How to use Matrix Calculator

Choose the matrix operation.
Enter one row per line with numeric cells separated as instructed; add matrix B when required.
Calculate and review dimensions and any numerical limitations.

Example: Matrix Calculator

Matrix Calculator: Inverse of A (2 × 2): [[-2, 1], [1.5, -0.5]].

You add

Operation: inverse Matrix A: 1, 2 3, 4 Matrix B (add, subtract or multiply): 5, 6 7, 8

You get

Inverse of A (2 × 2): [[-2, 1], [1.5, -0.5]]. A (2 × 2): [1, 2] [3, 4] Inverse of A (2 × 2): [-2, 1] [1.5, -0.5] Floating-point result; numeric pivots at or below 1e-10 of the largest input entry count as zero. Operation | Inverse of A A dimensions | 2 × 2 Result | [[-2, 1], [1.5, -0.5]]

Options

Matrix shape: Use one row per line. Addition needs matching dimensions, while multiplication needs the first column count to match the second row count.
Pivot threshold: Rank, inverse and related operations use the stated numerical threshold. Small pivots can be treated as zero.

Supported inputs and limits

Small bounded numeric matrices only, with floating-point arithmetic and a stated pivot threshold. Determinant and inverse need square matrices; singular or numerically unstable inverses refuse. No symbolic algebra or exact rational guarantee. Each matrix has 1–6 rows and columns and at most 4000 input characters. Cell magnitude is at most 10¹²; pivots at or below 10⁻¹⁰ of the largest input entry count as zero. Enter plain decimals with at most 60 characters, 40 digits and 20 fractional places per number; exponent notation is not accepted.

Where your input is processed

This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.

A refusal can reflect numerical sensitivity

Nearly dependent rows can make an inverse unstable even when an exact symbolic inverse exists. Small changes in scale or entered rounding can alter a numerical rank. Check the input precision and threshold before interpreting the result as a statement about an exact mathematical matrix.

Questions about Matrix Calculator

Why must matrix dimensions match for addition?

Each entry is added to the entry at the same position, so both matrices need the same row and column counts.

Can every square matrix be inverted?

No. A singular matrix has no inverse. Values near numerical singularity can also make a floating-point inverse unreliable.

Is a computed rank exact?

The reported numeric rank uses a pivot threshold. Very small perturbations can affect rank for nearly dependent rows or columns.

Project manager: Tony Hines · Content updated 4 October 2026 · Report a problem

Matrix Calculator

Calculate result controls