Percentage Calculator

A percentage is a number out of 100. The word comes from the Latin per centum, "by the hundred". So 25% means 25 out of every 100, which is the same as the fraction 1/4 or the decimal 0.25. Percentages make it easy to compare amounts of different sizes, which is why they appear in discounts, taxes, grades, interest rates and statistics.

• X% of Y: multiply Y by X and divide by 100. Example: 15% of 200 = 200 × 15 ÷ 100 = 30.
• X is what percent of Y: divide X by Y and multiply by 100. Example: 30 ÷ 120 × 100 = 25%.
• X is Y% of what number: divide X by Y and multiply by 100. Example: 50 is 20% of 250.
• Percentage change: (new − old) ÷ old × 100. A positive result is an increase, a negative one a decrease.
• Add or subtract a percentage: multiply by (1 + percent ÷ 100) to add, or (1 − percent ÷ 100) to subtract.

• A 20% discount on a $85 jacket takes off $17, so you pay $68.
• A price rising from $40 to $46 is a 15% increase.
• Scoring 42 out of 50 on a test is 84%.
• If a 13% sales tax adds $6.50, the price before tax was $50.

Use this table to check a result in your head. Each cell is the percentage of the number in the left column.

To turn a percentage into a decimal, divide by 100. To turn it into a fraction, put it over 100 and simplify. These are the ones that come up most.

Each change is (new − old) ÷ old × 100. Use it for prices, salaries, populations, grades and anything that goes up or down.

When you know the final amount and the percentage that was applied, divide by the matching factor. For a decrease, divide by (1 − percent ÷ 100). For an increase, divide by (1 + percent ÷ 100).

• A jacket costs $68 after 20% off: 68 ÷ 0.80 = $85 before the discount.
• A price of $90 after 25% off: 90 ÷ 0.75 = $120 originally.
• A bill of $66 after a 10% increase: 66 ÷ 1.10 = $60 before the increase.
• A total of $113 with 13% tax: 113 ÷ 1.13 = $100 before tax.

• 10%: move the decimal point one place to the left (10% of 85 is 8.5).
• 1%: move it two places to the left (1% of 85 is 0.85).
• 5%: half of 10%. 15%: 10% plus 5%. 20%: double 10%.
• 25%: divide by 4. 50%: divide by 2. 75%: divide by 4 and multiply by 3.
• Tip of 18%: take 10%, then add 5% and three lots of 1%.

These are easy to mix up. If an interest rate goes from 4% to 5%, it rose by one percentage point, but that is a 25% increase in the rate itself (1 ÷ 4). When you read news about rates or polls, check which of the two is meant.

• Taking a percentage of the wrong base. A 20% discount is taken off the original price, not the sale price.
• Adding and subtracting percentages directly. +50% then −50% does not return you to the start.
• Forgetting that the percentage change formula divides by the old value, so the order of the two numbers matters.
• Mixing up "percent" and "percentage points" when talking about rates.

To find 15% of the number in cell A1, type =A1*15% (or =A1*0.15). For percentage change from A1 to B1, use =(B1-A1)/A1 and format the cell as Percentage. For the share of one cell in a total, use =A1/SUM(A1:A10).