Percent error calculator
Compare experimental and theoretical values and measure the size of the miss as a percentage.
What this calculator covers
Use this percent error calculator when you need to compare a measured result against a reference value and express the miss on a common percentage scale.
The steps separate the signed difference from the absolute difference, which makes it easier to see why percent error ignores direction before the final percentage is computed.
Frequently asked questions
- What is percent error used for?
- Percent error is used in science and engineering to express how close a measured or experimental result is to an accepted reference value. It puts the miss on a percentage scale so results from different experiments can be compared even when the underlying magnitudes differ.
- Why does the formula use absolute value?
- Percent error measures the size of the deviation, not its direction. Using the absolute value means an experimental result that is too high and one that is too low by the same amount produce the same percent error, making it a magnitude-only measure.
- What is the difference between percent error and percent difference?
- Percent error compares a measured value against a known theoretical or accepted reference. Percent difference compares two measured values when neither is considered the definitive reference, using their average as the denominator instead of one fixed benchmark.
- Can the theoretical value be zero?
- No. Because the theoretical value appears in the denominator, a zero reference makes the calculation undefined. If your reference value is zero, a different error metric that does not divide by the reference is needed.
Tool
Run the calculation
Result
RESULT · PERCENT ERROR
â„–116
Primary result
5.00%
Comparing experimental value 9.5 against theoretical value 10 gives a percent error of 5%.
- Signed difference
- -0.5
- Absolute difference
- 0.5
- Percent error
- 5%
Step-by-step solution
- 1.Subtract theoretical from experimental to get the signed difference -0.5.
- 2.Take the absolute value so the error becomes 0.5.
- 3.Divide by |theoretical| and multiply by 100 to get 5%.
Walkthrough
Visual walkthrough
Percent error measures how large the miss is relative to the theoretical target, ignoring direction.
01
Find the measurement gap
9.5 - 10 = -0.5
The raw difference says whether the experimental result landed above or below the theoretical benchmark.
02
Ignore the direction
|difference| = 0.5
Percent error focuses on size of the miss, so the sign is removed.
03
Scale by the theoretical value
|experimental - theoretical| / |theoretical| x 100
Dividing by the theoretical magnitude makes the error comparable across different scales.
5%