Use this Percentage Calculator to enter values, adjust options, and review results in a compact responsive workspace.
Results are calculated automatically as you enter data.
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A percentage is a way to describe a number as parts out of 100. The word “percent” means “per hundred,” so \(25\%\) means \(25\) out of \(100\), or \(\frac{25}{100}\).
Percentages are useful because they make different quantities easier to compare. Saying that a score is \(45\) out of \(60\) may be less immediate than saying it is \(75\%\). Saying a value changed from \(80\) to \(92\) is helpful, but saying it rose by \(15\%\) shows the size of the change relative to the original value.
The same idea appears in many everyday calculations, including grade percentages, measurements, survey results, growth rates, decreases, and comparisons between two values.
Percentages help turn raw numbers into context. A difference of \(10\) can be large or small depending on the starting amount. A change from \(20\) to \(30\) is a \(50\%\) increase, while a change from \(200\) to \(210\) is only a \(5\%\) increase.
They also help compare values that use different scales. A student who earns \(18\) out of \(20\) and another who earns \(45\) out of \(50\) both earned \(90\%\). Two measurements can also be compared by percent change even when their absolute differences are measured on different scales.
Most percentage calculations use the same basic relationship: divide one value by a base value, then multiply by \(100\) when you want the answer as a percent.
To find \(p\%\) of a value, convert the percent to a decimal by dividing by \(100\), then multiply by the value.
Where:
For example, \(15\%\) of \(240\) is:
When you know the part and the whole, the percent rate is:
If \(36\) is the part and \(240\) is the whole, then:
This is the same relationship as the previous example, just solved in the other direction.
Percent change compares a new value with an old value. The old value is the base.
A positive result means the value increased. A negative result means the value decreased.
For example, if a value rises from \(80\) to \(92\), the change is \(12\) and the old value is \(80\):
If a value falls from \(80\) to \(68\), the result is:
That can be written as “a \(15\%\) decrease.”
To find a value after a percentage decrease, subtract the percentage portion from the original value:
To find a value after a percentage increase, add the percentage portion to the original value:
Where \(d\) and \(i\) are entered as whole percentage numbers, such as \(20\) for \(20\%\).
The selector does not include dedicated Tax, Tip, Markup, Margin, or ROI modes. Use Value After Increase for a total after adding a tax rate, What is X% of Y? for a tip portion, and Percentage Change for markup or a simple ROI when cost is the old value and selling price or gain value is the new value.
Margin is not a direct mode. Calculate profit first, then use X is what % of Y? with profit as the part and selling price as the whole.
Sometimes you know the final value and need to work backward.
If the final value is after a percentage decrease, the original value is:
If the final value is after a percentage increase, the original value is:
These formulas reverse the decrease or increase. They are only available when the denominator is not zero. For example, a \(100\%\) decrease leaves no finite way to recover the original value from the final value alone.
A grade percentage compares the earned score with the total possible score:
If a student earns \(45\) points out of \(60\), then:
Grade mode reports a raw percentage from the entered scores. It does not apply institutional grading policies, letter-grade cutoffs, weighting, curves, or extra-credit rules beyond the numbers entered.
Percent difference compares two values without treating one value as the original and the other as the new value. It uses the average of the two values as the base.
This is most useful when the two values are comparable measurements or quantities, not a before-and-after change. When there is a clear starting value and ending value, percent change is usually the better choice.
Suppose you want \(12\%\) of \(350\).
So \(12\%\) of \(350\) is \(42\).
A value starts at \(120\) and decreases by \(25\%\).
The value after the decrease is \(90\).
If a value starts at \(90\) and increases by \(8\%\), the value after the increase is:
The value after the increase is \(97.2\).
Suppose the final value is \(138\) after a \(15\%\) increase.
Divide the final value by \(1 + 15/100\):
The original value before the increase was \(120\).
Percent change cannot be calculated when the old value is \(0\) because the formula divides by the old value.
Division by zero is undefined, so the calculation is unavailable. In a real explanation, it may be better to describe the change in absolute terms, such as “the value increased from \(0\) to \(25\),” instead of forcing a percent change.
