Percentage Calculator Formula: Percent of, Percent Change, and Reverse Percentage

A percentage calculator uses different formulas depending on the question you are asking. The formula for finding 20% of a number is not the same as the formula for percent change, percentage difference, or reverse percentage.

For a quick result, use the Calzivo Percentage Calculator. Choose the calculation type, enter the known values, and the calculator will apply the right formula automatically.

What Is the Percentage Calculator Formula?

The percentage calculator formula is the math used to compare a part with a whole, find a percent of a number, measure a change, or work backward from a final value.

Simple Definition

A percentage formula converts a value into a number out of 100. The most basic formula is:

Percentage = (Part / Whole) x 100

This formula answers questions like: 30 is what percent of 200?

Why Percent Means Per 100

Percent means “per 100.” So: 25% = 25 out of 100. That also means: 25% = 25 / 100 = 0.25.

Most percentage formulas work by converting the percent into a decimal, then multiplying or dividing.

How Percentages Connect Parts and Wholes

Percentage problems usually involve three values: part, whole, and percent. If you know two of them, you can usually calculate the third. The key is identifying which number is the whole, because the whole is the base of the calculation.

Basic Percentage Formula

The basic formula is used when you want to find what percent one number is of another, find a percentage of a number, or find the whole.

Formula for Finding What Percent One Number Is of Another

Use this formula when you know the part and the whole:

Percentage = (Part / Whole) x 100

Example: 30 is what percent of 200?
30 / 200 x 100 = 15%. So, 30 is 15% of 200.

Formula for Finding a Percentage of a Number

Use this formula when you know the percentage and the number:

Result = Number x (Percentage / 100)

Example: 20% of 150 = 150 x 0.20 = 30.

Formula for Finding the Whole When the Part and Percentage Are Known

Use this formula when you know the part and the percent, but not the full number:

Whole = Part / (Percentage / 100)

Example: 80 is 25% of what number?
Whole = 80 / 0.25 = 320.

Example Using Part, Whole, and Percent

Suppose a student scores 45 out of 60.

Part = 45, Whole = 60
Percentage = (45 / 60) x 100 = 75%

The grade is 75%. For grade-related calculations, you can also use the Grade Calculator or Percentage to GPA Calculator.

Percent of a Number Formula

The percent of a number formula is one of the most common percentage formulas.

When to Use This Formula

Use this formula for questions like discounts, tips, sales tax, grades, commissions, and budget categories.

Formula: Result = Percentage x Number

The practical formula is: Result = Number x (Percentage / 100). You can also think of it as: Result = Number x Percentage as a decimal.

Step-by-Step Example

Question: What is 18% of 250?

• Step 1: Convert percent to decimal: 18% = 0.18
• Step 2: Multiply by the number: 250 x 0.18 = 45

For shopping calculations, use the Discount Calculator or Sales Tax Calculator.

Percent Change Formula

Percent change measures how much a value changed compared with its original value.

Formula for Percentage Increase

Use this formula when the new value is higher than the original value:

Percentage Increase = ((New Value - Original Value) / Original Value) x 100

Example: Price from 50 to 65. (15 / 50) x 100 = 30%. Use the Percentage Increase Calculator.

Formula for Percentage Decrease

Use this formula when the new value is lower than the original value:

Percentage Decrease = ((Original Value - New Value) / Original Value) x 100

Example: Price from 80 to 60. (20 / 80) x 100 = 25%. Use the Percentage Decrease Calculator.

Why the Original Value Matters

The original value is the base. If you switch the base, the answer changes. For example, 50 to 65 is a 30% increase, but 65 to 50 is a 23.08% decrease.

Reverse Percentage Formula

Reverse percentage is used when you know the final value and the percentage change, but you want to find the original value.

Reverse Increase Formula

Use this when the final value includes an increase:

Original Value = Final Value / (1 + Percentage / 100)

Example: 120 / 1.20 = 100.

Reverse Decrease Formula

Use this when the final value includes a decrease:

Original Value = Final Value / (1 - Percentage / 100)

Example: 80 / 0.80 = 100. If an item is $80 after 20% off, the original price was $100.

Percentage Difference Formula

Percentage difference compares two values when neither value is clearly the original.

Percentage Difference = (|A - B| / ((A + B) / 2)) x 100

Compare 80 and 100: Difference is 20, Average is 90. 20 / 90 x 100 = 22.22%.

Value After Percentage Change Formula

• Adding a Percentage: Final Value = Original Value x (1 + Percentage / 100)
• Subtracting a Percentage: Final Value = Original Value x (1 - Percentage / 100)

Example: 75 x 1.12 = 84 (12% increase). 120 x 0.75 = 90 (25% discount).

How a Percentage Calculator Uses These Formulas

A percentage calculator applies these formulas based on the mode you choose, converts percent to decimal internally, and handles rounding for readability. For a step-by-step usage guide, read How to Use a Percentage Calculator Step by Step.

Common Percentage Formula Mistakes

FAQs

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