How to Calculate a Percentage (3 Types, With Examples)

There are three "calculate a percentage" questions people actually ask, and each has a one-line formula. Percent of a number: (percent ÷ 100) × number. What percent one number is of another: (part ÷ whole) × 100. Percentage change: (new − old) ÷ old × 100. Below is each one worked out with examples — plus a free percentage calculator that handles all three.

1. What is X% of Y? (a percentage of a number)

Formula: (percent ÷ 100) × number. "Percent" means "per hundred", so 20% is just 0.20. To find 20% of 150: 0.20 × 150 = 30. This is the version you use for tips, tax, and commissions. The Percentage Calculator does it instantly, and for shopping specifically the Discount Calculator shows the final price after a markdown.

Mental-math trick: 10% is just the number with the decimal moved one place left (10% of 150 = 15), so 20% is double that, 5% is half, and 15% = 10% + 5%. That covers most tip math in your head.

2. X is what percent of Y?

Formula: (part ÷ whole) × 100. If 30 people out of 150 said yes: 30 ÷ 150 × 100 = 20%. Use this for scores, completion rates, and "what share of the total" questions. Enter the two numbers in the Percentage Calculator and it returns the percent automatically.

3. Percentage change (increase or decrease)

Formula: (new − old) ÷ old × 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. Positive is an increase, negative is a decrease, and you always divide by the original value. This one has enough traps of its own that it gets a full guide: how to calculate percentage change, backed by the Percentage Change Calculator.

How to reverse a percentage

Know the result and want the original? To find the number before a percentage was added, divide by (1 + percent). A price of $120 that already includes 20% tax started at 120 ÷ 1.20 = $100. To reverse a discount, divide by (1 − percent): an item on sale for $80 after 20% off was 80 ÷ 0.80 = $100.

Common mistakes

• Percentage points ≠ percent. Going from 10% to 15% is a rise of 5 percentage points, but a 50% increase. Keep the two labels separate.
• Dividing by the wrong number in change problems — always divide by the starting (old) value, not the new one.
• Stacking percentages — 20% off then 10% off isn't 30% off; it's 0.80 × 0.90 = 28% off.

Bottom line

Three questions, three formulas: (percent ÷ 100) × number, (part ÷ whole) × 100, and (new − old) ÷ old × 100. Memorize the 10%-shortcut for mental math, and for everything else run it through the free calculator — no sign-up, instant answer.