How to Calculate a Percentage (Every Formula Explained)

"Percentage" covers several different problems that look similar but use different formulas. Most confusion comes from not noticing which one you are actually solving. This guide breaks percentages into the three questions you genuinely face in everyday life and gives you the formula and a mental shortcut for each.

What "percent" actually means

Percent means "per hundred." 25% is just another way of writing 25 per 100, or the fraction 25/100, or the decimal 0.25. Every percentage calculation is really a small piece of arithmetic with that decimal. Converting a percentage to a decimal — divide by 100 — is the move that unlocks everything else.

Problem 1: What is X% of a number?

This is the most common one: a discount, a tip, a tax, a commission.

Formula: result = number × (percent ÷ 100)

Example: What is 15% of 80?

15 ÷ 100 = 0.15 0.15 × 80 = 12

Mental shortcut: 10% of any number is that number with the decimal point moved one place left. 10% of 80 is 8. Then 5% is half of that — 4. So 15% is 8 + 4 = 12. Most everyday percentages can be built from 10% and 5% this way.

Problem 2: What percent change happened?

This is the one people get wrong most often, because they forget which number is the starting point. Used for price rises, growth rates, score improvements.

Formula: percent change = ((new − old) ÷ old) × 100

Example: A price rose from 50 to 65.

(65 − 50) ÷ 50 = 15 ÷ 50 = 0.3 0.3 × 100 = 30% increase

The critical detail: you always divide by the old value, not the new one. A change from 50 to 65 is a 30% increase, but a change from 65 back to 50 is a 23% decrease — the same gap, different percentages, because the starting number differs.

Problem 3: The reverse percentage

This is the trickiest, and the source of a classic mistake. You know a number after a percentage was applied, and you want the original.

Example: An item costs 120 after a 20% discount. What was the original price?

The wrong move is to add 20% of 120 back. That gives 144 — incorrect. The 20% was taken off the original, not off 120.

Correct approach: 120 represents 80% of the original (100% − 20%).

original = 120 ÷ 0.80 = 150

Check: 20% of 150 is 30, and 150 − 30 = 120. Correct.

Formula for a discount: original = final ÷ (1 − discount/100) Formula for a markup or tax already added: original = final ÷ (1 + rate/100)

"Percent off" vs "percent of"

These two phrases sound alike and mean opposite things:

• "40% off 90" means you subtract 40%. You pay 60% of 90 = 54.
• "40% of 90" means the result is that fraction. The answer is 36.

When you see a sale sign, it is "percent off." When a report says "40% of users," it is "percent of." Reading the phrase carefully prevents the most common percentage error there is.

Percentage points are not percentages

One more trap. If an interest rate goes from 4% to 6%, that is a rise of 2 percentage points — but a 50% increase (because 2 is half of the original 4). News headlines mix these up constantly. "Percentage points" measures the gap between two percentages; "percent change" measures the relative size of that gap.

Putting it together

Every percentage problem reduces to: identify which of the three questions you are asking, convert the percent to a decimal, and apply the matching formula. When the numbers are awkward — or you just want a check — the Percentage Calculator handles percent of a number, percent change, and reverse percentages with step-by-step working.

The short version

There are three percentage problems. Percent of a number: multiply by the decimal. Percent change: divide the difference by the old value. Reverse percentage: divide by (1 minus the discount) — never just add the percentage back. Watch the difference between "percent off" and "percent of," and don't confuse percentage points with percent change. The Percentage Calculator does all three if you want to skip the arithmetic.