Percent Error Calculator

Calculate the percentage error, absolute error, and relative error between an experimental/observed value and a known true accepted value.

Modify the values and click the Calculate button to use.

Percent Error Calculator

Sample Experiments:

Observed / Experimental Value (V_observed)

True / Accepted Theoretical Value (V_true)

Comprehensive Guide to Percent Error & Experimental Uncertainty

Percent error (or percentage error) is a mathematical metric used in physics, chemistry, engineering, and statistics to gauge the precision and accuracy of an experimental measurement against an established, accepted theoretical standard.

Absolute Error

The raw magnitude of the difference between measured and true values, ignoring sign.

|V_observed - V_true|

Relative Error

Compares the absolute error directly to the size of the true measurement.

|V_observed - V_true| / |V_true|

Percent Error

Expresses the relative error as a percentage out of 100%.

Relative Error × 100%

Common Sources of Experimental Error

Systematic Errors: Flaws in measurement equipment or procedural design (e.g. an uncalibrated digital scale or parallax viewing error).
Random Errors: Unpredictable environmental fluctuations (e.g. ambient temperature shifts, voltage flickers, or air currents).
Human Limitations: Reaction-time delays when using manual stopwatches or estimation errors when reading graduated cylinders.

Frequently Asked Questions

Can percent error be negative?

In standard scientific convention (such as high school and university chemistry/physics), percent error uses absolute value signs and is always positive. However, in engineering or calibration contexts, signed percent error is used to indicate whether a measurement overestimated (+) or underestimated (-) the true value.

What is considered an acceptable percent error in laboratory experiments?

Acceptable percent error depends on the field. In introductory student physics and chemistry labs, an error under 5% to 10% is generally considered excellent. In industrial manufacturing or pharmaceutical calibration, acceptable thresholds are often strict tolerances under 0.1% to 1%.

Why cannot the true value be zero?

Relative and percent error require dividing the absolute error by the true value. Division by zero is mathematically undefined.

What is the difference between percent error and percent difference?

Percent error compares an experimental measurement to a known accepted true value. Percent difference compares two experimental measurements with neither considered the standard, dividing by their average.