About this calculator
Two numbers, two different questions. Percentage difference asks how far apart two values are when neither is the 'right' one. Percentage error asks how far a measurement is from a known, accepted value.
Enter both numbers and you get both answers. For percentage error, put your measured value first and the accepted value second.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
50 versus 40
- Percentage difference
- 22.222222%
- Percentage error (first vs second)
- 25%
- Absolute error
- 10
- Average of the two
- 45
50 and 40 differ by 10, which is a 22.222222% difference; 50 is 25% above 40.
Show the working
- Percentage difference = |a − b| ÷ average × 100 = 10 ÷ 45 × 100 = 22.222222%. It treats the two values equally.
- Percentage error = (measured − accepted) ÷ |accepted| × 100 = (50 − 40) ÷ 40 × 100 = 25%. Here the first value is the measured one and the second the accepted one.
Measured 9.6 against accepted 9.81
- Percentage difference
- 2.163833%
- Percentage error (first vs second)
- -2.140673%
- Absolute error
- 0.21
- Average of the two
- 9.705
9.6 and 9.81 differ by 0.21, which is a 2.163833% difference; 9.6 is 2.140673% below 9.81.
Show the working
- Percentage difference = |a − b| ÷ average × 100 = 0.21 ÷ 9.705 × 100 = 2.163833%. It treats the two values equally.
- Percentage error = (measured − accepted) ÷ |accepted| × 100 = (9.6 − 9.81) ÷ 9.81 × 100 = -2.140673%. Here the first value is the measured one and the second the accepted one.
Two prices: 120 and 150
- Percentage difference
- 22.222222%
- Percentage error (first vs second)
- -20%
- Absolute error
- 30
- Average of the two
- 135
120 and 150 differ by 30, which is a 22.222222% difference; 120 is 20% below 150.
Show the working
- Percentage difference = |a − b| ÷ average × 100 = 30 ÷ 135 × 100 = 22.222222%. It treats the two values equally.
- Percentage error = (measured − accepted) ÷ |accepted| × 100 = (120 − 150) ÷ 150 × 100 = -20%. Here the first value is the measured one and the second the accepted one.
The formulas
- Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100
- Percentage error = (measured − accepted) ÷ |accepted| × 100
- Percentage change uses the starting value instead: see the percentage change calculator
Which one should I use?
Use difference when comparing two similar things with no reference, such as two shops' prices. Use error in a lab, where one figure is the textbook value. Use change when something moved from an old value to a new one.
Why the answers differ
The difference divides by the average of the two numbers, so swapping them changes nothing. Error and change divide by one chosen number, so swapping them gives a different percentage. 50 versus 40 is 22.2% different, but 50 is 25% above 40 and 40 is only 20% below 50.
Frequently asked questions
What is the percentage difference between two numbers?
The gap between them divided by their average, times 100.
How do I calculate percentage error?
Subtract the accepted value from your measured value, divide by the accepted value, and multiply by 100.
Can percentage error be negative?
Yes. Negative means your measurement was below the accepted value. Some teachers ask for the absolute value.
Why is the percentage difference not the same as the change?
Different reference points. Difference uses the average, change uses the starting value.
What if one value is zero?
Percentage error against zero is undefined, so that row is hidden. The difference still works unless both values are zero.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.