“Percent” just means “per hundred.” A percentage is a way of expressing one number as a fraction of another, scaled so the whole is always 100. Once you see it that way, the three questions people actually ask about percentages — and confuse constantly — become three tidy formulas.

Nearly every real-world percentage problem is one of these: finding a percent of a number, finding the percent change between two numbers, or figuring out what percent one number is ofanother. Here’s each, with the math worked out.

1. Percent of a number

To find a percentage of a value, turn the percent into a decimal (divide by 100) and multiply:

Result = (percent ÷ 100) × number.

What is 15% of 80? That’s 0.15 × 80 = 12. This is the tip-at-a-restaurant, sales-tax, commission calculation. A handy shortcut: percentages are reversible, so 15% of 80 equals 80% of 15 — both give 12, and sometimes the flip is easier to do in your head.

2. Percent change, from one value to another

To measure how much a number grew or shrank, compare the change to where you started:

Percent change = (new − old) ÷ old × 100.

A price rises from $40 to $50. The change is ($50 − $40) ÷ $40 × 100 = 10 ÷ 40 × 100 = +25%. A positive result is an increase; a negative one is a decrease. The critical detail is the denominator: you always divide by the original value, not the new one.

3. “X is what percent of Y?”

To express one number as a percentage of another, divide the part by the whole and scale up:

Percent = (part ÷ whole) × 100.

You got 18 questions right out of 24. That’s 18 ÷ 24 × 100 = 75%. Same structure covers “what portion of my budget was rent” or “what share of sales came from one product.”

The reversal error to avoid

The single most common percentage mistake is assuming a percentage increase and the matching decrease cancel out. They don’t, because the base changes underneath you.

A 50% gain followed by a 50% loss does not return you to the start — it leaves you down 25%.

Watch it happen: start with $100, gain 50% → $150. Now lose 50% of that $150 → you drop $75, landing at $75. The increase was calculated on $100, but the decrease was calculated on $150, so the two never offset. To fully recover from a 50% loss you actually need a 100% gain to get back to even.

A quick reference

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