Math

Equation of a Sphere Calculator

Get a sphere's volume, surface area and general-form constant from centre and radius.

Calculated Output

Volume 268.08

Surface area 201.06

General-form constant -2

Formula: (x − h)² + (y − k)² + (z − l)² = r²

Step-by-Step Breakdown

1. Values used:

2. Centre x = 1

3. Centre y = 2

4. Centre z = 3

5. Radius = 4

7. Volume = 268.08

8. Surface area = 201.06

9. General-form constant = -2

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The math behind it

Expanding gives a general form whose constant term is h² + k² + l² − r². Volume is (4/3)πr³ and surface area is 4πr².

Centre (1, 2, 3), r = 4 → volume ≈ 268.08, surface ≈ 201.06.

How do I recover the radius from general form?

Complete the square in x, y and z to find the centre and radius.