Percentage Error Calculator

What this tool does

Percentage Error Calculator finds |experimental − theoretical| ÷ |theoretical| × 100, the standard way to express how far a measured or experimental result lies from an accepted reference value, and also shows the plain absolute error and the symmetric percentage difference for comparison.

Lab reports and measurement exercises regularly ask for the percentage error between what you actually measured and the accepted or theoretical value, a way of expressing how far off a result is relative to the value it is being compared against. It is easy to confuse this with the related but different percentage difference calculation, which has no designated reference value.

This calculator applies the standard percentage error formula, the absolute difference between the experimental and theoretical values divided by the absolute theoretical value, times 100, which deliberately treats the theoretical value as the fixed reference point. It also shows the plain absolute error for reference and the symmetric percentage difference, which instead divides by the average of both values and makes no assumption about which one is the "correct" reference, so you can see how the two related calculations diverge.

How to use Percentage Error Calculator

1. Enter your Experimental / measured value.
2. Enter the Theoretical / accepted value you are comparing it against.
3. Read the Percentage error, which treats the theoretical value as the reference.
4. Check the Absolute error and Signed error for the raw difference, with its direction.
5. Compare against the Percentage difference, which is symmetric and uses the average of both values instead.

Tips for better results

• Percentage error is specifically for comparing against a known, accepted reference value; if neither value is more "correct" than the other, percentage difference is the more appropriate calculation.
• A positive signed error means the experimental value was higher than theoretical; a negative signed error means it was lower, which is useful context the plain percentage figure loses.
• Very small theoretical values can produce a surprisingly large percentage error even from a small absolute difference, since the formula divides by the theoretical value’s magnitude.
• Report both the absolute error and the percentage error in a lab write-up where possible, since the percentage alone can hide whether the actual magnitude of the discrepancy was practically significant.

Common use cases

• Reporting how close a measured experimental result came to a known theoretical or textbook value in a lab report.
• Checking the accuracy of a calculation, simulation or estimate against a known correct answer.
• Comparing manufacturing tolerances between a measured part dimension and its specified target value.
• Understanding the distinction between percentage error and percentage difference when writing up results.

Common mistakes to avoid

• Dividing by the experimental value instead of the theoretical value; the standard percentage error formula specifically uses the theoretical value as the denominator because it is treated as the fixed reference.
• Using percentage error when comparing two measured values where neither is a known accepted reference; percentage difference is the correct symmetric calculation in that case.
• Reporting only the percentage figure without the sign or absolute magnitude, which can obscure whether the result was too high or too low and how large the discrepancy actually was.