Percent Error Calculator
Calculate percent error between an experimental and a true value. Free percent error calculator showing the absolute error, signed difference and the full formula.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Percent Error Calculator Works
Enter your experimental (measured) value and the theoretical (true) value, and this calculator returns the percent error, the absolute error, and a signed percent difference that tells you whether you over- or under-estimated. It is the standard tool for chemistry, physics and lab reports.
The Formula
Percent error = |experimental − theoretical| ÷ |theoretical| × 100
The numerator is the absolute error — how far your measurement is from the true value, ignoring sign. Dividing by the absolute value of the theoretical value scales that gap relative to the quantity being measured, and multiplying by 100 expresses it as a percentage.
Worked Example
Suppose you measure the acceleration due to gravity as 9.7 m/s², and the accepted value is 9.8 m/s²:
- Absolute error = |9.7 − 9.8| = 0.1 m/s²
- Percent error = (0.1 ÷ 9.8) × 100 = ≈ 1.02%
- Signed difference = (9.7 − 9.8) ÷ 9.8 × 100 = −1.02% (an underestimate)
A percent error of about 1% is excellent for a classroom gravity experiment.
Reading the Results
| Quantity | Meaning |
|---|---|
| Percent error | Always positive — how far off you are, as a % of the true value |
| Absolute error | The raw difference in the original units |
| Signed % difference | Positive = overestimate, negative = underestimate |
Why Percent Error Matters
Percent error is the go-to measure of accuracy in experimental science. By scaling the raw error to the size of the quantity, it lets you compare results across very different measurements — a 0.1 unit miss matters far more for a small value than a large one. Pair it with repeated trials and a measure of precision such as standard deviation to fully characterise the quality of your data.
Frequently asked questions
How do I calculate percent error?+
Subtract the theoretical (true) value from your experimental (measured) value, take the absolute value of that difference, divide by the absolute value of the theoretical value, then multiply by 100. In symbols: percent error = |experimental − theoretical| ÷ |theoretical| × 100. The result is always reported as a positive percentage.
What is the difference between percent error and percent difference?+
Percent error compares a measured value to a known, accepted true value, so it tells you how close your measurement is to reality. Percent difference compares two measured values when neither is the accepted standard, and divides by their average. Use percent error in labs where a textbook or accepted value exists.
Can percent error be negative?+
The standard percent error uses absolute values, so it is always zero or positive. A signed version — sometimes called relative or fractional error — keeps the sign to show whether you overestimated (positive) or underestimated (negative) the true value. This calculator reports both.
What is a good percent error?+
It depends on the experiment. In a typical high-school or introductory chemistry lab, a percent error under about 5% is usually considered good, and under 10% is acceptable. Precision instruments and physics experiments may demand errors well below 1%. Always compare your result to the tolerance your assignment or method specifies.
Why can't the theoretical value be zero?+
Percent error divides by the theoretical value, and dividing by zero is undefined. If the accepted value is genuinely zero, percent error has no meaning; instead report the absolute error, or compare results using a different metric such as the absolute difference.