Sphere Calculator
Calculate volume, surface area, circumference, and radius of any sphere. Enter one known value to find all others.
| Property | Value | In Terms of π |
|---|
Sphere Formulas
Sphere formulas below express each property in terms of radius and also in terms of every other property.
| Property | Formula (in terms of r) | Approximate |
|---|---|---|
| Volume (V) | V = (4/3)πr³ | V ≈ 4.1888r³ |
| Surface Area (A) | A = 4πr² | A ≈ 12.5664r² |
| Circumference (C) | C = 2πr | C ≈ 6.2832r |
| Radius from V | r = (3V / 4π)^(1/3) | r ≈ 0.62035V^(1/3) |
| Radius from A | r = √(A / 4π) | r ≈ 0.2821√A |
| Radius from C | r = C / 2π | r ≈ 0.15915C |
Understanding Sphere Geometry
Sphere geometry describes one of the most symmetric shapes in three-dimensional space. Every point on the surface of a sphere is exactly equal in distance from the center, called the radius.
Volume of a Sphere
The volume formula V = (4/3)πr³ shows that volume scales with the cube of the radius. Doubling the radius increases volume by a factor of 8, making spheres efficient containers of volume relative to their surface area.
Surface Area of a Sphere
The surface area formula A = 4πr² shows that area scales with the square of the radius. A sphere has the smallest possible surface area for a given volume, which is why soap bubbles naturally form spherical shapes.
Circumference of a Sphere
The circumference C = 2πr refers to the great circle, the largest circle that can be drawn on a sphere’s surface. Earth’s equatorial circumference is approximately 40,075 km, implying a radius of about 6,371 km.
Frequently Asked Questions
The volume of a sphere is V = (4/3)πr³, where r is the radius. For example, a sphere with radius 5 cm has volume V = (4/3) × π × 5³ ≈ 523.6 cm³.
The surface area of a sphere is A = 4πr². For a sphere with radius 3 m, surface area = 4 × π × 3² ≈ 113.1 m².
The circumference of a sphere refers to its great circle and is calculated as C = 2πr. For radius 7 cm, circumference = 2 × π × 7 ≈ 43.98 cm.
To find radius from volume, use r = (3V / 4π)^(1/3). For V = 100 cm³: r = (300 / 4π)^(1/3) = (23.873)^(1/3) ≈ 2.879 cm.
To find radius from surface area, use r = √(A / 4π). For surface area A = 200 cm²: r = √(200 / (4π)) = √(15.915) ≈ 3.99 cm.