Percentage Calculator

// Which percentage calculation do you need?

For a tip or discount amount, choose Percent of a number: 15% of 80 is 12. A 15% discount takes 12 off the price, so you pay 68. The answer is the percentage amount, not the price after the discount.

For a score or share of a total, choose the What percent? calculation. Divide the part by the whole and multiply by 100: 12 out of 80 is 15%. A part can exceed the whole, so results above 100% are valid.

// Percentage change and percentage difference use different bases

Change compares an ending value with a starting value. From 80 to 92, the increase is 12. Divide 12 by the starting 80 and multiply by 100 to get a 15% increase. Reversing those values gives a 13.04% decrease because the starting value is now 92.

Difference treats the two values equally. Divide their absolute difference by their average, then multiply by 100. For 80 and 92, the average is 86, so the percentage difference is about 13.95%. Swapping the numbers leaves this answer unchanged.

A move from 10% to 15% is an increase of 5 percentage points and a relative increase of 50%. Percentage points are a subtraction of two percentages; percentage change divides that subtraction by the starting percentage.

// Zero, negative values, and rounding

Percent of and reverse percentage accept negative numbers. Reverse percentage cannot divide by a whole of zero. Percentage change here requires a positive starting value: a zero baseline is undefined, and a negative baseline can make the usual increase and decrease language misleading.

Percentage difference here compares nonnegative values. Comparing zero with a positive number gives 200%; two zeros are undefined because their average is zero. The calculator explains these cases instead of displaying Infinity or NaN. A previous answer stays labeled as the last valid result and cannot be copied with the copy button until the inputs are valid again.

The formula uses browser number precision. Displayed percentages round to two decimal places and amounts to six significant digits. Very small and large answers use scientific notation so a small nonzero value does not look like zero. The approximation sign beside the formula allows for that rounding.

// fair questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For example, 15 ÷ 100 × 80 = 12.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100. For example, 12 ÷ 80 × 100 = 15%. The whole must not be zero.

How do I calculate percentage increase or decrease?

Subtract the starting value from the ending value, divide by the starting value, and multiply by 100. With a positive starting value, a positive result is an increase and a negative result is a decrease.

What is the difference between percentage change and percentage difference?

Change uses the starting value as its denominator. Difference uses the average of two nonnegative values. Use change for before-and-after comparisons, and difference when neither number is the baseline.

How can I work out a percentage without a calculator?

Find 10% by dividing by ten. Halve that to get 5%, or double it to get 20%. For 15%, add the 10% and 5% amounts: 15% of 80 is 8 + 4 = 12.