Completing the Square Calculator

Convert a quadratic to vertex form by completing the square.

Enter Coefficients

ax² + bx + c

a (x² coefficient)

b (x coefficient)

c (constant)

Enter your values above and tap Calculate to see the result.

Vertex Form

Vertex (h, k)

Axis of Symmetry

Opens

Roots (x-intercepts)

The Process

ax²+bx+c
= a(x²+(b/a)x)+c
= a(x+(b/2a))² − b²/4a + c
h = −b/2a k = c−b²/4a

Related Calculators

Pro Tips

Results update as you type — change any field to see the effect immediately.

Check that every value uses the same unit before comparing results.

Use the copy button to paste the completing the square figures into a note or spreadsheet.

Nothing is sent to a server, so you can use this with private figures.