Percentage Calculator: Percent of a Number, Share and Change

"Percent" means per hundred, so a percentage is a ratio with 100 in the denominator. Nearly every percentage problem is one of three questions: what is P% of a number, what percent is one number of another, or what whole does a part and a percent imply. This guide works through each, then percentage change, and says which calculator does what. The Percentage Calculator answers the first question: enter a percentage and a number and it returns that percent of the number.

The Percent Relationship

The relationship behind all three problems is amount ÷ base = percent ÷ 100. The base is the whole, the amount is the part, and the percent is the part expressed per hundred. If 25 of 100 students passed, the pass rate is 25 ÷ 100 × 100 = 25%.

To use a percentage in arithmetic, convert it to a decimal by dividing by 100: 25% is 0.25, 7.5% is 0.075 and 150% is 1.5.

Problem 1: A Percent of a Number

Multiply the base by the decimal form of the percent.

15% of $200: 200 × 0.15 = $30
A 20% tip on an $85 bill: 85 × 0.20 = $17
7.5% sales tax on $240: 240 × 0.075 = $18

This is what the Percentage Calculator computes. For a price after an increase or decrease, fold the percent into one multiplier: a 15% rise on $120 is 120 × 1.15 = $138, and 30% off $120 is 120 × 0.70 = $84.

Problem 2: What Percent One Number Is of Another

Divide the part by the whole and multiply by 100.

$30 of $200: 30 ÷ 200 × 100 = 15%
45 of 180: 45 ÷ 180 × 100 = 25%
A company with $2 million of revenue and $1.6 million of costs keeps (2.0 − 1.6) ÷ 2.0 × 100 = 20% as profit margin.

The order matters: the whole goes in the denominator. 180 ÷ 45 would give 400%, which answers a different question.

Problem 3: Finding the Whole

Divide the part by the decimal form of the percent.

If $30 is 15% of a total, the total is 30 ÷ 0.15 = $200.
If 75 is 30% of a group, the group is 75 ÷ 0.30 = 250.

This is the problem behind "backing out" tax from a receipt total or working out a full price from a sale price and a discount.

Percentage Change

Percentage change compares a new value with an old one relative to the old value:

Percentage change = (new − old) ÷ old × 100

A stock that rises from $50 to $65 changed by (65 − 50) ÷ 50 × 100 = +30%; if it later falls to $45, the change from the original $50 is (45 − 50) ÷ 50 × 100 = −10%. The percentage change calculator takes the old and new values and returns the signed result.

Two things to keep straight. First, percentage points and percentage change are different: an interest rate moving from 2% to 3% is a rise of 1 percentage point but a 50% relative increase. Second, percentages don't cancel: a 100% markup from a $30 cost gives a $60 price, and a "50% off" sale on that price brings it straight back to $30.

A Few Everyday Cases

Credit card interest. A $5,000 balance at 18% APR accrues about 5,000 × 0.18 ÷ 12 = $75 of interest in a month.
Discounts. 25% off $64 is 64 × 0.25 = $16 off, so the price is $48; or go straight there with 64 × 0.75.
Scores. 42 correct out of 56 is 42 ÷ 56 × 100 = 75%.