Percentage Calculator

Example 1

A smartphone originally priced at $799 is on sale for 20% off. The buyer also needs to pay 8% sales tax on the discounted price. What is the final price?

Solution

First calculate the discount: 20% of $799 = 0.20 × $799 = $159.80.

Discounted price = $799 − $159.80 = $639.20.

Now add 8% sales tax: 8% of $639.20 = 0.08 × $639.20 = $51.14.

Answer

$690.34 is the final price after a 20% discount and 8% sales tax.

Source: IRS: Sales Tax Information

Example 2

A company's revenue increased from $1.2 million in 2024 to $1.5 million in 2025. Calculate the percentage change.

Solution

The formula for percentage change is: ((new value − old value) / old value) × 100.

Difference = $1,500,000 − $1,200,000 = $300,000.

Answer

25% increase in revenue from 2024 to 2025.

Source: Investopedia: Percentage Change

Example 3

In a class of 30 students, 18 scored above 80% on a test. What percentage of students scored above 80%? If the passing mark is 40%, how many students passed if 27 students scored above 40%?

Solution

Percentage scoring above 80% = (18 / 30) × 100 = 60%.

Percentage who passed = (27 / 30) × 100 = 90%.

Answer

60% of students scored above 80%, and 90% passed the test (scored above 40%).

Source: Khan Academy: Percentages

Example 4

A store offers a "Buy 3, Get 1 Free" promotion. What is the effective discount percentage? If items cost $15 each, what is the final unit price?

Solution

Total paid for 4 items: 3 × $15 = $45. Unit price = $45 / 4 = $11.25.

At $11.25 per item, the effective per-unit saving is $3.75 or 25% off the regular price.

Answer

25% effective discount. Unit price drops from $15.00 to $11.25.

Source: Khan Academy: Percentages in Retail

Glossary

Percentage – A way of expressing a number as a fraction of 100, denoted by the percent sign (%). A percentage represents a proportion relative to a whole divided into 100 equal parts.
Percent – Another term for percentage, derived from the Latin “per centum” meaning “out of a hundred.” One percent (1%) means one part per hundred.
Fraction – A numerical quantity expressed as one integer divided by another, such as 1/2 or 3/4. Fractions can be converted to percentages by dividing the numerator by the denominator and multiplying by 100.
Decimal – A number expressed in the base-10 numeral system using a decimal point, such as 0.75 or 1.25. Decimals are converted to percentages by multiplying by 100, and percentages are converted to decimals by dividing by 100.
Percentage increase – A measure of how much a value has grown relative to its original value, calculated as (new value – original value) / |original value| × 100%. A positive result indicates growth.
Percentage decrease – A measure of how much a value has declined relative to its original value, calculated as (new value – original value) / |original value| × 100%. A negative result indicates a decline.
Percentage change – The relative difference between two values expressed as a percentage, calculated as the difference divided by the original value multiplied by 100. It can be positive (increase) or negative (decrease).
Percentage point – The arithmetic difference between two percentages. If a rate rises from 5% to 7%, the increase is 2 percentage points. Percentage points differ from percent: a 2 percentage point increase on a base of 5% represents a 40% increase.
Base value – The reference value to which a percentage is applied or against which a proportion is measured. Choosing the correct base value is essential for accurate percentage calculations.
Annual percentage rate (APR) – The yearly interest rate charged on borrowed money or earned on investments, expressed as a percentage. APR includes the nominal interest rate and any fees or additional costs associated with the transaction.

Frequently Asked Questions

Yes. The percentage change mode works correctly with negative numbers. The calculator uses the absolute value of the original number in the denominator, which gives accurate results for both positive and negative starting values.

If the part value is greater than the total value, the percentage will exceed 100%. For example, if a company revenue this year is 250 and last year it was 200, this year revenue is 125% of last year.

"X as % of Y" tells you what percentage X represents out of Y. 25 as % of 200 is 12.5%. "X% of Y" calculates the actual numeric value that X% represents of Y. 25% of 200 equals 50. This calculator supports both modes separately.

Yes, you can enter decimal values for all inputs. The calculator rounds percentage results to 3 decimal places and numeric results to 3 decimal places.

The total value (Y) and original value fields have a minimum of 0.0001 to prevent division by zero. Percentages require a non-zero reference value because division by zero is mathematically undefined.

Percentage increase measures how much a value has grown relative to its original value. Percentage of measures what portion one value represents of another. This calculator supports both: use the "Percentage change" mode for increase or decrease and the "X is what % of Y?" mode for proportion calculations.

Yes. If the part exceeds the whole, the percentage exceeds 100%. This is common in growth contexts. A 150% increase means the new value is 2.5 times the original. In the "X as % of Y" mode, entering X = 150 and Y = 100 gives 150%.

For quick mental calculations, remember that 10% is simply dividing by 10, 5% is half of 10%, and 1% is dividing by 100. For example, 15% of 80 can be calculated as 10% (8) + 5% (4) = 12. This calculator gives exact results for any values.

A percentage point is the arithmetic difference between two percentages. If an interest rate rises from 5% to 7%, the increase is 2 percentage points. The same change represents a 40% increase in the rate. Percentage points describe the absolute difference, while percent describes the relative change.

Yes. A decrease produces a negative percentage change. If a value drops from 80 to 60, the change is (60 - 80) / 80 x 100 = -25%. The magnitude tells you the relative size of the decrease, and the sign tells you the direction.

Yes. Use the "X is what % of Y?" mode with your score as X and the total possible points as Y. For example, 36 out of 60 gives 60%. If your grading system uses weighted components, you can calculate each component separately and combine them manually.

Use the "What is X% of Y?" mode. Enter the discount percentage as X and the original price as Y. The result is the discount amount in currency units. Subtract this from the original price to get the final price. For example, 20% of 80 equals 16, so the discounted price is 80 minus 16 equals 64.

Divide the numerator by the denominator and multiply by 100. The fraction 3/4 becomes 3 divided by 4 equals 0.75, multiplied by 100 equals 75%. Use the "X is what % of Y?" mode with the numerator as X and the denominator as Y for instant conversion of any fraction to a percentage.

Divide the part value by the percentage expressed as a decimal. If 30 equals 15% of the total, divide 30 by 0.15 to get 200. This is the reverse of the "What is X% of Y?" calculation and is useful when you know a partial amount but need to find the whole.

Simple percentage growth applies the percentage to the original value each period. Compound percentage growth applies the percentage to the new value each period, causing exponential growth. This calculator handles single-period percentage changes only. For multi-period compounding, use a dedicated compound interest calculator.