CalcRover

Percentage Calculator

The three everyday percentage problems, each as its own mini-calculator: what is X% of a number, what percent one number is of another, and the percentage change between two values. Every answer shows its steps.

What is X% of Y?

% of=

X is what percent of Y?

isof

Percentage change from A to B

fromto=

The three percentage formulas

"Percent" means "per hundred", so every percentage problem is a multiplication or division by a factor of 100:

The classic mistake is mixing up percentage change with percentage points: going from 10% to 15% is a rise of 5 percentage points, but a 50% increase. Another: a 50% drop needs a 100% rise to get back — percent changes aren't symmetric because the base changes.

X% of Y = Y × X ÷ 100
X as a percent of Y = X ÷ Y × 100
change from A to B = (B − A) ÷ A × 100

Worked examples

Example 1: discount price

A $150 jacket is 20% off. What do you pay?

  1. Find 20% of 150.
    150 × 0.20 = 30
  2. Subtract the discount.
    150 − 30 = 120
  3. Shortcut: paying 80% directly.
    150 × 0.80 = 120

You pay $120 (the discount is $30).

Example 2: test score as a percent

You scored 45 out of 60 on a test. What percent is that?

  1. Divide the part by the whole.
    45 ÷ 60 = 0.75
  2. Multiply by 100.
    0.75 × 100 = 75%

75% — a C in most US grading scales.

Example 3: price increase

Rent went from $1,400 to $1,575. What's the percentage increase?

  1. Find the change.
    1,575 − 1,400 = 175
  2. Divide by the ORIGINAL value and convert to percent.
    175 ÷ 1,400 × 100 = 12.5%

A 12.5% increase. (Dividing by the new value would wrongly give 11.1%.)

FAQ

How do I calculate a percentage without a calculator?+

Build from 10%: move the decimal point one place left. For 35% of 80: 10% is 8, so 30% is 24, and 5% (half of 10%) is 4 — total 28. For 1%, move the decimal two places.

What's the difference between percent and percentage points?+

Points compare two percentages by subtraction; percent change compares them by division. An interest rate going from 4% to 6% rises 2 percentage points, which is a 50% increase.

Why is the percentage change different depending on direction?+

Because the base changes. From 100 to 150 is +50%, but from 150 back to 100 is −33.3%. Always divide by the starting value of that particular change.

Can a percentage be over 100?+

Yes. 250% of 40 is 100, and a price that triples has risen 200%. Over-100 percentages only break things that are shares of a whole — you can't score 110% of the available points.

What is reverse percentage — finding the original price?+

If a price after a 20% discount is $120, the original wasn't $120 + 20%. The sale price is 80% of the original, so divide: 120 ÷ 0.80 = $150.

Related calculators