a Percentage Calculator?
A percentage calculator converts everyday percent questions into simple arithmetic. Use it when you need to know what share one number is of another, what a percentage rate produces from a base value, or how much a number increased or decreased from an original amount. Those three tasks cover discounts, tips, tax, grade scores, growth rates, price changes, and many business reports.
The word percentage means per one hundred. A result of 25% means 25 out of every 100 parts. That makes percentages useful when two raw numbers are hard to compare directly. A 12 point score out of 15 and an 80 point score out of 100 are easier to compare once both are converted to percentages.
How Percentage Formulas Connect
Example: 35 out of every 100 parts are selected.
Example: applying a 20% rate to a base value.
Example: the changed share in an increase or decrease.
How to Calculate X Is What Percent of Y
Use this mode when you have a part and a total. Divide the part by the whole, then multiply by 100. If 25 students passed out of 200 students, the calculation is 25 / 200 x 100, which equals 12.5%. The same formula works for grades, completion rates, survey results, and any situation where one value belongs inside a larger total.
This mode can return values above 100% when the first number is larger than the second. That is mathematically valid. For example, 250 is 125% of 200. It can also return negative percentages if the part is negative, which may happen in accounting or change analysis.
How to Find What X Percent of Y Is
Use this mode when the percentage rate is known and you need the actual value. Convert the percent to a decimal by dividing by 100, then multiply by the number. A 20% tip on a 45 bill is 20 / 100 x 45, so the tip is 9. A 15% discount on 80 is 12, which means the sale price before tax would be 68.
This formula is also useful for tax, commission, interest estimates, budget allocations, and classroom problems. Negative percentages are allowed because they can represent deductions, losses, or reverse adjustments.
How to Calculate Percentage Increase or Decrease
Percentage change compares a new value with an original value. First subtract the original value from the new value. Then divide that change by the absolute value of the original number and multiply by 100. Going from 80 to 100 is a change of 20. Divide 20 by 80 and multiply by 100 to get a 25% increase.
For a decrease, the same formula returns a negative result. Going from 100 to 75 produces -25%, shown as a 25% decrease. Percentage change is undefined when the original value is zero because division by zero has no valid numeric answer. In that case, describe the absolute change instead of a percent change.
Common Percentage Formulas
| Question | Formula | Example |
|---|---|---|
| X is what percent of Y? | (X / Y) x 100 | 25 is 12.5% of 200 |
| What is X% of Y? | (X / 100) x Y | 15% of 80 is 12 |
| Percent change | ((New - Original) / Original) x 100 | 80 to 100 is a 25% increase |
When using percentages in financial decisions, remember that percent increase and percent decrease are not symmetric. A 50% decrease from 100 gives 50, but a 50% increase from 50 only returns to 75. To recover from 50 back to 100, the required increase is 100%.
Percentage Calculator FAQ
What is the formula for percentage? +
The basic percentage formula is part divided by whole, multiplied by 100. Written as a formula, it is (part / whole) x 100.
How do I calculate what percent one number is of another? +
Divide the first number by the second number, then multiply by 100. For example, 30 divided by 120 is 0.25, so 30 is 25% of 120.
How do I find 20% of a number? +
Convert 20% to 0.20 by dividing by 100, then multiply by the number. For example, 20% of 45 is 0.20 x 45 = 9.
What is the formula for percentage increase? +
Subtract the original value from the new value, divide by the original value, and multiply by 100. If the result is positive, it is a percentage increase.
What is the formula for percentage decrease? +
Subtract the original value from the new value, divide by the original value, and multiply by 100. If the result is negative, use its absolute value and describe it as a decrease.
Why is percentage change undefined when the original value is zero? +
Percentage change divides by the original value. When the original value is zero, that division is not defined, so a percentage change cannot be calculated.
Learn More About Percentages
For a deeper refresher, Math is Fun's percent guide explains percents as values out of 100 with worked examples. OpenStax Prealgebra covers percent equations, applications, and percent increase or decrease. For a general reference, the Wikipedia percentage article summarizes the definition, notation, and common calculation variants.
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