Table of Contents
What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum" meaning "by the hundred."
50% = 50/100 = 0.50 = one half
Percentages are everywhere: discounts, taxes, tips, interest rates, statistics, grades, and more. Understanding them is essential for everyday math.
Calculate X% of Y
The most common percentage question: "What is X percent of Y?"
Formula
Result = Y × (X ÷ 100)
Examples
What is 20% of 150?
150 × (20 ÷ 100) = 150 × 0.20 = 30
What is 15% of $85? (calculating tip)
$85 × 0.15 = $12.75
What is 8.5% of $200? (calculating tax)
$200 × 0.085 = $17
X is What % of Y?
When you know two numbers and want to find the percentage relationship.
Formula
Percentage = (X ÷ Y) × 100
Examples
25 is what % of 200?
(25 ÷ 200) × 100 = 0.125 × 100 = 12.5%
You scored 45 out of 60. What's your %?
(45 ÷ 60) × 100 = 75%
$15 tip on $75 bill. What %?
(15 ÷ 75) × 100 = 20%
Percentage Change
Calculate how much something has increased or decreased as a percentage.
Formula
% Change = ((New - Old) ÷ Old) × 100
Increase Example
Stock went from $50 to $65
((65 - 50) ÷ 50) × 100 = +30%
Decrease Example
Price dropped from $80 to $60
((60 - 80) ÷ 80) × 100 = -25%
Note: Positive result = increase, Negative result = decrease
Increase/Decrease by %
Calculate a new value after increasing or decreasing by a percentage.
Increase by X%
New = Original × (1 + X/100)
$100 increased by 25%:
$100 × 1.25 = $125
Decrease by X%
New = Original × (1 - X/100)
$100 decreased by 25%:
$100 × 0.75 = $75
Discount Example
Original price $80, 30% off:
$80 × (1 - 0.30) = $80 × 0.70 = $56
You save $24
Real-World Applications
Sales Tax
Item costs $49.99, tax rate is 8.25%:
Tax: $49.99 × 0.0825 = $4.12
Total: $49.99 + $4.12 = $54.11
Restaurant Tips
Bill is $67.50, you want to tip 20%:
Tip: $67.50 × 0.20 = $13.50
Salary Raise
Current salary $50,000, getting 5% raise:
New salary: $50,000 × 1.05 = $52,500
Loan Interest
Borrowed $10,000 at 6% annual interest:
Annual interest: $10,000 × 0.06 = $600/year
Investment Return
Invested $5,000, now worth $6,500. What's the return?
((6500 - 5000) ÷ 5000) × 100 = 30% return
Quick Mental Math Tips
10% Shortcut
Just move the decimal point one place left.
10% of $85 = $8.50
50% Shortcut
Just divide by 2.
50% of $86 = $43
25% Shortcut
Divide by 4, or find 50% then halve it.
25% of $80 = $20
15% Tip Shortcut
Find 10%, then add half of that.
15% of $60: $6 + $3 = $9
20% Shortcut
Find 10% and double it.
20% of $45: $4.50 × 2 = $9
Flip Trick
X% of Y = Y% of X (same answer!)
8% of 50 = 50% of 8 = 4
Calculate Any Percentage Instantly
Use our free percentage calculator for quick, accurate results!
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