Percent Error Calculator
Percent error calculator to compare experimental vs true values. Compute percent error, absolute and relative error, or solve for experimental and true values.
Full original guide (expanded)
Percent Error Calculator
Compute percent error between an experimental value and a true value, or solve for the experimental or true value from a given percent error. The tool also reports absolute and relative error and shows the full working.
Interactive percent error calculator
This calculator accepts plain numbers or scientific notation (e.g. 1.23e-4).
Units cancel out in the percent error calculation, so you can use any consistent unit system.
Percent error: definition and intuition
Percent error quantifies how far an experimental or observed value is from a true or accepted value, expressed as a percentage of the true value. It is a dimensionless measure used in physics, chemistry, engineering and statistics to assess the quality of measurements and to compare different measurement methods.
A small percent error means your measurement is close to the reference value; a large percent error signals either experimental issues (systematic error, poor calibration, instrument limits) or that the underlying model or assumption may not be appropriate.
Formulas used in this calculator
Absolute percent error (most common)
\[ \text{percent error} = \frac{\left|E - T\right|}{\left|T\right|} \times 100\% \]
where:
- \(E\) = experimental, observed or measured value
- \(T\) = true, accepted, reference or theoretical value
Signed percent error (optional)
\[ \text{percent error}_{\text{signed}} = \frac{E - T}{T} \times 100\% \]
A positive value means the experimental result is higher than the true value; a negative value means it is lower. Many lab manuals, however, still prefer the absolute version for reporting.
Absolute and relative error
\[ \text{absolute error} = \left|E - T\right| \]
\[ \text{relative error} = \frac{\left|E - T\right|}{\left|T\right|} \]
Solving for the experimental value from percent error
Starting from the absolute percent error formula and solving for \(E\) gives two solutions:
\[ E = T \left(1 \pm \frac{P}{100}\right) \]
where \(P\) is the percent error (in percent, not in fractional form). One solution corresponds to \(E\) above \(T\), the other to \(E\) below \(T\).
Solving for the true value from percent error
Similarly, solving for \(T\) when the experimental value \(E\) and percent error \(P\) are known gives:
\[ T = \frac{E}{1 \pm \frac{P}{100}} \]
Again, there are two possible values of \(T\) that produce the same percent error with a fixed \(E\). In real experiments, the physical context usually tells you which one is meaningful.
Worked example
Suppose you measure the density of a material and obtain an experimental value of \(E = 56.891\ \text{g/cm}^3\), while the reference table gives a true value of \(T = 62.327\ \text{g/cm}^3\).
- Compute the absolute error: \[ \left|E - T\right| = \left|56.891 - 62.327\right| = 5.436 \]
- Compute the relative error: \[ \frac{\left|E - T\right|}{\left|T\right|} = \frac{5.436}{62.327} \approx 0.08722 \]
- Convert to a percentage: \[ \text{percent error} = 0.08722 \times 100\% \approx 8.72\% \]
The measurement has a percent error of about \(8.7\%\) relative to the reference density.
Good practice for reporting percent error
- State clearly whether you are using absolute or signed percent error.
- Use a number of significant figures that matches the precision of your measurement and of the reference value. Rounding to two or three significant figures in the percent error is often reasonable.
- Discuss possible sources of error: instrument resolution, calibration, environmental conditions, assumptions in the model, and human factors (reading errors, timing, etc.).
- Compare percent errors across different methods or instruments only when they are measuring the same quantity under comparable conditions.
Related tools
For deeper analysis of experimental data, you may also find these calculators useful:
Percent error FAQ
Is percent error the same as measurement uncertainty?
No. Percent error compares a single result to a reference value. Measurement uncertainty describes the distribution of possible values around a result, often based on repeated trials and instrument specifications. You can have a small percent error but still a relatively large uncertainty, or vice versa.
What if the true value is not known?
If no accepted reference value exists, percent error is not defined in the strict sense. In this case you typically use standard deviation, confidence intervals, or percent difference between repeated measurements or between different methods.
Formula (LaTeX) + variables + units
\text{percent error} = \frac{\left|E - T\right|}{\left|T\right|} \times 100\%
\text{percent error}_{\text{signed}} = \frac{E - T}{T} \times 100\%
\text{absolute error} = \left|E - T\right|
\text{relative error} = \frac{\left|E - T\right|}{\left|T\right|}
E = T \left(1 \pm \frac{P}{100}\right)
T = \frac{E}{1 \pm \frac{P}{100}}
Absolute percent error (most common) \[ \text{percent error} = \frac{\left|E - T\right|}{\left|T\right|} \times 100\% \] where: \(E\) = experimental, observed or measured value \(T\) = true, accepted, reference or theoretical value
Signed percent error (optional) \[ \text{percent error}_{\text{signed}} = \frac{E - T}{T} \times 100\% \] A positive value means the experimental result is higher than the true value; a negative value means it is lower. Many lab manuals, however, still prefer the absolute version for reporting.
Absolute and relative error \[ \text{absolute error} = \left|E - T\right| \] \[ \text{relative error} = \frac{\left|E - T\right|}{\left|T\right|} \]
\[ E = T \left(1 \pm \frac{P}{100}\right) \] where \(P\) is the percent error (in percent, not in fractional form). One solution corresponds to \(E\) above \(T\), the other to \(E\) below \(T\).
- No variables provided in audit spec.
- Percentage Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/percentage-calculator - Standard Deviation Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/standard-deviation - Statistics Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/statistics - One-way ANOVA Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/one-way-anova
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.