MDETERM function

Returns the matrix determinant of an array. Matrix determinants are generally used for solving systems of mathematical equations that involve several variables.



Argument Description Remarks
array A numeric array with an equal number of rows and columns.

=MDETERM(A1:C3) equals

A1*(B2*C3-B3*C2) + A2*(B3*C1-B1*C3) + A3*(B1*C2-B2*C1)

General remarks

MDETERM is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete. For example, the determinant of a singular matrix may differ from zero by 1E-16.


To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.

Data Data Data Data
1 3 8 5
1 3 6 1
1 1 1 0
7 3 10 2
Formula Description (Result)    
=MDETERM(A2:D5) Determinant of the matrix in the table (88)    
=MDETERM({3,6,1;1,1,0;3,10,2}) Determinant of the matrix as an array constant (1)    
=MDETERM({3,6;1,1}) Determinant of the matrix in the array constant (-3)    
=MDETERM({1,3,8,5;1,3,6,1}) Returns an error because the array does not have an equal number of rows and columns (#VALUE!)    

See also

MINVERSE function

MMULT function

TRANSPOSE function

List of all functions (by category)

Applies to:
Excel for Mac 2011