Percent Error Calculator
Calculate percent error from a theoretical and a measured value for your lab report. If you measured several times, get the mean, standard deviation and standard error too.
When repeated values are given, their mean is used instead of the measured value.
Formula
percent error = (|measured − theory|)/(|theory|) × 100. It helps to state whether the measurement came out high or low, which the signed relative error shows. The standard deviation of repeated values is the sample standard deviation (divided by n−1).
Worked example: percent error from real lab data
- Zener regulator output: theory (simulation) 5.592 V, measured 5.605 V → (|5.605 − 5.592|)/(5.592) × 100 = 0.23%
- The same circuit under a heavy load, zener current: theory 29.1 µA, measured 460 µA → 1,481% error
- When the theory is close to zero a percent error means nothing. Report the absolute error (430 µA) and the measurement uncertainty instead; the zener regulator guide goes through it.
How far part tolerances move the theory
| Source | How far the theory can move |
|---|---|
| SourceOne resistor (±1%) | How far the theory can move−1.0% ~ +1.0% |
| SourceOne resistor (±5%) | How far the theory can move−5.0% ~ +5.0% |
| SourceOne capacitor (±10%) | How far the theory can move−10.0% ~ +10.0% |
| SourceTime constant τ = RC (R ±5%, C ±10%) | How far the theory can move−14.5% ~ +15.5% |
| SourceCutoff (1)/(2πRC) (R ±5%, C ±10%) | How far the theory can move−13.4% ~ +17.0% |
| SourceDivider ratio of two equal resistors (±5% each) | How far the theory can move−5.0% ~ +5.0% |
Part tolerances alone can move the theory this far. A percent error inside this range can be put down to the parts; check the meter's own error with the multimeter accuracy calculator.
Using it in practice
Step by step
- Enter the theoretical (calculated or nominal) value and your measured value to get the percent error.
- If you repeated the measurement, paste all readings to get the mean, the standard deviation and the standard error of the mean.
- Report the mean with its spread, and compare the percent error with the tolerance of the parts and the meter.
Common mistakes
- Dropping the sign. A measured value below theory gives a negative error. The sign tells you which way the circuit is off, so keep it in your table even if the report asks for magnitude.
- Calling every difference an error. A 220 Ω resistor with 5% tolerance can legally measure 209 Ω to 231 Ω. A 3% "error" there is within spec, not a mistake.
- Confusing percent error with percent difference. Percent error compares against a reference value; percent difference compares two measurements against their average. Use the one your lab manual asks for.
Reading the spread
The standard deviation here uses n−1, the usual choice for a small set of readings. It describes how much single readings scatter; the standard error tells you how well the mean is known and shrinks as you take more readings. If the percent error is much larger than the scatter, the cause is systematic (a wrong assumption, meter loading, a different component value) rather than random noise, and taking more readings will not fix it.
Worked example: five readings of one resistor
A 4.7 kΩ resistor is measured five times: 4.68, 4.71, 4.69, 4.70 and 4.67 kΩ.
- Mean: 23.45 kΩ ÷ 5 = 4.690 kΩ.
- Sample standard deviation: the squared deviations add to 0.0010 kΩ², divided by n − 1 = 4 gives 0.00025, and its square root is 0.016 kΩ.
- Standard error of the mean: 0.016 kΩ divided by the square root of 5 is 0.007 kΩ.
- Percent error against 4.7 kΩ: −0.21%, far inside the part's 5% tolerance.
Paste the five values into the calculator to get the same numbers. The scatter (16 Ω) is close to the meter's own resolution, so the readings tell you more about the meter than about the resistor.
Writing the numbers into a results table
Give the mean with the spread you actually used and say which one it is, for example R = 4.690 ± 0.007 kΩ (mean ± standard error, n = 5). Round the spread to one or two figures and the mean to the same decimal place, as on the significant figures page. Keep the signed error in the table, because "−0.21%" says the resistor measured low, which a magnitude alone hides. When the meter's accuracy is larger than the scatter, quote the meter uncertainty instead, since repeating a reading cannot remove a calibration error.
Frequently asked questions
What is a good percent error in a lab?
It depends on the experiment and the instruments. In introductory circuit labs, results within a few percent are common because resistors are often ±5% and meters add their own error. Compare your percent error with the part tolerances and meter accuracy rather than a fixed number.
Should percent error be positive or negative?
Percent error is usually reported as a positive magnitude. The signed relative error, also shown here, tells you whether the measurement was higher (+) or lower (−) than theory, which is useful when explaining the cause.