Percentage Calculator
A percentage calculator instantly computes percentages for any scenario. Find what percent one number is of another, calculate a percentage of a number, or determine the percentage change between two values. Enter your numbers in the panel for an instant result.
What Is a Percentage Calculator?
A percentage calculator is a tool that performs percentage-based arithmetic instantly and accurately. Instead of working through the formula by hand, you enter your known values and the calculator applies the correct formula to return the result in seconds. This tool covers the three most common percentage problems: finding a percentage of a number, finding what percent one number is of another, and calculating the percentage change between two values.
Percentages appear everywhere in daily life, from calculating discounts and tax to measuring investment returns, grade points, and statistical changes. Whether you are working out a 20% tip at a restaurant, figuring out how much you saved on a sale, or measuring business growth, a percentage calculator eliminates manual errors and delivers the answer immediately. You can also use the AI tab in the calculator panel to get a full step-by-step explanation of any percentage problem.
How to Calculate Percentages
Finding a Percentage of a Number
To find X% of Y, multiply Y by X divided by 100. This is the most common percentage calculation used for discounts, taxes, tips, and commissions. For example, to find 15% of 200, multiply 200 by 0.15 to get 30. The formula is straightforward and applies to any numeric value regardless of scale. For all three types of percent-of-number problems in one place, use the percent of a number calculator.
Finding What Percent X Is of Y
To find what percentage X is of Y, divide X by Y and multiply by 100. This is used when you know both values and need to express their relationship as a percentage. For example, 45 out of 300 = (45 ÷ 300) × 100 = 15%. This calculation is commonly used for test scores, market share analysis, and budget tracking. You can also use the AI statistics solver for more complex statistical percentage problems.
Calculating Percentage Change
Percentage change measures how much a value has increased or decreased relative to its original value. Divide the difference (new minus old) by the original value, then multiply by 100. A positive result means an increase; a negative result means a decrease. This formula is widely used in finance, economics, and performance tracking. According to the Investopedia percentage change formula, this calculation is fundamental to understanding investment returns and price movements. When two percentage rates are applied to each other rather than to a plain number, use the percentage of a percentage calculator to avoid the common error of adding the rates instead of multiplying.
Percentage Formula
The three core percentage formulas used by this calculator are based on standard mathematical principles taught in schools and used by professionals worldwide. Understanding them allows you to solve any percentage problem without a calculator if needed. The percentage formulas explained by Math Is Fun provide an excellent foundation for understanding why these formulas work.
| Calculation Type | Formula | Example |
|---|---|---|
| X% of Y | Y × (X ÷ 100) | 15% of 200 = 30 |
| X is what % of Y | (X ÷ Y) × 100 | 45 of 300 = 15% |
| % Change | ((New − Old) ÷ Old) × 100 | 80 to 100 = 25% increase |
How to Calculate Percentage of a Percentage
To find a percentage of a percentage, apply the percentage formula twice in succession. Convert the first percentage to a decimal, then find that fraction of the second percentage value. For example, to find 50% of 20%, convert 50% to 0.50, then multiply by 20%: 0.50 × 20% = 10%. This means 50% of 20% equals 10%.
This type of calculation appears frequently in finance (compound discounts, tiered commissions), probability (joint probabilities expressed as percentages), and tax calculations (a tax on a tax). For instance, if a store applies a 10% loyalty discount on top of a 20% sale price reduction, the combined effect is not simply 30%. The 20% discount is applied first, then the 10% discount is applied to the already-reduced price, resulting in a total discount of 28% off the original price.
Khan Academy percentage lessons cover percentages in depth for learners at every level.
