Percentage Calculator

What Is a Percentage?

A percentage expresses a number as a part of 100. Percentages are commonly used to compare values, describe changes, calculate discounts and taxes, analyze grades, and measure proportions.

The word percentage comes from the idea of "per hundred." A percentage therefore provides a common way to express a proportion regardless of the size of the numbers being compared. For example, 25 out of 100 and 250 out of 1,000 represent the same proportion: 25%.

The calculator above handles several common percentage problems, including finding a percentage of a number, determining what percentage one number is of another, calculating percentage change, finding an original value, and calculating percentage difference.

Percentages are useful because they make different quantities easier to compare. A change from 50 to 60, for example, is an increase of 10 units, but expressing it as a 20% increase gives additional context about the size of the change relative to the original value.

How to Calculate a Percentage

To calculate a percentage of a number, convert the percentage to a decimal and multiply it by the number. To convert a percentage to a decimal, divide it by 100. For example, 25% becomes 0.25 and 7.5% becomes 0.075.

For example, 20% of 250 is 50 because 0.20 × 250 = 50. The percentage tells you what fraction of the original number should be used in the calculation.

This method works for whole numbers as well as decimal values. For instance, 12.5% of 80 is 10 because 0.125 × 80 = 10. The calculator can perform these conversions automatically so you can work directly with the percentage you have.

What percentage is one number of another?

When you know a part and a whole, divide the part by the whole and multiply by 100. This tells you what percentage the part represents relative to the whole. For example, 50 is 20% of 250.

The order of the values matters in this calculation. The number representing the smaller portion is normally the part, while the number representing the complete amount is the whole or reference value. Changing the reference value can produce a completely different percentage.

How do you calculate percentage change?

Percentage change compares a new value with a starting value. Subtract the starting value from the new value, divide by the starting value, and multiply by 100.

A positive result indicates an increase, while a negative result indicates a decrease. For example, if a price increases from $80 to $100, the change is $20. Dividing $20 by the original $80 gives 0.25, which corresponds to a 25% increase.

The original or starting value is important when calculating percentage change. A $20 change from $80 to $100 is not the same percentage change as a $20 change from $100 to $120 because the reference values are different.

Common Percentage Examples

The following examples show several of the most common percentage calculations. They can also help you identify which type of calculation to select in the calculator above.

Percentage Change vs. Percentage Difference

Percentage change uses a starting value as the reference point. It tells you how much a value increased or decreased relative to where it started. This makes percentage change particularly useful for tracking prices, revenue, population, measurements, expenses, and other values over time.

Percentage difference compares two values without treating either value as the starting point. This makes it useful when comparing two independent measurements or values where neither one should be considered the original amount.

For example, if a product price changes from $80 to $100, the percentage change is based on the original $80. If you simply want to compare $80 and $100 as two independent values, percentage difference uses the average of their magnitudes as the reference.

These two calculations can produce different answers even when they use the same two numbers. Choosing the correct calculation depends on whether one value is a starting point or whether the two values are simply being compared.

If you are comparing proportional quantities, our Ratio Calculator can help. For a collection of values, the Average Calculator can help you calculate the mean before making percentage comparisons.

How to Find the Original Number From a Percentage

Sometimes you know a percentage and the resulting amount, but you need to determine the original number. For example, you may know that $60 represents 30% of a total and want to find the total amount.

To find the original number, convert the percentage to a decimal and divide the known amount by that decimal. In the example above, $60 ÷ 0.30 = $200, so $60 is 30% of $200.

This type of calculation is useful when working backward from a percentage. It can be helpful for finding an original price after a discount, determining a total from a known portion, or interpreting a percentage-based measurement.

Percentages in Discounts and Sale Prices

Percentages are frequently used when calculating discounts. If an item costs $100 and has a 20% discount, the discount amount is $20 and the price after the discount is $80.

The important distinction is between the discount percentage and the final price. The percentage represents the portion removed from the original price, while the remaining percentage represents the portion that is still paid. A 20% discount therefore means you pay 80% of the original price.

For more complicated financial calculations, you may also find our Interest Calculator or Loan Calculator useful.

Percentages, Taxes, and Fees

Sales taxes and service fees are another common use for percentages. If a tax rate is 8% and the taxable amount is $500, the tax is $40. The final amount after adding the tax would therefore be $540.

When working with taxes or fees, it is important to identify whether the percentage is being applied to the original amount, a discounted amount, or another calculated subtotal. Applying the same percentage to different reference values can produce different results.

Percentages in Grades and Test Scores

Percentages are widely used to represent test scores. If a student answers 45 questions correctly out of 50, the score is 90% because 45 divided by 50 equals 0.90.

Percentage scores can make results easier to compare when tests contain different numbers of questions. A score of 18 out of 20 and a score of 45 out of 50 both represent 90%.

If you are working with school or course results, the Grade Calculator can be useful alongside the Percentage Calculator.

Percentages in Business and Finance

Businesses use percentages to describe revenue growth, profit margins, expenses, conversion rates, discounts, market changes, and many other measurements. A percentage allows a business to compare changes even when the underlying amounts are different.

For example, if monthly revenue increases from $20,000 to $22,000, the increase is $2,000. Expressing that change as a percentage shows that revenue increased by 10% relative to the starting amount.

Percentages are also commonly used for interest rates and financial growth. If you are analyzing borrowing costs, our Mortgage Calculator and Loan Calculator can provide more detailed calculations for those situations.

Where Percentages Are Used

Percentages appear in many everyday and professional calculations, including:

• Discounts and sale prices
• Taxes and fees
• Interest rates
• Business reports
• Test scores and grades
• Statistics
• Growth comparisons
• Budgets and expenses

Because percentages provide a standardized way to describe proportions, they are useful across many different fields. The same basic percentage principles can be applied to shopping, education, business, statistics, personal finance, and everyday comparisons.

Understanding Percentage Points

Percentage points are different from percentage change. Percentage points describe the direct difference between two percentages, while percentage change describes the relative change between the two values.

For example, if an interest rate increases from 5% to 6%, the rate increased by 1 percentage point. However, relative to the original 5% rate, the percentage change is 20%.

This distinction is important when reading financial reports, statistics, surveys, and business information. Saying that a rate increased by one percentage point is not equivalent to saying that it increased by 1%.

Percentage Calculator Tips

Before calculating a percentage, first identify what the percentage is being measured against. The reference value is one of the most important parts of a percentage calculation because changing the reference can change the result.

• Identify the reference value before calculating.
• Use percentage change when there is a clear starting value.
• Use percentage difference when comparing independent values.
• Remember that 1% equals 0.01 as a decimal.
• Check whether your answer should be expressed as a number or a percentage.
• Keep the original value in mind when calculating an increase or decrease.
• Check the units of the numbers before interpreting the result.

Common Percentage Mistakes

One common mistake is using the wrong reference value. Percentage change should normally use the original or starting value as the denominator. Using the new value instead can produce a different result.

Another common mistake is confusing a percentage with a percentage point. A change from 10% to 12% is a 2 percentage-point increase, but the relative percentage change is 20%.

It is also easy to confuse a percentage with a decimal. A percentage must be divided by 100 before it is used as a decimal multiplier. For example, 15% is 0.15, not 15.

Frequently Asked Questions