Solve the three most common percentage questions in one place: finding X% of Y, figuring out what percent X is of Y, or calculating the percent change (increase or decrease) between two numbers. Switch modes to match the question you're trying to answer.
20% of 150 = (20/100) × 150 = 30.
Nearly all everyday percentage questions fall into one of three categories: finding a percentage of a number, finding what percentage one number is of another, and finding the percent change between two numbers. Each uses a slightly different rearrangement of the same basic relationship.
Example: 20% of 150 = (20/100) × 150 = 30.
Example: 30 is what percent of 150? (30/150) × 100 = 20%.
Example: a price rising from $80 to $92 is a change of ((92−80)/80) × 100 = 15% increase. A negative result indicates a percentage decrease.
| Question type | Formula | Example |
|---|---|---|
| X% of Y | (X/100) × Y | 20% of 150 = 30 |
| X is what % of Y | (X/Y) × 100 | 30 of 150 = 20% |
| % change Old→New | ((New−Old)/Old) × 100 | 80→92 = +15% |
Example — Tip calculation: An 18% tip on a $64 bill is (18/100) × 64 = $11.52, for a total of $75.52.
Example — Reverse discount: If a $45 item is on sale after a 25% discount, the original price was 45 ÷ (1 − 0.25) = $60.
Example — Percentage-point vs. percent example: An interest rate rising from 4% to 6% is a 2 percentage-point increase, but a 50% relative (percent) increase — (6−4)/4 × 100 = 50%.
Why isn't a 20% increase followed by a 20% decrease back to the original number? Because the decrease is calculated on the new, larger amount, not the original — so the final value ends up lower than where you started.
What's the difference between percent and percentage points? Percentage points measure the raw difference between two percentages, while percent describes a relative change — they diverge whenever the starting percentage isn't small.
How do I calculate a percentage discount? Multiply the original price by the discount percentage to find the amount saved, then subtract that from the original price for the final cost.
How do I find the original price before a discount was applied? Divide the discounted (sale) price by (1 − discount rate as a decimal); this reverses the standard discount calculation.
How do I calculate percentage increase for a raise or price hike? Use the percent change formula: subtract the old value from the new value, divide by the old value, then multiply by 100.
Why do some statistics report both "percent" and "percentage point" changes? Because they answer different questions — percent shows the relative size of the change, while percentage points show the raw gap, and reporting both avoids ambiguity, especially for rates like interest or unemployment.
How is percentage used to calculate a tip or sales commission? Both use the basic X% of Y formula — multiply the bill or sale amount by the tip or commission rate (as a decimal) to find the amount owed.
If a value grows from 80 to 100, the percent change is (100−80)/80 × 100 = 25% — note the denominator uses the original (starting) value, not the new one, which is a common point of confusion.
Percent change: The relative difference between an old and new value, expressed as a percentage of the old value.
Percentage point: A unit representing an absolute difference between two percentages, distinct from a percent change.