Equation of Sphere Calculator

Convert between the standard and general forms of a sphere from its center and radius.

Last updated: June 2026 | By Patchworkr Team

Sphere Parameters

Center h

Center k

Center m

Radius

Center h is required.

Standard form: (x - h)^2 + (y - k)^2 + (z - m)^2 = r^2. General form: x^2 + y^2 + z^2 + Dx + Ey + Fz + G = 0.

Live Results

Enter center coordinates and radius to generate equations.

Formulas

Standard form: (x - h)^2 + (y - k)^2 + (z - m)^2 = r^2

General form: x^2 + y^2 + z^2 + Dx + Ey + Fz + G = 0

Coefficients: D = -2h, E = -2k, F = -2m, G = h^2 + k^2 + m^2 - r^2

Example: center (1, 2, 3), radius 4

Standard form: (x - 1)^2 + (y - 2)^2 + (z - 3)^2 = 16

General form: x^2 + y^2 + z^2 - 2x - 4y - 6z - 2 = 0

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