Calculate constant error, absolute error, and variable error from target and observed values, including 2D bias and radial error metrics.

Use the same units for targets and observations. Variable error measures spread, not accuracy relative to the target.

Separate numbers with commas, spaces, newlines or semicolons. Commas are separators, never thousands marks.

Units, preprocessing and display

Related Calculators

Variable Error Formula

The following formulas calculate variable error from repeated observations. One-dimensional VE is the standard deviation of observed values (equivalently, signed errors). Population bivariate variable error is sqrt(ฮฃ[(x โˆ’ meanX)ยฒ + (y โˆ’ meanY)ยฒ]/n); the nโˆ’1 version is labeled sample-adjusted 2D spread. This is not the SD of radial distances. Mean radial error measures distance to the target instead.

Signed error (one trial): eแตข = Xแตข - T Variable Error (VE), population SD: VE = sqrt(ฮฃ (Xแตข - Xฬ„)ยฒ / n) Variable Error (VE), sample SD: VE = sqrt(ฮฃ (Xแตข - Xฬ„)ยฒ / (n - 1))

Variables:

  • Xi is an observed (measured) value on trial i.
  • T is the target (true/reference) value.
  • ei is the signed error for trial i (can be positive or negative).
  • Xฬ„ is the mean of the observed values.
  • n is the number of trials used in the calculation.

To calculate variable error, collect observations, compute their mean, then use the population denominator (n) or sample denominator (nโˆ’1) as appropriate. Sample spread requires at least two observations. Enter complete numbers without thousands separators; malformed entries are rejected. Optional one-pass z-score filtering or clipping changes the dataset and is a heuristic, not a formal outlier test. In 2D, preprocessing uses distance from the entered target. Relative SD is 100 ร— SD / |mean|, is undefined at mean zero, and needs ratio-scale data with a meaningful zero.

What is Variable Error?

Variable error is a measure of precision/consistency across repeated measurements or trials. It quantifies how much the observations vary around their mean (or, equivalently, how much the signed errors vary around the constant error). Variable error is always nonโ€‘negative: smaller values indicate more consistent performance/measurement, while larger values indicate more variability.

How to Calculate Variable Error?

The following steps outline how to calculate the Variable Error.

  1. Choose a target (true/reference) value T.
  2. Collect multiple observed (measured) values Xi from repeated trials.
  3. Compute the mean of the observed values: Xฬ„.
  4. Compute variable error (VE) as the standard deviation of the observed values (using n or nโˆ’1 as appropriate).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Target (T) = 100 units; Observed values (X): 105, 98, 102, 100 units

Signed errors: 5, โˆ’2, 2, 0. Constant Error (CE) = 1.25 units, Absolute Error (AE) = 2.25 units, Variable Error (VE, population) โ‰ˆ 2.586 units (VE, sample) โ‰ˆ 2.986 units.