Percentage Calculator

Step 1: Select the type of percentage problem you want to solve from the dropdown. There are three options:
- "What is X% of Y?" — finds a percentage of a number (e.g., what is 20% of 85?)
- "X is what % of Y?" — finds what percentage one number is of another (e.g., 17 is what percent of 85?)
- "X is Y% of what?" — finds the original number when you know a part and the percentage (e.g., 17 is 20% of what?)

Step 2: Enter Value A. Depending on the mode, this is either the percentage, the part, or the known value. The label adjusts based on your selection.

Step 3: Enter Value B. This is the second number in the calculation — the whole, the base, or the percentage.

Step 4: Click Calculate. The result appears instantly with a step-by-step breakdown showing the math. Switch modes and calculate again to solve different types of percentage problems without leaving the page.

A percentage is a number expressed as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." When you say 25%, you mean 25 out of 100, or one quarter. Percentages provide a universal way to express proportions, making it easy to compare ratios of different sizes.

Percentages are everywhere in daily life. Sales tax adds a percentage to your purchase price. Tip calculators find a percentage of your restaurant bill. Interest rates on savings accounts and loans are expressed as percentages. Grades in school are often given as percentages. Discounts at stores are shown as "20% off" or "50% off." Weather forecasts give precipitation probability as a percentage. Nutritional information shows daily values as percentages.

The reason percentages are so useful is standardization. Saying "15 out of 60 students passed" and "25 out of 100 students passed" is harder to compare than saying "25% passed" versus "25% passed." Converting to a common base of 100 makes comparisons instant and intuitive.

Converting between percentages, decimals, and fractions: To convert a percentage to a decimal, divide by 100 (25% = 0.25). To convert a decimal to a percentage, multiply by 100 (0.75 = 75%). To convert a percentage to a fraction, put it over 100 and simplify (25% = 25/100 = 1/4).

Percentages can exceed 100%. A 150% increase means something grew to 2.5 times its original value. Stock market returns, population growth, and inflation figures can all exceed 100%. Percentages can also be less than 1% — interest rates, chemical concentrations, and statistical margins of error are often expressed as fractions of a percent like 0.25% or 0.5%.

Every percentage problem involves three values: the percentage (P), the part, and the whole. Knowing any two, you can find the third. This calculator solves all three forms.

Form 1: "What is P% of Y?" — Finding the part

Result = Y × P ÷ 100

Example: What is 15% of 80?
Result = 80 × 15 ÷ 100 = 12

This is the most common percentage question. You use it to calculate tips, discounts, taxes, and commissions. The shortcut: convert the percentage to a decimal first (15% = 0.15), then multiply (80 × 0.15 = 12).

Form 2: "X is what % of Y?" — Finding the percentage

Percentage = (X ÷ Y) × 100

Example: 42 is what percent of 200?
Percentage = (42 ÷ 200) × 100 = 21%

You use this when you know two numbers and need the ratio. Common uses: test scores (you got 42 out of 50 — what percentage?), market share, completion rates, and comparing two quantities.

Form 3: "X is P% of what?" — Finding the whole

Whole = X ÷ (P ÷ 100)

Example: 30 is 25% of what?
Whole = 30 ÷ 0.25 = 120

You use this when you know the part and the percentage but not the original amount. Common uses: working backwards from a sale price to find the original, calculating totals from a known portion, and reverse tax calculations.

All three forms are rearrangements of the same equation: P × Whole = Part × 100.

Example 1: What is 20% of $85? (Calculating a tip)
Select "What is X% of Y?" mode. Enter 20 as Value A and 85 as Value B. Result: 17. The calculation: 85 × 20 ÷ 100 = 17. Your tip is $17, making the total bill $102.

Example 2: 42 is what percent of 50? (Finding a test score)
Select "X is what % of Y?" mode. Enter 42 as Value A and 50 as Value B. Result: 84%. The calculation: 42 ÷ 50 × 100 = 84%. You scored 84% on the test.

Example 3: 30 is 25% of what? (Finding the original price)
Select "X is Y% of what?" mode. Enter 30 as Value A and 25 as Value B. Result: 120. The calculation: 30 ÷ 0.25 = 120. The original price before the 75% discount was $120.

Example 4: What is 8.25% of $999? (Calculating sales tax)
Select "What is X% of Y?" mode. Enter 8.25 as Value A and 999 as Value B. Result: 82.42. The tax is $82.42, making the total $1,081.42.

Pick the right mode. The most common mistake is using the wrong form. Ask yourself: "Do I know the percentage and want the part? Do I know two numbers and want the percentage? Or do I know the part and percentage and want the whole?"

Use the 10% shortcut for mental math. Finding 10% of any number is easy — just move the decimal point one place left. 10% of 250 is 25. From there, you can derive other percentages: 5% is half of 10%, 20% is double 10%, and 15% is 10% + 5%.

Remember that percentage of and percentage off are different. 20% of $100 is $20 (the amount). 20% off $100 means the price drops by $20 to $80 (the discounted price). This calculator finds the percentage of — subtract from the original for the discounted price.

Percentages over 100% are valid. If someone says prices increased by 150%, the new price is 2.5 times the original. A 200% increase means the value tripled. Do not confuse "200% increase" with "200% of the original" — they are different.

Order matters for successive percentages. A 20% increase followed by a 20% decrease does not return to the original value. $100 + 20% = $120, then $120 − 20% = $96. The final value is 4% less than the start.