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Matrix Rank Calculator
Find the rank of any matrix and see the row echelon form produced by Gaussian elimination.
Find the rank of a matrix
Rank: — · Size: —
Rows: — · Columns: —
Full rank: —
How to use the Matrix Rank Calculator
- Type your matrix with one row per line and values separated by spaces.
- Click Calculate rank to run Gaussian elimination on the matrix.
- Read the rank, the size and the resulting row echelon form.
Features
- Rank of any rectangular matrix
- Row echelon form shown step by step
- Partial pivoting for numeric stability
- Runs locally, no uploads
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Frequently Asked Questions
Common questions about the free online matrix rank calculator.
The rank is the number of linearly independent rows or columns. It also equals the number of
non-zero rows in row echelon form.
Type rows separated by semicolons or new lines, with the values in each row separated by
spaces, such as 1 2 3; 2 4 6.
Row echelon form is the staircase shape produced by elimination, where each pivot sits to the
right of the one above it.
Yes. Any number of rows and columns is accepted, and the rank can never exceed the smaller of
the two dimensions.
The tool uses Gaussian elimination with partial pivoting and treats values below a tiny
tolerance as zero for stability.
A matrix has full rank when its rank equals the smaller dimension, so all of its rows or
columns are independent.
No. The matrix is processed entirely in your browser, so nothing is transmitted and nothing
is stored.
Rounding or repeated rows often reduce the rank. A row that is a multiple of another row adds
no new independent direction.
Last updated: October 10, 2026