Free to use, no account
SVD Calculator
Decompose a small rectangular matrix A into compact factors U, Σ and Vᵀ. See singular values, estimated numerical rank, the reconstructed matrix and its error, then download the results as CSV.
How do I calculate an SVD?
Enter a rectangular matrix with one row per line and values separated by spaces or commas. The calculator estimates A = UΣVᵀ and checks how closely the factors reconstruct your matrix.
Frequently asked questions
How do I calculate an SVD?
Enter a rectangular matrix with one row per line and values separated by spaces or commas. The calculator estimates A = UΣVᵀ and checks how closely the factors reconstruct your matrix.
Is my matrix uploaded?
No. The decomposition runs locally in your browser; the matrix is not uploaded or saved by this tool.
What is singular value decomposition?
SVD factors a matrix as A = UΣVᵀ, where the singular values in Σ describe the strength of orthogonal directions.
Can this calculator handle rectangular matrices?
Yes. Enter between 2 and 8 rows and columns; the returned factors use a compact rectangular form.
Is the numerical rank exact?
No. It is estimated using a floating-point tolerance, so very small singular values may be treated as zero.