The complete practical guide to percentages
Percent means “per hundred.” A percentage is a ratio expressed relative to 100, but the correct calculation depends on what you are comparing.
Find a percentage of an amount
Multiply the amount by the percentage divided by 100. For a 12% commission on $850: 850 × 0.12 = $102. For 2.5% of 480, multiply 480 by 0.025 to get 12.
This is useful for commissions, charitable contributions, tax estimates and portions of a budget. Remember to identify the correct base amount before calculating.
Find what percentage one value is of another
Divide the part by the whole and multiply by 100. If 42 of 60 questions were answered correctly, 42 ÷ 60 × 100 = 70%. A whole of zero cannot be used as a denominator.
Percentage change
Subtract the original value from the new value, divide by the absolute value of the original, and multiply by 100. For a price rising from $80 to $92, the change is 12 ÷ 80 × 100 = 15%. The denominator is the original value, not the final value.
Reverse a percentage
When the final price is known, divide it by (1 + percentage change/100). A $72 price after a 10% reduction had an original price of $72 ÷ 0.90 = $80. A decrease of exactly 100% cannot be reversed from a final value of zero to a unique starting value.
Discounts, tax and tips
A 25% discount on $120 saves $30 and produces a $90 sale price. If 6% sales tax applies to the discounted price, the total is $95.40. Taxes and discounts may be applied differently by jurisdiction or store; always check the actual checkout.
For a $75 restaurant bill with an 18% tip, the tip is $13.50 and the total is $88.50. Split among three people, that is $29.50 each before any separate fees.
Margin versus markup
Both start with profit = selling price − cost. A product costing $60 and selling for $100 earns $40 gross profit. Its margin is $40 ÷ $100 = 40%; its markup is $40 ÷ $60 ≈ 66.67%. Confusing these measures can cause underpricing.
Compound growth
Compounding applies each period’s percentage change to the updated balance. At 5% growth per period, $1,000 becomes $1,050 after one period and $1,102.50 after two. The formula is starting value × (1 + rate/100) raised to the number of periods. Real-world returns can vary.
Rounding and precision
Round only after performing the relevant calculation whenever possible. For financial transactions, intermediate rounding and provider-specific rules can change results by a few cents. Use these free tools for planning and verify final amounts against authoritative statements.