Percentage Calculator

Calculate percentages easily with multiple calculation types. Choose the type that matches your needs.

Calculate Percentage of a Number

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Find What Percent One Number Is of Another

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Calculate Percentage Increase or Decrease

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Percentage Formulas

1. Find Percentage of a Total

To find what percentage one number is of another, divide the part by the whole and multiply by 100.

$$\textbf{Percentage} = \left(\frac{\textbf{Part}}{\textbf{Whole}}\right) \times 100$$

Example: 42 out of 50 = (42 ÷ 50) × 100 = 84%

2. Find Percentage Change (Increase or Decrease)

To calculate the percentage change between two numbers, find the difference and divide by the original value.

$$\textbf{Percentage~Change} = \left(\frac{\textbf{New~Value} - \textbf{Old~Value}}{\textbf{Old~Value}}\right) \times 100$$

Example: From $2,342 to $2,500 = ((2500 - 2342) ÷ 2342) × 100 = 6.75% increase

3. Find the Total from a Percentage

When you know a percentage and the amount it represents, find the total by dividing.

$$\textbf{Total} = \frac{\textbf{Amount}}{\textbf{Percentage} \div 100}$$

Example: $15 is 25% off, find original: 15 ÷ 0.75 = $20

4. Find Amount from Percentage of Total

To find what amount a percentage represents, multiply the total by the percentage (as a decimal).

$$\textbf{Amount} = \textbf{Total} \times \left(\frac{\textbf{Percentage}}{100}\right)$$

Example: 8.9% of $800 = 800 × 0.089 = $71.20

5. Increase or Decrease by a Percentage

To increase or decrease a number by a percentage, multiply by (1 + percentage) for increase or (1 - percentage) for decrease.

increase:

$$\textbf{Increased~Value} = \textbf{Original} \times \left(1 + \frac{\textbf{Percentage}}{100}\right)$$

decrease:

$$\textbf{Decreased~Value} = \textbf{Original} \times \left(1 - \frac{\textbf{Percentage}}{100}\right)$$

Example: $113 + 25% = 113 × 1.25 = $141.25

Worked Examples with Step-by-Step Solutions

Example 1: Finding Test Score Percentage

Problem: You answered 42 questions correctly out of 50 total questions. What is your score as a percentage?

**Step 1:** Identify the values

Correct answers (Part) = 42, Total questions (Whole) = 50

**Step 2:** Apply the formula

$$\textbf{Percentage} = \left(\frac{42}{50}\right) \times 100$$

**Step 3:** Calculate

= 0.84 × 100 = 84%

**Answer:** Your test score is **84%**

Example 2: Calculating Percentage Increase in Earnings

Problem: Your earnings increased from $2,342 in November to $2,500 in December. What is the percentage increase?

**Step 1:** Find the difference

Difference = $2,500 - $2,342 = $158

**Step 2:** Apply the percentage change formula

$$\textbf{Percentage~Change} = \left(\frac{158}{2342}\right) \times 100$$

**Step 3:** Calculate

= 0.06746 × 100 = 6.746%

**Answer:** Your earnings increased by **6.75%**

Example 3: Finding Original Price from Sale Price

Problem: A shirt is on sale for $15, which is 25% off. What was the original price?

**Step 1:** Understand what $15 represents

If 25% off, then $15 = 75% of original price (100% - 25% = 75%)

**Step 2:** Apply the formula

$$\textbf{Original~Price} = \frac{15}{0.75}$$

**Step 3:** Calculate

= $20.00

**Answer:** The original price was **$20.00**

frequently_asked_questions

How do I calculate what percentage one number is of another?

Divide the first number (part) by the second number (whole) and multiply by 100. For example, to find what percentage 30 is of 120: (30 ÷ 120) × 100 = 25%. This formula works for test scores, completion rates, and any part-to-whole comparisons.

What's the difference between percentage increase and percentage decrease?

Percentage increase shows growth from the original value (positive result), while percentage decrease shows reduction (negative result). Both use the same formula: ((New - Old) ÷ Old) × 100. If the result is positive, it's an increase; if negative, it's a decrease. For example, going from 100 to 120 is a 20% increase, while 120 to 100 is a 16.67% decrease.

How do I find the original price before a discount?

Divide the sale price by (100% minus the discount percentage). For example, if something costs $60 after a 20% discount: $60 ÷ 0.80 = $75 original price. This works because the sale price represents 80% (100% - 20%) of the original.

How do I calculate sales tax or tips using percentages?

Multiply the base amount by the percentage (as a decimal). For 8.9% sales tax on $800: $800 × 0.089 = $71.20 tax. For a 20% tip on a $45 meal: $45 × 0.20 = $9.00 tip. To find the total including tax or tip, use: Amount × (1 + percentage as decimal).

Why are percentage increases and decreases not symmetrical?

Because percentages are calculated from different base values. A 50% increase from 100 gives 150, but a 50% decrease from 150 gives 75, not back to 100. This happens because the increase uses 100 as the base, while the decrease uses 150 as the base. To reverse a percentage change, you must use the reciprocal calculation.

Our goal is to provide accurate and user-friendly calculators for educational and informational purposes. Each calculator undergoes expert review and verification before publication, so you can use it confidently and get reliable results every time.

Expert Verified
Kiran Khalid

Kiran Khalid

Math Specialist

Kiran Khalid has verified all percentage calculation methods, formulas, and use cases in this calculator. From basic percentage calculations to complex percentage increase/decrease scenarios, every formula has been mathematically validated to ensure accuracy in real-world applications.

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