MDETERM Function

Excel Functions › Math & Trig

All versions Math & Trig

The Excel MDETERM function returns the matrix determinant of a square array — a single number that tells you whether a matrix can be inverted and how it scales area or volume.


Quick answer:
=MDETERM({1,2;3,4}) determinant of a 2×2 matrix = -2

Syntax

=MDETERM(array)
ArgumentDescription
arrayRequiredA square numeric range or array constant (same number of rows as columns). In an array constant, commas separate columns and semicolons separate rows.

How to use it

MDETERM works on a square matrix — 2×2, 3×3, and so on. It returns one scalar, so you can type it in a single cell with no spilling.

=MDETERM({1,2;3,4}) // 1*4 - 2*3 = -2
=MDETERM({3,0;0,5}) // diagonal: 3*5 = 15

The determinant is the key test for invertibility: if MDETERM returns 0, the matrix is singular and MINVERSE cannot invert it. A non-zero determinant means an inverse exists.

Must be square. If the array has an unequal number of rows and columns — or any cell is blank or text — MDETERM returns #VALUE!. Tiny floating-point dust (like 1E-16) can appear instead of an exact 0 for nearly-singular matrices.

Try it: interactive demo

Live demo

Pick a MDETERM example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

What does the determinant tell me?
It is a single number summarizing a square matrix. A non-zero determinant means the matrix is invertible; a determinant of 0 means it is singular (no inverse). Geometrically it is the factor by which the matrix scales area (2×2) or volume (3×3).
Why does MDETERM return a #VALUE! error?
The array is not square (unequal rows and columns), or it contains a blank cell or text. Make sure every cell holds a number and the matrix is n×n.
How do I write a matrix as an array constant?
Use commas between columns and semicolons between rows inside braces. {1,2;3,4} is the 2×2 matrix with rows 1,2 and 3,4.
Why do I get a tiny number instead of exactly 0?
For matrices that are very close to singular, floating-point arithmetic can leave a tiny residue like 1.5E-16 instead of a clean 0. Treat values that small as zero.

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Related functions: MINVERSE · MMULT · MUNIT · SUMPRODUCT · TRANSPOSE