Learn how to calculate percentage using the 3 core formulas: finding what percent, finding a percentage of a number, and finding the whole. With real-life examples.
The word "percentage" comes from the Latin per centum, meaning "per hundred." A percentage is simply a way of expressing a fraction as a number out of 100. Despite this simple definition, percentage problems come in three distinct types — and most people only know how to solve one of them. This guide explains all three, with worked examples for each.
Every percentage problem falls into one of three categories, depending on which piece of information you're solving for:
All three use the same underlying formula: Percentage (P) = Part (V2) ÷ Whole (V1) × 100
Rearranging this formula gives you the solution for each type:
Formula: P = (Part ÷ Whole) × 100
You scored 34 out of 40 on a test. What is your percentage?
P = (34 ÷ 40) × 100 = 0.85 × 100 = 85%
Your monthly sales target is $50,000. You achieved $43,500. What percentage of your target did you hit?
P = (43,500 ÷ 50,000) × 100 = 0.87 × 100 = 87%
280 out of 350 survey respondents said they would recommend your product. What percentage is that?
P = (280 ÷ 350) × 100 = 0.8 × 100 = 80%
Formula: Part = (Percentage ÷ 100) × Whole
Or equivalently: multiply the whole by the decimal form of the percentage.
A $120 jacket is on sale for 25% off. How much is the discount?
Discount = (25 ÷ 100) × 120 = 0.25 × 120 = $30
Sale price = $120 − $30 = $90
You're buying a $85 item with 8.5% sales tax. How much is the tax?
Tax = 0.085 × $85 = $7.23
Total = $85 + $7.23 = $92.23
You want to save 15% of your $3,800 monthly paycheck. How much should you save each month?
Savings = 0.15 × $3,800 = $570/month
Formula: Whole = Part ÷ (Percentage ÷ 100)
This is the reverse percentage calculation — working backwards from a known part and percentage to find the original total.
A jacket is now $90 after a 25% discount. What was the original price?
The sale price ($90) represents 75% of the original (100% − 25% = 75%).
Original = $90 ÷ 0.75 = $120
You answered 34 questions correctly and scored 85%. How many questions were on the test?
Total = 34 ÷ 0.85 = 40 questions
A survey found 280 people would recommend your product, representing 80% of respondents. How many people responded?
Total = 280 ÷ 0.80 = 350 respondents
Percentage change is used to compare a new value to an original value:
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result = percentage increase. A negative result = percentage decrease.
Your salary increased from $55,000 to $62,000. What's the percentage increase?
Change = (($62,000 − $55,000) ÷ $55,000) × 100 = ($7,000 ÷ $55,000) × 100 = 12.7% increase
A stock fell from $145 to $118. What's the percentage decrease?
Change = (($118 − $145) ÷ $145) × 100 = (−$27 ÷ $145) × 100 = −18.6% (decrease)
These shortcuts help you estimate percentages quickly without a calculator:
A useful mathematical identity: x% of y = y% of x. This means 8% of 50 = 50% of 8 = 4. When the percentage seems difficult to calculate directly, swap the numbers to see if the alternative is easier.
This distinction matters enormously in statistics and finance. A percentage point is an absolute change in percentage values; a percentage change is a relative change.
Example: Interest rates rise from 3% to 5%. This is a 2 percentage point increase, but a 66.7% increase in the interest rate itself. Confusing these two measures is one of the most common errors in financial reporting.
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