About

In experimental sciences, quantifying the deviation between an observed measurement and a theoretical constant is fundamental. This tool computes the accuracy of experimental data by comparing it against an accepted standard. Whether validating a titration in chemistry or measuring gravitational acceleration in physics, understanding the magnitude of error helps determine the validity of a method. A low relative error indicates high accuracy, while high error suggests systematic or random issues in the experimental setup.

Formulas

The calculation of experimental error involves three distinct metrics:

Absolute Error: The magnitude of the difference.

E_abs = | x_meas − x_true |

Relative Error: The error normalized by the true value.

E_rel = | x_meas − x_true || x_true |

Percent Error: Relative error expressed as a percentage.

%Error = E_rel × 100%

Reference Data

Measurement Context	Accepted Value x_t	Unit	Common Precision
Speed of Light in Vacuum	299,792,458	m/s	Exact
Gravitational Acceleration	9.80665	m/s²	5 sig figs
Avogadro Constant	6.022 × 10²³	mol^-1	4 sig figs
Gas Constant (R)	8.314	J/(mol⋅K)	4 sig figs
Planck Constant (h)	6.626 × 10^-34	J⋅s	4 sig figs
Elementary Charge (e)	1.602 × 10^-19	C	4 sig figs
Density of Water (4°C)	1000	kg/m³	Integer
Atmospheric Pressure	101,325	Pa	6 sig figs

Frequently Asked Questions

The absolute value ensures the error is positive. In error analysis, we are typically concerned with the magnitude of the deviation, not whether the measured value was higher or lower than the true value.

Enter values using the standard "e" format. For example, to input Avogadro's number, type 6.022e23. To input the mass of an electron, type 9.109e-31. The calculator parses these automatically.

If the true value is exactly zero, relative error and percent error are undefined because division by zero is mathematically impossible. In such cases, one must rely solely on Absolute Error or use a different reference standard.

Yes. Generally, the error should be reported to the same decimal place as the measurement (for absolute error) or to the number of significant figures dictated by the least precise input (for relative error). This tool attempts to match precision based on input length.