Common Percentage Calculations
The table below shows the results of applying common percentage values to frequently used base numbers. Use these as quick references without needing to calculate.
| Value | 5% | 10% | 15% | 20% | 25% | 50% | 75% |
|---|---|---|---|---|---|---|---|
| 50 | 2.5 | 5 | 7.5 | 10 | 12.5 | 25 | 37.5 |
| 100 | 5 | 10 | 15 | 20 | 25 | 50 | 75 |
| 200 | 10 | 20 | 30 | 40 | 50 | 100 | 150 |
| 500 | 25 | 50 | 75 | 100 | 125 | 250 | 375 |
| 1,000 | 50 | 100 | 150 | 200 | 250 | 500 | 750 |
| 2,500 | 125 | 250 | 375 | 500 | 625 | 1,250 | 1,875 |
| 5,000 | 250 | 500 | 750 | 1,000 | 1,250 | 2,500 | 3,750 |
| 10,000 | 500 | 1,000 | 1,500 | 2,000 | 2,500 | 5,000 | 7,500 |
Percentage Increase vs Percentage Decrease
Percentage increase and percentage decrease both use the same formula — ((New − Old) / Old) × 100 — but the interpretation differs based on the sign of the result. A positive result is a percentage increase; a negative result is a percentage decrease.
An important distinction: a 50% increase followed by a 50% decrease does not return to the original value. If you start at 100, a 50% increase brings you to 150, and then a 50% decrease on 150 brings you to 75 — not 100. This asymmetry is why percentage increases and decreases must always be applied to the current base value, not the original.
Another common misconception is that a 100% increase doubles a value (correct), but it takes a 50% decrease to reverse it (since the new base is twice as large). For pricing, investments, and salaries, this distinction matters significantly. The sales tax calculator applies percentage increases in a similar way when adding tax to a base price.
Percentage Calculator Examples
Example — What Is 15% of 200?
Using Mode 1 (X% of Y): Result = 200 × (15 ÷ 100) = 200 × 0.15 = 30. This means 15% of 200 is 30. A practical use: if a $200 restaurant bill attracts a 15% service charge, the tip amount is $30 and the total becomes $230. You can also use the tip calculator for restaurant-specific calculations that also split the bill per person.
Example — 45 Is What Percent of 300?
Using Mode 2 (X is what % of Y): Result = (45 ÷ 300) × 100 = 0.15 × 100 = 15%. So 45 is 15% of 300. This type of calculation is useful for finding a student's test score as a percentage, determining a product's market share, or measuring how much of a budget has been spent. If you scored 45 out of 300 marks, your score is 15%.
Example — Percentage Change From 80 to 100
Using Mode 3 (% Change): Result = ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25%. The value increased by 25%. In reverse, from 100 back to 80 would be a ((80 − 100) ÷ 100) × 100 = −20% decrease. Note that the percentage increase and the percentage decrease are not equal in magnitude due to the different base values used in each direction.
Frequently Asked Questions
How do I calculate a percentage?
To find X% of Y, use the formula: Result = Y × (X ÷ 100). Multiply the total value by the percentage expressed as a decimal. For example, 15% of 200 = 200 × 0.15 = 30. Enter your values in the calculator panel on the left for an instant result.
What is percentage of a percentage?
Percentage of a percentage means finding a percent of a percent value. Apply the formula twice. For example, 50% of 20% means: 20% × (50 ÷ 100) = 20% × 0.50 = 10%. So 50% of 20% equals 10%. This appears in compound discounts, tiered commissions, and probability calculations.
How do I find percentage increase?
Percentage increase = ((New Value − Original Value) ÷ Original Value) × 100. For example, a price that rises from $80 to $100: ((100 − 80) ÷ 80) × 100 = 25% increase. Use Mode 3 (% Change) in the calculator panel and enter 80 as the original value and 100 as the new value.
What is 20% of 50?
20% of 50 = 50 × (20 ÷ 100) = 50 × 0.20 = 10. The answer is 10. This follows the standard formula for finding X% of Y, where X = 20 and Y = 50.
How do I reverse a percentage?
To find the original value before a percentage was applied, divide the current value by (1 + the percentage as a decimal) for increases, or by (1 − the percentage as a decimal) for decreases. For example, if a value after a 20% increase is 120, the original = 120 ÷ 1.20 = 100. If a value after a 25% decrease is 75, the original = 75 ÷ 0.75 = 100.