# Matrix determinant calculator

## World's simplest number tool

Quickly find the determinant of a matrix in your browser. To get the determinant, just enter your matrix in the input field, adjust row and column separators in the options below, and this utility will instantly compute the matrix's determinant. Created by developers for developers.

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Matrix determinant calculator tool
What is a matrix determinant calculator?

This is an online browser-based utility for finding the determinant of a square matrix. There are many ways to calculate the determinant. For example, for a 2x2 matrix, the Leibniz formula can be used; for a 3x3 matrix, the Laplace formula or rule of Sarrus can be applied. This tool supports any NxN matrices and the most effective algorithm for doing it is Gaussian elimination, which is used here. It uses elementary matrix operations to transform a matrix into the upper triangular form. In this form, the determinant is equal to the product of the diagonal elements. By default input matrix's elements are separated by spaces and rows by newlines but you can adjust the delimiters that separate columns and rows in the options above. You can also adjust the accuracy of the calculated determinant by setting the number of digits after the decimal point. That's numberwang!

Matrix determinant calculator examples
Click to use

The Determinant of a 3x3 Matrix

In this example, we find the determinant of a matrix with dimensions 3 by 3. For this particular matrix, we find that it's equal to -25.

2 1 3
3 2 7
5 6 0

-25

**Required options**

Matrix column delimiter.
(By default a space.)

Matrix row delimiter.
(By default a newline.)

Upper Triangular Matrix

In this example, we calculate the determinant of an upper triangular matrix. In this case, it is very simple to find the determinant. It's equal to the product of all diagonal elements, which are 0.009, 0.09, 0.9 and 9. The product of these numbers is less than 1. To find the determinant precisely, we set the accuracy to 6 decimal digits.

0.009 0.08 0.7 6
0 0.09 0.8 7
0 0 0.9 8
0 0 0 9

0.006561

**Required options**

Matrix column delimiter.
(By default a space.)

Matrix row delimiter.
(By default a newline.)

Number of digits after
the decimal point.

Matrix with Proportional Rows

This example computes the determinant of a 9x9 matrix. If you look closely, you can see that 1st and 6th rows are proportional (with the ratio 1:2). In this case, we immediately know that the determinant is zero because if two matrix rows (or columns) are proportional (or equal), then the matrix is singular and the determinant is zero.

3 1 -2 4 1 -1 4 3 2
-4 -5 -2 -3 -5 -7 9 -9 4
2 -8 1 -8 5 2 -5 -7 8
1 9 -8 0 4 1 -9 -3 -7
-5 2 7 -6 -1 -4 1 -9 8
6 2 -4 8 2 -2 8 6 4
-6 -3 1 9 -5 -8 1 -7 -6
-5 -3 9 8 -9 0 -3 2 6
3 -4 -5 5 7 4 7 -5 0

0

**Required options**

Matrix column delimiter.
(By default a space.)

Matrix row delimiter.
(By default a newline.)

Pro tips
Master online number tools

You can pass input to this tool via

__?input__query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinenumbertools.com/matrix-determinant-calculator

__?input__=2%201%203%0A3%202%207%0A5%206%200&input-element-separator=%20&input-row-separator=%5Cn
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