Why can't I divide by zero?

A share of zero, or a change starting from zero, has no defined percentage. The calculator tells you instead of showing a misleading number.

Is a 50% rise then a 50% fall back to the start?

No. 100 → 150 → 75. Each percentage applies to a different base.

How do I find the original number from a percentage?

Divide the part by the percentage as a decimal. If 30 is 20% of a number, the number is 30 ÷ 0.20 = 150.

What is the difference between percent and percentage points?

Percentage points are the plain difference between two percentages. Percent change compares that difference to the starting percentage.

Can a percentage be more than 100?

Yes. If a value more than doubles, the increase is over 100%; going from 50 to 150 is a 200% increase.

Math

Percentage Calculator

Three everyday percentage questions in one place: how much is X% of a number, what share one number is of another, and how much something went up or down.

Pick the type of question.
Enter the two numbers.
Read the answer and the worked formula underneath.

Percentage (%)

Of number

Enter values to see the result.

How it works

A percentage is simply a number out of 100. The calculator turns every question into a fraction of 100 and then shows the arithmetic it used, so you can check the answer by hand. For “X% of Y” it divides X by 100 and multiplies by Y. For “A is what percent of B” it divides A by B and multiplies the result by 100.

For percentage change it subtracts the old value from the new value and divides by the size of the old value. Using the absolute value of the starting number means a move from −50 to −25 is correctly reported as a rise. If the starting value is zero, there is no meaningful percentage, so the calculator explains that rather than printing infinity.

Everything is worked out in your browser as you type, so you can change either number and watch the answer update instantly.

Formula

X% of Y = (X ÷ 100) × Y

A as % of B = (A ÷ B) × 100

Change % = (New − Old) ÷ |Old| × 100

Worked examples

A price rises from 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase.

Tip on a meal

15% of 64 = (15 ÷ 100) × 64 = 9.60. A 15% tip on a 64 bill is 9.60.

Exam score

You scored 42 out of 60. (42 ÷ 60) × 100 = 70%, so your mark is 70%.

Rent increase

Rent goes from 1,200 to 1,290. (1,290 − 1,200) ÷ 1,200 × 100 = 7.5% increase.

Understanding the result

A positive change is an increase and a negative change is a decrease. Percentage change is always measured against the original (old) value, so going 80 → 100 is +25%, while 100 → 80 is −20%.

Common mistakes

Measuring change against the new value instead of the original. 80 → 100 is +25%, not +20%.
Adding percentages that apply to different bases, such as a 10% rise followed by a 10% fall, and expecting to end where you started.
Confusing percentage points with percent. An interest rate moving from 4% to 5% is a 1 percentage point rise but a 25% increase.
Forgetting to convert the percent to a decimal before multiplying — 8% is 0.08, not 8.

When to use it

Working out tips, commissions, and service charges.
Comparing prices, salaries, or bills from one year to the next.
Turning test scores or survey results into percentages.
Checking a percentage someone quoted to you in an advert or report.

FAQs

Why can't I divide by zero?: A share of zero, or a change starting from zero, has no defined percentage. The calculator tells you instead of showing a misleading number.
Is a 50% rise then a 50% fall back to the start?: No. 100 → 150 → 75. Each percentage applies to a different base.
How do I find the original number from a percentage?: Divide the part by the percentage as a decimal. If 30 is 20% of a number, the number is 30 ÷ 0.20 = 150.
What is the difference between percent and percentage points?: Percentage points are the plain difference between two percentages. Percent change compares that difference to the starting percentage.
Can a percentage be more than 100?: Yes. If a value more than doubles, the increase is over 100%; going from 50 to 150 is a 200% increase.