Percentage Calculator

A percentage is a way of writing a number as a fraction of 100. This percentage calculator answers three common questions: what is X% of a number, what percent one number is of another, and the percent change between two values.

What is a percentage?

The word percent means "per hundred". Writing 25% is the same as writing the fraction 25/100, or the decimal 0.25. Percentages make numbers of different sizes easy to compare. Saying that 45 out of 60 questions were correct and that 30 out of 40 were correct is hard to compare directly. Saying 75% in both cases makes it clear the scores are equal.

The calculator has three modes. Each mode answers a different question, so each uses a different formula.

How to calculate a percentage of a number

This mode answers the question "what is X% of Y?". It converts the percentage to a fraction of 100 and multiplies:

$P = \frac{X}{100} \times Y$

where P is the part, X the percentage and Y the value the percentage is taken from.

Worked example

What is 25% of 200?

1. Divide the percentage by 100: 25 / 100 = 0.25
2. Multiply by the value: 0.25 × 200 = 50

So 25% of 200 is 50.

The same steps work for everyday amounts. A 15% tip on a 48.00 bill is (15 / 100) × 48 = 7.20. A 20% discount on a 60.00 item takes off (20 / 100) × 60 = 12.00.

How to find what percent one number is of another

This mode answers the question "X is what percent of Y?". It divides the part by the whole and scales the result to 100:

$Q = \frac{X}{Y} \times 100$

where Q is the resulting percentage, X the part and Y the whole.

The whole (Y) cannot be zero, because dividing by zero is undefined. The calculator shows an error message instead of a result in that case.

Worked example

30 is what percent of 120?

1. Divide the part by the whole: 30 / 120 = 0.25
2. Multiply by 100: 0.25 × 100 = 25

So 30 is 25% of 120. In the same way, a test score of 45 out of 60 is (45 / 60) × 100 = 75%.

How to calculate percent change

This mode answers the question "by what percent did a value change from A to B?". It compares the difference to the size of the starting value:

$C = \frac{B - A}{|A|} \times 100$

where C is the percent change, A the starting value and B the ending value. The bars around A mean its absolute value, which is A without its minus sign.

The starting value (A) cannot be zero, because there is no starting amount to compare against. A positive result is an increase, a negative result is a decrease, and zero means no change. The calculator labels the direction next to the number.

Worked example

A price rises from 80 to 100. What is the percent change?

1. Find the difference: 100 − 80 = 20
2. Divide by the starting value: 20 / 80 = 0.25
3. Multiply by 100: 0.25 × 100 = 25

The price increased by 25%. A drop from 50 to 40 works the same way: (40 − 50) / 50 × 100 = −20%, a 20% decrease.

Why the formula uses the absolute value

Dividing by the absolute value of A keeps the sign of the result meaningful when the starting value is negative. A change from −10 to −5 is a gain of 5. With that absolute value in the denominator, the result is ((−5) − (−10)) / 10 × 100 = +50%, an increase. Dividing by −10 instead would flip the sign and wrongly report a decrease.

Percent change is not symmetric

The direction of the change matters. Going from 80 to 100 is a 25% increase, but going from 100 to 80 is only a 20% decrease. The two results differ because each one is measured against a different starting value.

Rounding and display

Results are shown with up to six decimal places. Results smaller than 1 keep six significant digits, so a value like 0.0000001 is not rounded away to zero. Very large results (at or above 10^15) and very small ones (below 10^-9) are shown in scientific notation with six significant digits. A result displays as 0 only when it is exactly zero.

Frequently asked questions

How do I calculate a percentage of a number by hand?

Divide the percentage by 100, then multiply by the number. For 30% of 250: 30 / 100 = 0.3, and 0.3 × 250 = 75.

Can a percentage be more than 100?

Yes. 150% of 40 is (150 / 100) × 40 = 60. A percent change can also exceed 100: going from 50 to 120 is a ((120 − 50) / 50) × 100 = 140% increase.

Why does the calculator refuse a whole or starting value of zero?

Both formulas divide by that value, and division by zero is undefined. "X is what percent of 0" and "percent change from 0" have no numeric answer, so the calculator shows an error instead.

What is the difference between a percent change and percentage points?

Percentage points measure a simple difference between two percentages. Percent change measures that difference relative to the starting value. If an interest rate moves from 4% to 5%, it rises by 1 percentage point, but the percent change is ((5 − 4) / 4) × 100 = 25%.

Why is a 25% increase not undone by a 25% decrease?

Each step is measured against its own starting value. Raising 80 by 25% gives 100. Lowering 100 by 25% gives 75, not 80, because the second 25% is taken from the larger number.