Percentage Calculator — Free Online Percent Calculator

How to Use the Percentage Calculator

1. Select the calculation type: Choose from five different percentage operations using the dropdown menu at the top. Options include finding a percentage of a number, determining what percentage one number is of another, calculating percentage change between two values, adding a percentage to a number, or subtracting a percentage from a number.
2. Enter the first value (X): Type the first number into the input field. The label changes based on your selected operation. For "What is X% of Y?", enter the percentage here. For "% change from X to Y", enter the original value.
3. Enter the second value (Y): Type the second number into the corresponding field. Again, the label adjusts to match the operation. For percentage-of calculations, this is the number you want the percentage of. For percentage change, this is the new value.
4. Review your results: The right panel instantly displays the calculated result in large text, the mathematical formula used for transparency, and a plain-English explanation of what the result means. No need to press any button — results update in real time as you type.

When you switch between calculation modes, the input values automatically update to sensible defaults so you can immediately see how each mode works. Experiment freely with different values and modes to solve any percentage problem you encounter.

Percentage Calculator Formulas

Variables Explained

• X (First Value): Depending on the mode, this represents either the percentage rate, the part value, or the starting number. It is the first operand in each formula and changes meaning based on which calculation you select.
• Y (Second Value): This represents either the whole number, the total value, or the ending number. It serves as the second operand and provides the reference point for the calculation.
• Result: The computed output, which can be a number (for "What is X% of Y?", "Add", or "Subtract" modes) or a percentage (for "is what %" and "% change" modes). The calculator automatically formats the result with appropriate symbols.

Step-by-Step Example

Calculate the percentage change from 250 to 325:

1. Identify the values: Original (X) = 250, New (Y) = 325
2. Calculate the difference: 325 - 250 = 75
3. Divide by the absolute value of the original: 75 / 250 = 0.30
4. Multiply by 100 to get the percentage: 0.30 x 100 = 30%

The value increased by 30% from 250 to 325. This is a positive percentage change, indicating growth. If the result were negative, it would represent a decrease.

Practical Examples

Example 1: Jennifer's Sales Tax Calculation

Jennifer is shopping for a new laptop priced at $899.99 in a state with 8.25% sales tax. She wants to know the total cost including tax. Using the "Add X% to Y" mode with X = 8.25 and Y = 899.99:

• Tax amount: $899.99 x (8.25 / 100) = $74.25
• Total price: $899.99 + $74.25 = $974.24

Jennifer now knows she needs approximately $974.24 to purchase the laptop. This helps her budget accurately and avoid surprises at the checkout counter. Percentage calculations like these are essential for everyday shopping decisions.

Example 2: Michael's Investment Return

Michael invested $15,000 in a diversified stock portfolio last year and it is now worth $17,250. He wants to calculate his return on investment. Using the "% change from X to Y" mode with X = 15,000 and Y = 17,250:

• Gain: $17,250 - $15,000 = $2,250
• Percentage return: ($2,250 / $15,000) x 100 = 15%

Michael earned a 15% return on his investment over the year. He can compare this to benchmark indices like the S&P 500 to evaluate his portfolio's performance. For more detailed investment analysis, try our compound interest calculator.

Example 3: Lisa's Store Discount

Lisa found a winter coat originally priced at $240 with a 35% off clearance tag. She needs to know the sale price. Using "Subtract X% from Y" with X = 35 and Y = 240:

• Discount amount: $240 x (35 / 100) = $84.00
• Sale price: $240 - $84 = $156.00

The coat costs $156.00 after the 35% discount. Lisa saves $84.00, which is a substantial reduction. If the store offers an additional 10% off at checkout, she can run a second calculation on $156.00 to find her final price — note that a 35% discount followed by a 10% discount is not the same as a single 45% discount.

Example 4: Robert's Grade Calculation

Robert scored 42 out of 50 on his math exam and wants to know his percentage score. Using "X is what % of Y?" with X = 42 and Y = 50:

• Percentage: (42 / 50) x 100 = 84%

Robert scored 84% on his exam, which is typically a B grade. For comprehensive grade tracking across multiple assignments, check out our grade calculator.

Common Percentage Reference Table

Tips and Complete Guide

Quick Mental Math Shortcuts for Percentages

Knowing a few mental math tricks can help you estimate percentages quickly without a calculator. To find 10% of any number, simply move the decimal point one place to the left: 10% of 350 = 35. To find 5%, take 10% and halve it: 5% of 350 = 17.50. To find 1%, move the decimal two places left: 1% of 350 = 3.50. You can combine these building blocks for any percentage — for example, 15% = 10% + 5%, and 25% = half of 50% (which itself is half the number).

Understanding Percentage Points vs. Percentages

A common source of confusion is the difference between percentage points and percentages. If an interest rate rises from 3% to 5%, it has increased by 2 percentage points, but the percentage increase is actually 66.67% (because 2/3 x 100 = 66.67%). Similarly, if unemployment drops from 8% to 6%, that is a 2 percentage point decrease but a 25% relative decrease. Media and financial reports often use these terms interchangeably, leading to misunderstandings. Always pay attention to context to understand which measure is being used.

Compounding Percentages

When multiple percentage changes are applied sequentially, they compound rather than simply add up. A 10% increase followed by a 10% decrease does not return to the original value. If you start with $100, a 10% increase gives you $110. Then a 10% decrease from $110 yields $99, which is less than the original $100. This compounding effect is especially important in finance, where returns compound over time. For compound calculations over multiple periods, our compound interest calculator provides detailed projections.

Percentages in Statistics and Data Analysis

In statistics, percentages help communicate proportions and probabilities. Confidence intervals are expressed as percentages (e.g., 95% confidence interval). Statistical significance is often reported as a p-value, where p less than 0.05 (5%) indicates a statistically significant result. Percentages also form the basis of pie charts and stacked bar charts in data visualization. When working with statistical data, understanding percentages helps you interpret survey results, medical studies, and market research accurately.

Common Mistakes to Avoid

• Confusing percentage points with percentages: A rate changing from 5% to 8% is a 3 percentage point increase, but a 60% relative increase. These are very different statements and are frequently confused in everyday conversation and media.
• Stacking discounts incorrectly: A 20% discount plus an additional 10% off is not 30% off. The second discount applies to the already-reduced price: $100 x 0.80 x 0.90 = $72, not $70.
• Reversing percentage changes: To reverse a 25% increase, you need a 20% decrease, not a 25% decrease. If $100 increases by 25% to $125, then 25% of $125 is $31.25, and $125 - $31.25 = $93.75, not $100.
• Dividing by zero in percentage calculations: When the original value is zero, percentage change is undefined. Our calculator handles this edge case by returning zero, but mathematically, you cannot divide by zero.
• Forgetting to convert percentages to decimals: When using percentages in formulas, remember to divide by 100 first. Using 18 instead of 0.18 in a calculation will give results that are 100 times too large.

Frequently Asked Questions