4×4 Determinant Calculator
Calculate the determinant of a 4×4 matrix step by step. Free 4×4 determinant calculator with cofactor expansion, exact fractions, and a worked example that answers 30.
Find the determinant of any 4×4 matrix with a full worked solution. The grid below is preset to 4×4 and loaded with an example whose determinant is 30.
How to find the determinant of a 4×4 matrix
- 1
Enter the entries
Fill in all 16 numbers of your 4×4 matrix. The size is already set for you.
- 2
Reduce to triangular form
Row operations clear each column below the pivot until the matrix is upper triangular.
- 3
Read the determinant
The result appears at the top, together with whether the 4×4 matrix is invertible.
About 4×4 determinants
From 4×4 upward, row reduction to triangular form is far quicker than expanding 24 cofactor terms.
The example above works out to 30. Because it is non-zero, that matrix is invertible and its rows are linearly independent. Change any entry and the whole solution updates as you type.
Other matrix sizes
Frequently asked questions
How do you find the determinant of a 4×4 matrix? ▾
Row-reduce the matrix to upper triangular form, tracking each row swap as a sign change, then multiply the diagonal entries. Cofactor expansion would need 24 products, so reduction is much faster.
How many terms does a 4×4 cofactor expansion have? ▾
A full cofactor expansion of an 4x4 matrix has 24 products. That is why this calculator uses row reduction to triangular form.
What does it mean if a 4×4 determinant is zero? ▾
A zero determinant means the 4 rows are linearly dependent — one is a combination of the others. The matrix is singular, has no inverse, and the associated system of 4 equations does not have a unique solution.
Can this 4×4 determinant calculator handle fractions? ▾
Yes. Type entries like 3/4 or -1/2 and the answer comes back as an exact fraction rather than a rounded decimal.
About this Calculator
Calculate the determinant of a 4×4 matrix step by step. Free 4×4 determinant calculator with cofactor expansion, exact fractions, and a worked example that answers 30.