What is percent error?

Percent error is a measure of how far an experimental or observed value is from a known true value, expressed as a percentage of the true value. It is commonly used in physics, chemistry, engineering and statistics to quantify measurement accuracy.

What is the formula for percent error?

The most common formula for percent error is: percent error = |E - T| / |T| × 100%, where E is the experimental (measured) value and T is the true (accepted) value. Many textbooks and labs define percent error using the absolute value so that the result is always non negative.

Can percent error be negative?

Percent error can be reported as signed or absolute. If you drop the absolute value and compute (E - T) / T × 100%, then negative percent error means the experimental value is lower than the true value, while positive percent error means it is higher. In formal reports, many instructors prefer absolute percent error.

What is a good percent error in experiments?

What counts as a good percent error depends on the context. In basic physics or chemistry labs, percent errors under about 5% are often considered acceptable, while precision instruments may require errors well under 1%. For rough estimates and real world measurements, larger percent errors may be acceptable if the result is still useful for decision making.

What is the difference between percent error and percent difference?

Percent error compares an experimental value to a true, accepted or reference value and divides by the true value. Percent difference compares two experimental values of the same quantity, often using the average of the two values in the denominator. They answer slightly different questions and should not be interchanged in lab reports.

Can percent error be greater than 100 percent?

Yes, percent error can be greater than 100 percent whenever the difference between the experimental and true value is larger than the true value itself. For example, if the true value is 10 and the measured value is 25, the percent error is |25 - 10| / 10 × 100% = 150%.

Percent Error Calculator – Calculate Percentage Error

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.

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.

Percent Error Calculator

Interactive percent error calculator

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