Cramer Rule Calculator

Work out cramer rule instantly with clear inputs, formula shown and shareable results.

About Cramer Rule Calculator

Cramer's rule solves a square system by determinants: replace the column belonging to a variable with the constants, take the determinant and divide by the coefficient determinant.

Formula

Cramer's rule

xₖ = det(Aₖ) / det(A), where Aₖ has column k replaced by the constants

Worked example

With the default values below, Cramer Rule Calculator returns x of 1.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First equation coefficients and constant: 2, -1, 3, 9
Second equation: 1, 1, 1, 6
Third equation: 1, -1, 1, 2

Results

x: 1.00000000
y: 2.00000000
z: 3.00000000
Coefficient determinant D: -2.00000000

Step by step

1Values used
2Cramer's rule
3x= 1.00000000
4y= 2.00000000
5z= 3.00000000
6Coefficient determinant D= -2.00000000

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

For the sample system?

D = −2, and the three substituted determinants give x = 1, y = 2, z = 3.

Is it practical for large systems?

No. It needs n + 1 determinants, so Gaussian elimination is vastly faster beyond about 3 × 3.