Percentage Calculator

Solve Common Percentage Problems

Percentage Calculator Formula

Formula

\[ \text{What is } X\% \text{ of } Y? \;\Rightarrow\; \frac{X}{100} \times Y \\ X \text{ is what percent of } Y? \;\Rightarrow\; \frac{X}{Y} \times 100\% \\ X \text{ is } Y\% \text{ of what number?} \;\Rightarrow\; \frac{X \times 100}{Y} \]

Where:

$X$ — the percentage (or the part value, depending on the problem type)
$Y$ — the base number (or the percentage, in the third problem type)

A percentage means "per hundred", so every percentage problem reduces to multiplying or dividing by 100. The three formulas above are simply rearrangements of the same relationship: $\text{part} = \frac{\text{percent}}{100} \times \text{whole}$.

Percentage Calculator – Calculation Example

Example: a shop offers a 20% discount on a $200 item. How much do you save? Choose "What is X% of Y?", enter X = 20 and Y = 200.

\[ \frac{20}{100} \times 200 = 0.2 \times 200 = 40 \]

Result: 20% of 200 is 40, so the discount is $40 and the sale price is $160.

Check with the other modes: 40 is what percent of 200? $\frac{40}{200} \times 100 = 20\%$. And 40 is 20% of what number? $\frac{40 \times 100}{20} = 200$. All three modes agree.

How to use the calculator

Open the Select type of calculation dropdown and choose the problem you need: "What is X% of Y?", "X is what percent of Y?", or "X is Y% of what number?".
Enter the first number in the X field. In mode 1 this is the percentage; in modes 2 and 3 it is the value or part.
Enter the second number in the Y field. In mode 1 this is the base number; in modes 2 and 3 it plays the opposite role.
Read the Result field. In mode 2 the answer includes the % sign; in the other modes it is a plain number.
Change any value or switch the mode — the result updates automatically.

What percentages are and how to read the result

A percentage expresses one number as a fraction of another with the denominator fixed at 100. Saying "20%" is the same as saying $\frac{20}{100}$ or 0.2. Because the denominator is always 100, percentages make it easy to compare proportions of different-sized quantities: a 20% markup on a small item and a 20% markup on a large one represent the same relative change, even though the dollar amounts differ.

The three modes of this calculator cover the three ways these quantities relate to each other. Mode 1 finds the part when you know the whole and the percentage — typical for discounts, taxes, tips, and interest. Mode 2 finds the percentage when you know the part and the whole — useful for test scores, market share, or "how much did I actually save?". Mode 3 recovers the whole when you know a part and its percentage — for example, if a $40 discount was 20% of the original price, the original price was $\frac{40 \times 100}{20} = 200$.

Interpreting the result depends on context. A result of "40" in mode 1 carries the same units as Y (dollars, kilograms, people), because you computed a fraction of Y. A result of "20%" in mode 2 is dimensionless — a pure ratio. In mode 3 the result again carries the units of X. Keeping units in mind helps you sanity-check every answer.

Assumptions, limitations, and practical tips

Y cannot be zero in modes 2 and 3. Dividing by zero is undefined, so the calculator shows an error if you enter Y = 0 with those modes.
Percentages can exceed 100. If X is larger than Y in mode 2, the result is greater than 100% — perfectly valid, for example when this year's sales are 130% of last year's.
Negative values are allowed. A negative X or Y can represent losses, drops, or debts; the formulas still work, but make sure the sign matches your real-world meaning.
Results are rounded to 4 decimal places. For repeated calculations (e.g., compound interest over many periods), small rounding differences can accumulate; use a dedicated tool for those cases.
Don't confuse percentage of with percentage change. This calculator answers "what is X% of Y" type questions. If you need the increase or decrease between two values, use the Percentage Change calculator or the Percentage Increase calculator instead.

For related tasks, the Average Percentage calculator combines several percentages into one, the Percentage Difference calculator compares two numbers of equal standing, and the Reverse Percentage calculator handles mode-3 style problems with a dedicated interface.

Frequently Asked Questions

How do I calculate a percentage by hand without a calculator?

Convert the percent to a decimal by moving the decimal point two places left, then multiply. For example, 15% of 80 is 0.15 × 80 = 12. For 10% shortcuts, just divide by 10; for 5%, take half of the 10% value. So 25% of 60 = 10% (6) + 10% (6) + 5% (3) = 15.

What is the difference between a percentage and a percentage point?

A percentage point is the simple arithmetic difference between two percentages. If an interest rate rises from 4% to 6%, that is a 2 percentage point increase, but a 50% relative increase in the rate. Confusing the two is a common mistake in finance and news reporting. This calculator works with percentages (ratios out of 100), not percentage point differences.

Can a percentage be more than 100%?

Yes. A percentage is just a ratio, and ratios can exceed the whole. If a company's sales grow from $1 million to $1.3 million, this year's sales are 130% of last year's. Anything above 100% simply means the part is larger than the base you are comparing against.

How do I convert a fraction or decimal into a percentage?

Divide the numerator by the denominator, then multiply by 100 and add the % sign. For example, ½ = 0.5 = 50%, and 3⁄8 = 0.375 = 37.5%. To go the other way, drop the % sign and divide by 100: 45% becomes 0.45. This works because percent literally means 'per hundred'.

Why does adding and then removing the same percentage not return the original number?

Because the base changes. Take 100, add 20% and you get 120. Remove 20% of 120 and you get 96, not 100 — the second 20% is taken from a larger number. To undo a 20% increase, divide by 1.2: 120 ÷ 1.2 = 100. Use mode 3 of this calculator to reverse such changes correctly.

How do I calculate a tip or a discounted price quickly?

For a tip, compute the percentage of the bill: a 15% tip on $60 is 0.15 × 60 = $9. For a discount, find the percentage of the price, then subtract it: 25% off $80 means you save 0.25 × 80 = $20 and pay $60. Alternatively, multiply by the complement: 25% off means paying 75%, and 0.75 × 80 = $60.

Is there a way to check my percentage result is correct?

Use the three modes together. If mode 1 says 20% of 200 is 40, then mode 2 should confirm that 40 is 20% of 200, and mode 3 should confirm that 40 is 20% of the number 200. All three answers must agree, since they are rearrangements of the same relationship part = (percent ÷ 100) × whole.