A result with a percent sign is a percentage rate or relative comparison. This includes percent rate, percent change, increase, decrease, grade, and percent difference.
A result without a percent sign is an amount or value. This includes finding a percent of a number, recovering an original value, or finding a value after a percentage decrease or increase.
| Result type | What it means |
|---|---|
| Percent of a value | The amount represented by the selected percent |
| Percent rate | The part as a percentage of the whole |
| Percent change, increase, or decrease | How much a value changed relative to the old value |
| Value after decrease or increase | The value after applying the selected percentage change |
| Original value | The estimated value before a percentage decrease or increase |
| Grade | Earned score as a percentage of total score |
| Percent difference | Difference between two values relative to their average |
Displayed results may be rounded for readability. The calculator formats results with up to \(8\) digits after the decimal point, so a repeating decimal such as \(33.333333\ldots\%\) may appear as a rounded value.
If the result shows a dash instead of a number, at least one input is missing, invalid, or the selected formula cannot produce a finite result. A common cause is division by zero.
For percentage fields, enter \(15\) for \(15\%\), not \(0.15\). Entering \(0.15\) means \(0.15\%\), which is much smaller.
Use plain numbers only. Do not type percent signs, currency symbols, or thousands separators into the numeric inputs. For example, use \(1200\), not \$1,200.
A move from \(10\%\) to \(12\%\) is an increase of \(2\) percentage points. Relative to the original \(10\%\), it is a \(20\%\) increase because:
Percentage points compare two percentages directly. Percent change compares the change with the starting value.
Percent change uses the old value as the base. Percent difference uses the average of the two values as the base. They answer different questions and can produce different percentages.
A value after a decrease uses \(1 - p/100\). A value after an increase uses \(1 + p/100\). Reversing the sign changes the result.
When a calculation has several steps, rounding in the middle can change the final result. It is usually better to keep extra decimal places while calculating, then round the final answer to a practical number of decimal places.
Use percentages when you need to:
Percentage calculations are only as meaningful as the values entered. A percentage can make a comparison easier to understand, but it does not explain why a value changed or whether the result is good, bad, fair, or acceptable.
Some calculations require a nonzero denominator. For example, percent rate cannot be calculated when the whole is \(0\), percent change cannot be calculated when the old value is \(0\), grade percentage requires nonnegative score inputs and a positive total score, and percent difference is unavailable when the average of the two values is \(0\).
Negative numbers may be mathematically valid in some modes, but they may not make practical sense for scores, counts, measurements, or rates. Always check whether the inputs make sense for the situation.
A \(100\%\) decrease in an original-value calculation makes the denominator zero, so the original value cannot be recovered from the final value alone. Similarly, a \(-100\%\) increase in an original-value calculation makes the denominator zero.
Percent difference uses the average of the two values as its denominator. If the average is zero, the calculation is unavailable. If both values are negative, the arithmetic average is also negative, which can make the displayed result hard to interpret. Percent difference is usually most meaningful for positive comparable quantities.
Displayed results are rounded to a readable format with up to \(8\) decimal places. The exact internal arithmetic may have more precision than the displayed result, and decimal separators may follow the browser or device locale.
For decisions involving grades, legal obligations, safety, engineering, health, employment, or official records, double-check the result and use the rules or standards that apply to the situation. A general percentage calculation is not a substitute for professional advice.
Percent means “per hundred.” A value of \(30\%\) means \(30\) out of \(100\), or \(\frac{30}{100}\).
Enter \(15\) for \(15\%\). The calculator treats percentage inputs as whole percentage numbers, so \(0.15\) means \(0.15\%\), not \(15\%\).
A dash means the calculator does not have a valid finite result to display. This can happen when an input is blank, contains non-numeric characters, or causes division by zero.
Percent change compares a new value with an old value and uses the old value as the base. Percent difference compares two values without treating either one as the original value and uses their average as the base.
A percent change is negative when the new value is smaller than the old value. For example, changing from \(100\) to \(80\) gives \(-20\%\), which can also be described as a \(20\%\) decrease.
Multiply the original value by \(1 - p/100\), where \(p\) is the decrease percentage. For example, a \(25\%\) decrease uses a multiplier of \(0.75\).
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