MATH CALCULATOR
Sphere Equation Calculator
Calculate the equation of a sphere using our online calculator.
What is the Sphere Equation Calculator & How does it work?
A sphere is a three-dimensional geometric shape that consists of all points in space equidistant from a given point, called its center. The distance from the center to any point on the sphere’s surface is known as the radius.
The equation of a sphere with center ((h, k, l)) and radius (r) in three-dimensional space is given by:This equation describes all points that are exactly (r) units away from the center ((h, k, l)). By inputting specific values for the center and radius, you can determine whether a point lies on the surface of the sphere.
The equation of a sphere with center ((h, k, l)) and radius (r) in three-dimensional space is given by:
(x – h)^2 + (y – k)^2 + (z – l)^2 = r^2
(x, y, z) = coordinates of a point on the sphere’s surface
(h, k, l) = coordinates of the center of the sphere
r = radius of the sphere
(h, k, l) = coordinates of the center of the sphere
r = radius of the sphere
Parameters
Equation of the Sphere—
Frequently Asked Questions
How do I find the equation of a sphere?
Use the formula (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h, k, l) is the center and r is the radius.
What does each variable represent in the sphere equation?
x, y, z are coordinates of a point on the sphere; h, k, l are the center coordinates; r is the radius.
Can this calculator handle spheres not centered at the origin?
Yes, the calculator can handle spheres with any center (h, k, l) in three-dimensional space.
What if I only know two points on the sphere and its radius?
You would need to find the midpoint of the line segment connecting the two points to determine the center (h, k, l).
Is there a limit to the size of the radius I can use?
No, the calculator can handle any positive real number for the radius.
Results are for informational purposes only and do not constitute professional advice.