Percentage Calculator — Percent of, Change & Difference

Common percentages of 80
Percent	Amount	What's left
5%	4	76
10%	8	72
15%	12	68
18%	14.4	65.6
20%	16	64
25%	20	60
30%	24	56
50%	40	40
75%	60	20

Common percentages of 80

Percent

Amount

What's left

10%

15%

18%

14.4

65.6

20%

25%

30%

50%

75%

The six percentage questions

Every percentage problem is one of a few shapes. The calculator puts all of them on one screen, each written as the question you would ask:

Question	Formula	Example
What is P% of X?	P ÷ 100 × X	15% of 80 = 12
X is what % of Y?	X ÷ Y × 100	12 of 48 = 25%
X is P% of what?	X ÷ (P ÷ 100)	30 is 20% of 150
Percent change from A to B	(B − A) ÷ A × 100	50 → 65 = +30%
Increase or decrease X by P%	X × (1 ± P ÷ 100)	80 − 20% = 64
Percent difference of A and B	\|A − B\| ÷ average × 100	40 and 60 = 40%

The percent sign simply means “hundredths”: NIST’s guide to units defines % as the number 0.01. So 15% is 0.15, 150% is 1.5, and 0.5% is 0.005.

How to calculate a percentage of a number

Multiply the number by the percent and divide by 100 — or, the same thing, multiply by the percent written as a decimal.

Example. A $64 dinner and an 18% tip: 0.18 × 64 = $11.52.

Mental shortcuts work because percentages scale:

10% — move the decimal point one place left: 10% of 64 is 6.4.
5% — half of 10%: 3.2.
20% — double 10%: 12.8.
15% — 10% plus 5%: 6.4 + 3.2 = 9.6.
1% — move the decimal point two places: 0.64.

The table next to the calculator lists the common percentages of the number in question 1, and what is left after taking each one off — handy for tips and discounts.

How to find what percent one number is of another

Divide the part by the whole, then multiply by 100.

Example. You answered 43 questions right out of 50: 43 ÷ 50 = 0.86 → 86%.

The order matters: 12 is 25% of 48, but 48 is 400% of 12. The whole — what you are comparing against — always goes on the bottom.

Percent change: increase and decrease

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

Example. Your electric bill went from $120 to $138: (138 − 120) ÷ 120 × 100 = +15%. Had it fallen to $102, the change would be (102 − 120) ÷ 120 × 100 = −15%.

Two things trip people up:

The starting value is the base. 50 → 65 is +30%, but 65 → 50 is −23.1%, because the same 15 is measured against a different number.
Changes do not cancel. A 10% raise followed by a 10% pay cut leaves you 1% below where you started (100 → 110 → 99). Two 50% drops leave a quarter, not nothing.

To apply a change rather than measure one, multiply by 1 plus or minus the percent: a $250 price raised 8% is 250 × 1.08 = $270; cut 30% it is 250 × 0.70 = $175.

Percent difference

When neither value is “the original” — two quotes, two measurements, two stores’ prices — use the percent difference, which divides the gap by the average of the two:

percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100

Example. Two contractors quote $4,000 and $6,000: the gap is $2,000 and the average is $5,000, so they differ by 40% — the same whichever you list first. As a percent change from the cheaper quote it would be +50%, and from the dearer one −33.3%.

Percent, decimal and fraction

Percent	Decimal	Fraction
1%	0.01	1/100
5%	0.05	1/20
10%	0.1	1/10
12.5%	0.125	1/8
20%	0.2	1/5
25%	0.25	1/4
33⅓%	0.333…	1/3
50%	0.5	1/2
75%	0.75	3/4
150%	1.5	3/2

To turn a percent into a decimal, divide by 100; to go back, multiply by 100. For working with the fractions themselves, the fraction calculator shows each step.

Percentages in everyday money

Discounts: “30% off” means you pay 70% of the price — question 5 with decrease. For several discounts in a row and sales tax on top, use the percent off calculator.
Tips: 18–20% of the bill is question 1; the tip calculator also splits it between people.
Raises and price increases: question 4 tells you how big a change really was.

For anything beyond percentages — roots, powers, logarithms — the scientific calculator is on the way.

Frequently asked questions

How do I calculate a percentage of a number?

Turn the percent into a decimal by dividing by 100, then multiply. 15% of 80 is 0.15 × 80 = 12; 7.5% of 240 is 0.075 × 240 = 18. To do it in your head, find 10% by moving the decimal point one place left, then scale: 15% is 10% plus half of 10%.

How do I work out what percent one number is of another?

Divide the part by the whole and multiply by 100. 12 out of 48 is 12 ÷ 48 = 0.25, which is 25%. A test score of 43 out of 50 is 43 ÷ 50 × 100 = 86%.

How do I calculate percent increase or decrease?

Subtract the old value from the new one, divide by the old value and multiply by 100. A rent that goes from $1,500 to $1,620 rose (1,620 − 1,500) ÷ 1,500 × 100 = 8%. A negative answer is a decrease.

Why doesn't a 10% increase followed by a 10% decrease get me back to where I started?

Because the second percentage is taken of a different number. 100 plus 10% is 110; 10% of 110 is 11, so taking it off leaves 99. To undo a 10% increase you need a decrease of 10 ÷ 110 ≈ 9.09%.

What is the difference between percent change and percent difference?

Percent change compares a new value with an original one, so the direction matters: 50 to 65 is +30%, but 65 to 50 is −23.1%. Percent difference compares two values on equal terms, dividing their gap by their average: 50 and 65 differ by 26.1% either way.

What is a percentage point?

The plain difference between two percentages. If a rate goes from 3% to 4%, it rose by 1 percentage point — but by 33.3 percent, because 1 is a third of 3. News reports and loan offers often use the two interchangeably, which can make a change look smaller or bigger than it is.