Percentages come up everywhere — discounts, tax, grades, tips, growth rates — but "percentage math" is actually five or six distinct formulas that get mixed up constantly. Here's each one explained with real numbers, so you know exactly which formula fits the question you're actually asking.
X% of Y
The most basic case: what is 20% of 150? Convert the percentage to a decimal and multiply: 0.20 × 150 = 30. This is the formula behind tips, discounts, and commission calculations.
X is What Percent of Y
The reverse question: 30 is what percent of 150? Divide the part by the whole, then multiply by 100: (30 ÷ 150) × 100 = 20%. This is the formula for things like "what percentage of my paycheck goes to rent" or "what share of the vote did a candidate get."
Percentage Increase and Decrease
To find the percentage change between two values, subtract the original from the new value, divide by the original, then multiply by 100:
- Increase: (New − Old) ÷ Old × 100. Going from $100 to $130 is a 30% increase.
- Decrease: Same formula — the result is just negative. Going from $100 to $70 is a -30% change, i.e. a 30% decrease.
Reverse Percentage
If you know the new value and the percentage change, but need the original, don't just apply the inverse percentage — the base has shifted. To reverse an increase, divide by (1 + the decimal rate); to reverse a decrease, divide by (1 − the decimal rate).
Example: a jacket now costs $120 after a 20% increase. The original price is 120 ÷ 1.20 = $100 — not 120 × 0.80, which gives a different (wrong) number entirely.
Percentage Change vs. Percentage Difference
These sound like the same thing and aren't. Percentage change is directional and uses a fixed original value as its base — going from 50 to 75 is +50%, but going back from 75 to 50 is a different number, -33.3%, because the base changed. Percentage difference is used when there's no clear "original" value — comparing two prices from different stores, for instance — and typically uses the average of the two numbers as the base, giving a single, non-directional result.
Calculating It Instantly
Rather than tracking which formula applies to which question, our free Percentage Calculator covers all of these cases directly — X% of Y, X is what % of Y, percentage increase/decrease, reverse percentage, and percentage difference — with instant results.
FAQ
What's the difference between percentage change and percentage difference? Percentage change compares a new value to an original, fixed starting point — it's directional, so going from 50 to 75 is a +50% change, but going from 75 back to 50 is a -33.3% change, not -50%. Percentage difference compares two values to each other with no designated "original," typically using their average as the base, and is always expressed as a positive number.
How do I reverse a percentage increase to find the original price? Divide the new value by (1 + the percentage as a decimal), not by (1 - the percentage). For example, if a price rose 20% to $120, the original was 120 / 1.20 = $100 — dividing by 0.80 instead would give the wrong answer, since that formula is for reversing a decrease, not an increase.
Why don't two percentages of the same thing simply add together? Because each percentage after the first is applied to a new base value, not the original one. A 10% increase followed by a 10% decrease doesn't return you to the start — $100 up 10% is $110, then down 10% is $99, not $100 — because the second 10% was calculated from $110, not $100.
What does "percentage points" mean, and how is it different from percent? A percentage point is the raw arithmetic difference between two percentages, while "percent" describes a relative change. If an interest rate moves from 5% to 7%, that's a 2 percentage point increase, but a 40% relative increase (2 is 40% of 5) — both descriptions are correct, they're just answering different questions.