Work out equation of a sphere instantly with clear inputs, formula shown and shareable results.
A sphere is the set of points at a fixed distance r from a centre (a, b, c), which the distance formula turns into (x − a)² + (y − b)² + (z − c)² = r².
Standard form
(x − a)² + (y − b)² + (z − c)² = r²
Expanded form
x² + y² + z² − 2ax − 2by − 2cz + (a² + b² + c² − r²) = 0
Halve and negate each linear coefficient: the x term −2a gives a, and so on. Then complete the square to find r².
There is no real sphere; the equation describes an imaginary sphere or a single point when r² = 0.