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THE FEUTEX TOOLKIT

2D Mahalanobis Distance

Measure a point displacement while accounting for correlated variable scales.

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01 Your input
02 Your result
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FormulaDistance = sqrt(((dx/sx)**2-2*r*dx*dy/(sx*sy)+(dy/sy)**2)/(1-r**2)); Squared Distance = ((dx/sx)**2-2*r*dx*dy/(sx*sy)+(dy/sy)**2)/(1-r**2)
Sources and model references

Made for real tasks

  • Measure a point displacement while accounting for correlated variable scales.
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Worked example

Inputs

X displacement from mean
2 number
Y displacement from mean
1 number
X standard deviation
2 number
Y standard deviation
1 number
Correlation
0.5 correlation

Expected results

Distance
1.154700538 number
Squared Distance
1.333333333 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter x displacement from mean, y displacement from mean, x standard deviation, y standard deviation, correlation.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "dx": 2,
  "dy": 1,
  "sx": 2,
  "sy": 1,
  "r": 0.5
}

Accuracy and scope

Requires a nonsingular covariance model. A distance alone does not establish outlier significance.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.