Percentage Calculations: Beyond Basic Math

Percentages are ratios scaled to 100. Here are the patterns that cover 90% of real-world problems.

Percent of a Number

To find 18% of 250, multiply 0.18 × 250 = 45. Converting to decimal keeps things simple.

Percent Change

Percent change = (new - old) / old. If a price goes from 40 to 52, the change is (52 - 40) / 40 = 0.3 or 30%.

Discounts and Markups

A 20% discount on $80 is 0.8 × 80 = $64. A 25% markup on cost $40 gives price = 1.25 × 40 = $50. For sequential discounts, multiply factors (e.g., 20% then 10% is 0.8 × 0.9 = 0.72 or a 28% total discount).

Reverse Percent Problems

If the final price after a 20% discount is $72, the original was 72 / 0.8 = $90. Always divide by the remaining factor.

Compounding

Repeated percentage growth multiplies factors. Growing 5% for 12 months is 1.05^12 ≈ 1.795 or ~79.5% total growth.

Practice

Try the Percentage Calculator and Compound Interest to explore scenarios.