﻿ Spher defined by 4 points
 Sphere defined by 4 points calculator ▲
 Input points by certasian coordinates Point 1 X1 Y1 Z1 Point 2 X2 Y2 Z2 Point 3 X3 Y3 Z3 Point 4 X4 Y4 Z4
 Input points by spherical coordinates Point 1 r1 1 1 Point 2 r2 2 2 Point 3 r3 3 3 Point 4 r4 4 4
 Center point coordinates: X: Y: Z: Radius of sphere: r:
 Sphere volume: Sphere surface area:
 Sphere equation: x2 + y2 + z2 + x + y + z + = 0
 Sphere defined by 4 points ▲
 Volume: Surface area: Volume by surface area: Surface area by volume:
Sphere equation.
The equation of a sphere with center at point (h, k, l) is:
(x − h)2 + (y − k)2 + (z − l)2 = r2
The equivalent form of sphere equation is:
x2 + y2 + z2 + Dx + Ey + Fz + G = 0

The relations between the coefficients are:
D = − 2h           E = − 2k           F = − 2l           G = h2 + k2 + l2 − r2
The angle θ between two points
P1 (x1 , y1 , z1) and P2 (x2 , y2 , z2) both points lays on the sphere.

The arc length between those two points are:     L = θr
The equation of sphere passing through 4 points: P1 (x1 , y1 , z1)
P2 (x2 , y2 , z2) , P3 (x3 , y3 , z3) and P4 (x4 , y4 , z4).
Because each point is located on the sphere, we get 4 equations with the unknowns coefficients D, E, F and G they can be valuated by solving the system of the equations by matrix methods (Cramer's rule).
 Where: t1 = −(x12 + y12 + z12) t2 = −(x22 + y22+ z22) t3 =−(x32 + y32 + z32) t4 =−(x42 + y42 + z42)
 T is the determinant value T =

 The center of the sphere is at coordinate:

 The radius of the sphere is: