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Sphere Calculator

Enter the required parameters of a sphere, and the calculator will determine its radius, volume, surface area, and circumference, with detailed calculations shown.

Calculation With:

Volume (r):

pi π:

In term of:

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Sphere Calculator

The Sphere Calculator allows you to calculate the radius, volume, surface area, and circumference of a sphere with high precision. Quickly analyze any sphere using key parameters.

What is a Sphere?

A sphere is a three-dimensional object where all points on the surface are equidistant from the center.

Sphere

Radius of a Sphere

You can calculate the radius depending on the known parameter:

From Volume: $$ r = \left(\frac{3V}{4\pi}\right)^{1/3} $$
From Surface Area: $$ r = \sqrt{\frac{A}{4\pi}} $$
From Circumference: $$ r = \frac{C}{2\pi} $$

Surface Area of a Sphere

From Radius: $$ A = 4\pi r^2 $$
From Volume: $$ A = \pi^{1/3} (6V)^{2/3} $$
From Circumference: $$ A = \frac{C^2}{\pi} $$

Volume of a Sphere

From Radius: $$ V = \frac{4}{3}\pi r^3 $$
From Surface Area: $$ V = \frac{A^{3/2}}{6\sqrt{\pi}} $$
From Circumference: $$ V = \frac{C^3}{6\pi^2} $$

Circumference of a Sphere

From Radius: $$ C = 2\pi r $$
From Surface Area: $$ C = \sqrt{\pi A} $$
From Volume: $$ C = \pi^{2/3} (6V)^{1/3} $$

Examples

Example 1: Volume from Radius

Find the volume of a sphere with radius 3 cm:

$$ V = \frac{4}{3} \pi r^3 = \frac{4}{3} \cdot 3.14 \cdot 3^3 = 113.04 \, \text{cm}^3 $$

Example 2: Surface Area from Circumference

Find the surface area of a sphere with circumference 4 m:

$$ A = \frac{C^2}{\pi} = \frac{4^2}{3.14} = 5.095 \, \text{m}^2 $$

Example 3: Radius from Surface Area

Find the radius of a sphere with surface area 4 cm²:

$$ r = \sqrt{\frac{A}{4\pi}} = \sqrt{\frac{4}{4\cdot 3.14}} = 0.564 \, \text{cm} $$

How the Sphere Calculator Works

Input:

Select a known parameter: Radius, Volume, Surface Area, or Circumference.
Enter the value of the selected parameter.
Click Calculate.

Output:

Radius
Volume
Surface Area
Circumference

The calculator automatically computes all parameters and presents them clearly.

FAQs

Is a circle the same as a sphere?

No. A circle is 2D, lying on a plane, while a sphere is 3D, with points equidistant from the center.

What is an arc of a circle?

An arc is a portion of a circle’s circumference. There are two types: minor arc and major arc.

What are the basic types of angles?

Acute angle < 90°
Right angle = 90°
Obtuse angle > 90°

Conclusion

The Sphere Calculator is a useful geometry tool for computing all properties of a sphere quickly and accurately. Ideal for students, teachers, and professionals.

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