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Sphere Volume Calculator

A sphere is a perfectly symmetrical three-dimensional solid consisting of all points equidistant from a central point. This free Sphere Volume Calcula

Mathematics
Formula & Methodology
Sphere Volume = (4 ÷ 3) × π × Radius³ = 4/3 πr³ Surface Area = 4 × π × Radius² = 4πr² Diameter = 2 × Radius = 2r

To compute the volume of a sphere: 1. Measure or identify the sphere radius (r) from the center to the outer shell. 2. Cube the radius by multiplying it by itself three times (r³). 3. Multiply by π and by 4/3 (approx 4.18879): Volume = (4/3) × π × r³. If you only know diameter, divide by 2 first to obtain the radius.

Sphere Volume ((4/3)πr³)

523.5988

Overview

A sphere is a perfectly symmetrical three-dimensional solid consisting of all points equidistant from a central point. This free Sphere Volume Calculator computes internal cubic volume, external surface area, and diameter from the radius.

Sphere volume is widely used in astronomy (planetary and stellar mass/volume estimates), sports ball manufacturing (basketballs, soccer balls), storage of pressurized natural gas in spherical tanks, and pharmaceutical spherical bead dosing.

Worked Examples

Example 1: Sphere with Radius = 5 cm

Input: Radius = 5

  1. