Percent means per hundred
The percent sign tells you that a quantity is being expressed out of 100. Dividing a percentage by 100 converts it to a decimal; multiplying a decimal by 100 converts it back to a percentage.
62% = 62 ÷ 100 = 0.62
The core percentage formula
When you know a value and its total, calculate the percentage with:
Percentage = Value ÷ Total × 100
The value is the part being measured. The total is the reference whole. Both must use the same unit.
Worked example 1: exam result
A student answers 42 of 50 questions correctly.
42 ÷ 50 × 100 = 84%
Find X% of Y
When the percentage is known, multiply the number by the percentage divided by 100.
Result = Y × X ÷ 100
Worked example 2: percentage of a number
15% of 320 = 320 × 15 ÷ 100 = 48
Rearrange the formula for reverse questions
If the part and percentage are known but the total is missing, divide the part by the decimal percentage.
Total = Value ÷ (Percentage ÷ 100)
Worked example 3: find the original total
If 45 is 30% of a total, then 45 ÷ 0.30 = 150.
Percentage change uses the original value
Percentage change is a related but distinct formula. Subtract the original value from the new value, then divide by the absolute original value.
Percentage change = (New − Original) ÷ |Original| × 100
This formula is undefined when the original value is zero.
Percentage change vs. percentage points
A rate moving from 20% to 25% rises by 5 percentage points. Relative to the original 20%, the percentage increase is (25 − 20) ÷ 20 × 100 = 25%. These statements describe the same movement in different ways.
Related calculators
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