Variable Error Calculator

Enter the target value and observed values into the calculator to determine the variable error.

1D (Single Axis)

2D (Spatial)

Options

Enter a target value and a series of observed values. We’ll compute Constant Error (bias), Absolute Error (mean absolute error), and Variable Error (precision).

Target (T)

Observed values (separate by commas, spaces, or new lines)

Unit label (optional) Denominator Outlier rule Z threshold (for filter/winsor) Decimal places

Related Calculators

Variable Error Formula

The following formulas are used to calculate variable error from repeated observations (trials). Variable error is the standard deviation (SD) of the observed values (equivalently, the SD of the signed errors).

Signed error (one trial): e_i = X_i - T Variable Error (VE), population SD: VE = sqrt( Σ (X_i - X̄)^2 / n ) Variable Error (VE), sample SD: VE = sqrt( Σ (X_i - X̄)^2 / (n-1) )

Variables:

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

To calculate variable error, collect multiple observations, compute the mean of the observations, then compute the standard deviation using either the population denominator (n) or the sample denominator (n−1) depending on your context.

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 non‑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.

Choose a target (true/reference) value T.
Collect multiple observed (measured) values X_i from repeated trials.
Compute the mean of the observed values: X̄.
Compute variable error (VE) as the standard deviation of the observed values (using n or n−1 as appropriate).
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, −2, 2, 0. Constant Error (CE) = 1.25 units, Absolute Error (AE) = 2.25 units, Variable Error (VE, population) ≈ 2.585 units (VE, sample) ≈ 2.988 units.