Percentage Calculator

About the Percentage Calculator

Percent means per hundred, so $p\%$ is the fraction $\frac{p}{100}$ . Almost every percentage question is the relationship $\text{part} = \frac{p}{100} \times \text{whole}$ rearranged to find the missing value.

Choose the type of question, enter the two values you know, and the calculator shows how the formula is rearranged and evaluated.

What is a percentage?

A percentage is a ratio expressed out of 100. The word comes from the Latin per centum, by the hundred, so 18% means 18 for every 100 and equals the fraction $\frac{18}{100}$ or the decimal 0.18. Writing ratios this way puts quantities of very different sizes on a common scale: a score of 45 out of 60 and a score of 75 out of 100 are both 75%.

Every percentage problem involves three quantities: the whole (the base you are taking a percentage of), the part, and the rate $p$ . If you know any two, the third follows from the single relationship part $= \frac{p}{100} \times$ whole. Percentage change is the special case where the part is the difference between a new and an old value and the whole is the old value.

How to use the Percentage Calculator

Pick the question type: percent of a number, what percent, percentage change, or find the whole.
Enter the two values. Decimals and negative numbers are accepted.
Press Calculate to see the conversion to a decimal, the multiplication or division, and a check.

Formulas

Percent of a number

\text{part} = \frac{p}{100} \times \text{whole}

What percent

p = \frac{\text{part}}{\text{whole}} \times 100

Percentage change

\Delta\% = \frac{\text{new} - \text{old}}{|\text{old}|} \times 100

Whole from a part

\text{whole} = \frac{\text{part}}{p / 100}

Worked example: 18% of 250

The worked example finds 18% of 250. The percent is first divided by 100 to give the decimal 0.18, and multiplying by 250 gives 45. The check runs the calculation backwards, $45 \div 250 \times 100 = 18\%$ , confirming that nothing was lost in the conversion.

The solution below is generated by the same engine that powers the calculator above.

Final answer

45

How we read your problem

Find a percentage of a number.

Step-by-step solution

Convert the percent to a decimal by dividing by 100
$18\% = \frac{18}{100} = 0.18$
Multiply the decimal by the number
$0.18 \times 250 = 45$

Formulas used

Percent of a number
$\text{result} = \frac{P}{100} \times X$

18 percent means 18 out of every 100, so 18% of 250 is 45.

Verification

Check: 45 ÷ 250 × 100 = 18%

Detailed explanation

Choosing the right mode

Read the question for the word of: the number after it is almost always the whole. "What is 18% of 250?" gives the rate and the whole, so use the percent-of mode. "45 is what percent of 60?" gives the part and the whole, so use what-percent, which returns 75%. "45 is 75% of what number?" gives the part and the rate and asks for the whole, and the calculator divides $45 \div 0.75$ to get 60.

Percentage change and why the base matters

Percentage change always compares the difference with the starting value. Going from 80 to 92 is an increase of 12, and $\frac{12}{80} = 0.15$ , so the calculator reports a 15% increase. Going from 50 to 40 is a 20% decrease, because the drop of 10 is measured against 50. Reverse the direction, 40 up to 50, and the change is 25%, not 20%, because the base is now 40. This asymmetry is why a rise followed by an equal percentage fall does not return to the starting value.

Repeated changes multiply rather than add. A 10% rise multiplies by 1.10 and a further 10% rise multiplies by 1.10 again, giving 1.21 overall, a 21% increase. The same idea gives compound interest, discounts on discounts and successive price increases.

Percentages of percentages work the same way. A 20% discount followed by an extra 10% off the sale price is not 30% off: the price is multiplied by 0.80 and then by 0.90, which is 0.72, so the total saving is 28%.

Common mistakes

Dividing by the new value instead of the original when computing percentage change.
Forgetting to divide the percent by 100 before multiplying.
Assuming a 20% rise followed by a 20% fall returns to the start; it ends 4% lower.
Adding successive percentage changes: two 10% increases make 21%, not 20%.
Confusing percentage points with percent; a rate moving from 4% to 5% is a rise of one percentage point but of 25%.

Tips

10% of a number is that number with the decimal point moved one place left; build other percents from it.
$x\%$ of $y$ equals $y\%$ of $x$ , so 8% of 50 is the same as 50% of 8.
A change of −25% means the new value is 75% of the old one.
Turn a percent change into a multiplier: a 15% increase is ×1.15 and a 15% decrease is ×0.85.
For a quick sanity check, 50% is half, 25% is a quarter and 1% is one hundredth of the whole.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percent by 100 and multiply by the number. For 18% of 250: $0.18 \times 250 = 45$ .

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100. 45 out of 60 is $\frac{45}{60} \times 100 = 75\%$ .

How is percentage increase calculated?

Subtract the original value from the new value, divide by the original, and multiply by 100. From 80 to 92 is $\frac{12}{80} \times 100 = 15\%$ .

Can a percentage be more than 100?

Yes. A value can be 150% of another, and growth can exceed 100% when a quantity more than doubles.

Why can't I compute percentage change from zero?

The formula divides by the original value, and division by zero is undefined, so no finite percentage describes a change from 0.

How do I find the original price before a discount?

If the sale price is 75% of the original, divide the sale price by 0.75. Use the "A is P% of what number" mode.

How do I calculate a percentage decrease?

Subtract the new value from the original, divide by the original and multiply by 100. From 50 to 40: $\frac{10}{50} \times 100 = 20\%$ decrease. The calculator shows a decrease as a negative change.

What is the difference between percent and percentage points?

Percentage points measure the plain difference between two percentages, while percent measures the relative change. From 4% to 5% is +1 percentage point but a 25% relative increase.

Solve your percentage question

Pick a mode above, enter the two numbers you know and get the missing value with the formula, the steps and a check.

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