Condition Number Calculator

Condition Number Calculator

Calculate the 2-norm condition number of a matrix from its singular values.

Last updated: June 2026 | By Patchworkr Team

Matrix Analyzer

Enter rows on separate lines and separate each row with commas.

Enter rows separated by newlines and columns separated by commas. All rows must have the same number of columns and contain numeric values.

Condition Number

14.933034

Interpretation

Moderately conditioned

Sigma Max

5.464986

Sigma Min

0.365966

What Is a Condition Number?

The condition number measures how sensitive the matrix is to small changes in the input.

How to Use It

  1. Enter the matrix, one row per line.
  2. Separate columns with commas.
  3. Read the condition number and interpretation on the right.

What does a high condition number mean?

A high condition number means the matrix is sensitive to small changes.

Can rectangular matrices be used?

Yes. The calculation is based on A^T A, so rectangular matrices are supported.

What if the matrix is invalid?

The calculator rejects empty rows, uneven row lengths, and non-numeric values.

Why use singular values?

Singular values directly capture numerical stretching and compression.

Formula

κ(A) = σ_max / σ_min

Related Tools