3x3 Determinant Calculator

Work out 3x3 determinant instantly with clear inputs, formula shown and shareable results.

About 3x3 Determinant Calculator

Expanding along the first row gives det = a(ei − fh) − b(di − fg) + c(dh − eg). Its absolute value is the volume of the parallelepiped spanned by the three rows.

Formula

3×3 determinant

det = a(ei − fh) − b(di − fg) + c(dh − eg)

Worked example

With the default values below, 3x3 Determinant Calculator returns Determinant of -306.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First row: 6, 1, 1
Second row: 4, -2, 5
Third row: 2, 8, 7

Results

Determinant: -306.00000000
Volume of the parallelepiped: 306.00000000
Trace: 11.00000000
Invertibility: Invertible

Step by step

1Values used
23×3 determinant
3Determinant= -306.00000000
4Volume of the parallelepiped= 306.00000000
5Trace= 11.00000000
6Invertibility= Invertible

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Determinant of [[6,1,1],[4,−2,5],[2,8,7]]?

6(−14 − 40) − 1(28 − 10) + 1(32 + 4) = −324 − 18 + 36 = −306.

Does the row I expand along matter?

No. Any row or column gives the same value, so choose the one with the most zeros.