3 × 3 matrix determinant

Calculate 3 × 3 matrix determinant using the values and assumptions you provide.

Your inputs stay in your browser. Displayed results are rounded to a maximum of 12 significant digits.

Method and assumptions

Method version 1.0.0 · Updated October 18, 2026

Calculate

Formula: aei + bfg + cdh − ceg − bdi − afh

Calculate 3 × 3 matrix determinant using the values and assumptions you provide.

a: Coefficient a
b: Coefficient b
c: Coefficient c
d: Coefficient d
e: Coefficient e
f: Coefficient f
g: Coefficient g
h: Coefficient h
i: Coefficient i

Results depend on the assumptions entered; verify professional or safety-critical decisions independently.

Calculate with code

These short examples use the same inputs and core calculation as this tool. Adapt validation and formatting to your application.

JavaScript

const [[a,b,c],[d,e,f],[g,h,i]] = [[1,2,3],[0,1,4],[5,6,0]];
console.log(a*(e*i-f*h)-b*(d*i-f*g)+c*(d*h-e*g)); // 1

TypeScript

const m: number[][] = [[1,2,3],[0,1,4],[5,6,0]];
const [a,b,c] = m[0]!, [d,e,f] = m[1]!, [g,h,i] = m[2]!;
console.log(a*(e*i-f*h)-b*(d*i-f*g)+c*(d*h-e*g)); // 1

Python

a,b,c,d,e,f,g,h,i = 1,2,3,0,1,4,5,6,0
print(a*(e*i-f*h)-b*(d*i-f*g)+c*(d*h-e*g))  # 1

Java

double det = 1*(1*0-4*6)-2*(0*0-4*5)+3*(0*6-1*5);
System.out.println(det); // 1

double det = 1*(1*0-4*6)-2*(0*0-4*5)+3*(0*6-1*5);
Console.WriteLine(det); // 1