Percentage difference calculator, and percent change.

A percentage difference calculator tells you how far apart two numbers are, as a percent of their average. It is the right question when neither number is the starting point, such as two prices for the same item or two test scores. This page gives that answer and, beside it, the percent change from the first number to the second, because people often search for one and need the other. Both sums are written out, so you can check them.

How to use the calculator

1. Leave What to compare on Two numbers.
2. Type the First number and the Second number. Commas and spaces inside a number are ignored, so 1,200 works.
3. Read the large card for the percentage difference. The cards under it show the percent change both ways and each number as a percent of the other.
4. Press Swap the two numbers to reverse the order. The percentage difference stays the same and the percent change flips.
5. Choose Decimal places to round the answers, then Copy result or Copy link.

The percentage difference formula

Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100. The vertical bars mean the size of the gap, with the sign dropped, so the answer never depends on which number you call a and which you call b.

Worked example with 20 and 30. The gap is |20 − 30| = 10. The average is (20 + 30) ÷ 2 = 25. Then 10 ÷ 25 = 0.4, and times 100 is 40%. Swap them to 30 and 20 and you still get 40%.

The percent change formula

Percent change = (new − old) ÷ |old| × 100. The old number is the base. With 20 as the old number and 30 as the new one: (30 − 20) ÷ 20 = 0.5, so a 50% increase. Going back from 30 to 20: (20 − 30) ÷ 30 = −0.3333, so a 33.33% decrease. The same two numbers give 50% one way and 33.33% the other, because each is measured against a different starting point.

Which one should I use

Use percent change when one number came first and the other came later: this month against last month, a price before and after a sale, a score before and after a course. Use percentage difference when the two numbers have no order: the price of the same item in two shops, the weights of two parcels, two measurements of the same thing. If you are unsure, ask whether one number is the starting point.

Things that are good to know

• For two positive numbers the percentage difference is never more than 200%. It reaches 100% when one number is three times the other: 1 and 3 give a gap of 2 over an average of 2.
• If one number is 0, the percentage difference is 200% for any other number, and there is no percent change from 0, because you cannot divide by 0.
• With a negative number, this page averages the sizes of the two numbers and divides the change by the size of the first. That keeps the answer easy to read, though some textbooks treat negatives differently.
• Percentage points are a different thing. Going from 10% to 15% is 5 percentage points, or a 50% increase. For that, use the percentage calculator.

A list of numbers

Switch What to compare to A list of numbers and paste a column, one number on each line or separated by commas. The table shows each value against the one before it. Take 120, 135, 128, 150 and 162. The steps are +12.5%, −5.19%, +17.19% and +8%, and from the first to the last the change is +35%. The percentage difference between 120 and 162 is 29.79%. Copy table puts the rows on the clipboard, ready to paste into a sheet.

For a share of a total or a discount, try the discount calculator. For the spread of a list, use the average calculator.