How to calculate a matrix determinant
- Set
Size (n × n)to the square matrix size. - Fill each matrix cell with a number or fraction.
- Select
Calculateto display the determinant and row steps. - Select
Copy resultorDownload result (.txt)to take the result out of the page.
Enter values in the matrix grid
Each cell accepts an integer, a signed number, a decimal, or a fraction such as 3/4 or -7/2. For a 2 × 2 calculation, enter the values below and select Calculate:
1 2
3 4
det A = -2The result area shows the determinant, matrix size, and status. A fractional determinant keeps its reduced fraction and includes a decimal approximation.
Input rules for matrix cells
Each cell must contain one plain number or one fraction. Decimal parts need digits on both sides of the decimal point, and a fraction needs a nonzero denominator.
- Empty cells produce an error before calculation.
- Expressions, variables, and extra symbols are rejected.
- The input grid is always square, so it cannot represent a rectangular matrix.
Changing Size (n × n) hides the result and error, rebuilds the grid, and removes its entries. Select Reset to rebuild the current-size grid and clear the result and error state.
How the determinant steps are calculated
The Steps area begins with the entered matrix, then shows row swaps and the row combinations used to reach upper-triangular form. A row swap flips the determinant sign. Eliminating entries below a pivot leaves the determinant unchanged, so the final value is the signed product of the diagonal entries.
If a required column has no nonzero pivot at or below the current row, the status becomes Singular and the result states det A = 0. The result also says that A has no inverse. Exact fractions are used throughout the calculation; general numerical conditioning is outside its checks.
What gets copied or downloaded
Copy resultcopies the entered matrix, determinant, matrix size, and status. It leaves out the visible row steps.Download result (.txt)saves those same fields asmatrix-determinant-result.txt.
Copy result depends on clipboard access. If that access fails, the page does not add an error message.
Use the result to check a matrix
For a homework check, enter the matrix and compare the displayed row operations with the hand calculation. A Singular status identifies a determinant of 0 and reports that A has no inverse.
For a square set of values copied from a spreadsheet, enter each value in the grid, inspect the exact determinant, and save the plain-text result with the matrix size and status.
Choose a related matrix calculator
Use the Math Calculators category to choose among matrix, equation, fraction, sequence, geometry, and other math calculators.
Choose Matrix Calculator for matrix addition, subtraction, multiplication, transposition, inverse, rank, or a solution to Ax = b. Choose Matrix Inverse Calculator when you need the inverse and Gauss-Jordan steps on [A | I]. For equations, use Algebra Calculator.
Frequently asked questions
How do I calculate the determinant of a matrix?
Set Size (n × n), fill each cell, select Calculate, and read the determinant and row-elimination steps. The calculation reduces the matrix to upper-triangular form, then multiplies the diagonal entries with row-swap signs included.
What size matrix can this determinant calculator handle?
It handles square matrices from 1 × 1 through 8 × 8. Change Size (n × n) to rebuild the grid at another size.
Can I enter fractions in the matrix determinant calculator?
Yes. Enter a fraction such as 3/4 in a cell. The arithmetic keeps reduced exact fractions and shows a decimal approximation when the final determinant is fractional.
Why does my matrix show as singular?
Your matrix shows as singular when a required elimination column has no nonzero pivot available. The determinant is then exactly 0, and the result says that A has no inverse.