Percentage formula reference

Basic percentage formula (percent of a number)

Used when you know the percentage and the amount, and want to find the result.

Formula: result = (percent ÷ 100) × amount

Example: 20% of 150 = (20 ÷ 100) × 150 = 30.

This is the calculation the first tab of the percentage calculator runs, and the same three-step logic is explained more slowly, with extra practice problems, on the step-by-step guide.

Reverse percentage formula (what percent is X of Y)

Used when you know two amounts and want to find what percentage the first represents of the second.

Formula: percent = (part ÷ total) × 100

Example: 30 is what percent of 150? (30 ÷ 150) × 100 = 20%.

This is the calculation the second tab of the percentage calculator runs. It's the same formula used to turn a test score or a survey result into a percentage: divide the part by the whole, then multiply by 100.

Percentage increase/decrease formula (apply a % to a number)

Used when you know a starting number and want to find its new value after increasing or decreasing it by a given percentage.

Increase formula: new value = original + (original × percent ÷ 100)

Decrease formula: new value = original − (original × percent ÷ 100)

Example (increase): increase 100 by 15%, so 100 + (100 × 15 ÷ 100) = 100 + 15 = 115.

Example (decrease): decrease 100 by 15%, so 100 − (100 × 15 ÷ 100) = 100 − 15 = 85.

This is the calculation the third tab of the percentage calculator runs: pick Increase or Decrease and it applies the right formula for you, which is faster than plugging numbers into the expression above by hand.

Percentage change formula (from one value to another)

Used when you have two absolute values, an old one and a new one, and want the percentage by which the value changed. This is a different question from "increase/decrease by a %" above: here you don't already know the percentage, you're solving for it.

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

Example: a price went from $80 to $92. Percentage change = ((92 − 80) ÷ 80) × 100 = 15%, meaning a 15% increase.

A negative result means a decrease: if the price had instead gone from $80 to $68, the formula gives ((68 − 80) ÷ 80) × 100 = −15%, a 15% decrease. This formula is not currently one of the calculator's three tabs; if you use it often, the general-purpose percentage calculator above still handles the increase/decrease direction once you already know the percentage.

Percentage difference formula (comparing two values, no direction)

Different again from percentage change: percentage difference compares two values symmetrically, without treating either one as the "original". It's used when there's no natural before/after relationship between the two numbers, for example comparing two products' prices rather than tracking one price over time.

Formula: percentage difference = (|value 1 − value 2| ÷ ((value 1 + value 2) ÷ 2)) × 100

Example: comparing 40 and 60: |40 − 60| ÷ ((40 + 60) ÷ 2) × 100 = 20 ÷ 50 × 100 = 40%.

Percentage points vs. a percentage change

A formula-reference page is a good place to be precise about this distinction, since it trips up even careful writers. If a discount rate moves from 20% to 25%, that is a change of 5 percentage points. But expressed as a percentage change of the rate itself, it's a 25% increase (5 ÷ 20 × 100). Both statements are correct; they're just answering different questions. When you read a percentage figure in a news article or a report, check which one is being described: a raw point difference, or a percentage change relative to the starting value calculated with the formula above.

Which formula should I use?

A quick way to decide which formula applies to your situation:

• You know a percentage and an amount, and want the result: use the basic percentage formula.
• You know two amounts and want to know what percent one is of the other: use the reverse percentage formula.
• You know a starting number and a percentage to apply, and want the new value: use the percentage increase/decrease formula.
• You know an old value and a new value, and want the percentage by which it changed: use the percentage change formula.
• You're comparing two values with no clear "before" and "after": use the percentage difference formula.

Worked practice problems

Try matching each of these to the right formula above before checking the answer.

1. A store marks a $40 item down by 15%. What's the new price? This is the increase/decrease formula: 40 − (40 × 15 ÷ 100) = 40 − 6 = $34.

2. Rent went from $1,200 to $1,320. By what percentage did it increase? This is the percentage change formula: ((1320 − 1200) ÷ 1200) × 100 = 10%.

3. Two vendors quote $250 and $300 for the same job, with no "before" price to compare against. How different are the quotes, as a percentage? This is the percentage difference formula: |250 − 300| ÷ ((250 + 300) ÷ 2) × 100 = 50 ÷ 275 × 100 ≈ 18.2%.

If a problem doesn't clearly fit one of the five formulas above, it often helps to first write out, in plain words, exactly what you already know and exactly what you're solving for; that usually narrows it down to one row of the decision list. For a slower, example-heavy walkthrough of the basic and reverse formulas specifically, see the how to calculate a percentage guide. None of the numbers you work through on this page are sent anywhere; see the privacy policy for the full explanation.