Equation of a Sphere Calculator

Your details

Choose how you want to define the sphere. All three modes produce the same standard and general equations.
The x-coordinate of the center of the sphere.
The y-coordinate of the center of the sphere.
The z-coordinate of the center of the sphere.
The radius of the sphere. Must be a positive number.
Standard equation
(x - 2)^2 + (y + 3)^2 + (z - 5)^2 = 16

The sphere equation in standard (center-radius) form.

General equationx^2 + y^2 + z^2 - 4x + 6y - 10z + 22 = 0
Center(2, -3, 5)
Radius4
Diameter8
Surface area201.0619
Volume268.0826
Great-circle circumference25.1327

Sphere centered at (2, -3, 5) with radius 4.

  • The standard equation of this sphere is: (x - 2)^2 + (y + 3)^2 + (z - 5)^2 = 16
  • Center: (2, -3, 5), Radius: 4, Diameter: 8
  • Surface area is 201.0619, and volume is 268.0826.
  • The great-circle circumference (largest cross-section) is 25.1327.

Next stepUse the general equation to check whether a given point lies inside (plug in x,y,z and compare to r^2) or outside the sphere.

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