What is the formula for the volume of a sphere?

The volume of a sphere is V = (4/3)πr³, where 'r' is the radius. This can also be written as V = πd³/6 using the diameter.

How do I calculate the surface area of a sphere?

The surface area of a sphere is A = 4πr², where 'r' is the radius. This means a sphere's surface area is exactly 4 times the area of a circle with the same radius.

What's the relationship between a sphere's volume and surface area?

For a sphere with radius r: Surface Area = 4πr² and Volume = (4/3)πr³. The surface area to volume ratio is 3/r, meaning smaller spheres have relatively more surface area compared to their volume.

How do I find the radius from the volume?

Rearrange the volume formula: r = ∛(3V/4π). For example, if V = 100 cm³, then r = ∛(300/(4π)) = ∛(23.87) ≈ 2.88 cm.

What is a hemisphere?

A hemisphere is half of a sphere. Its volume is (2/3)πr³ and its surface area (including the flat base) is 3πr². The curved surface area alone is 2πr².

How is a sphere different from a circle?

A circle is a 2D shape (a flat disk) while a sphere is a 3D shape (like a ball). A circle has area (πr²) and circumference (2πr), while a sphere has volume ((4/3)πr³) and surface area (4πr²).

Sphere Calculator

Calculate volume, surface area, diameter, and circumference of a sphere from its radius.

Unit of Measurement

Radius (r)

Distance from center to surface

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Volume

0 cm³

V = (4/3)πr³ = (4/3) × π × 5³ = 0

Surface Area

4πr²

0 cm²

Diameter

0 cm

Circumference

2πr

0 cm

Documentation

Understanding Spheres

A sphere is a perfectly round 3D shape where every point on its surface is equidistant from its center. Examples include balls, planets, and bubbles.

Volume

Surface Area

Circumference

Tip: A sphere has the smallest surface area for a given volume of any 3D shape.

Frequently Asked Questions

How to Use

About the Sphere Calculator

What it calculates

This sphere calculator solves mathematical and statistical problems using standard formulas. Calculate volume and surface area of a sphere.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Sphere Calculator.

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Sphere Calculator

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0 cm²

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Understanding Spheres

About the Sphere Calculator

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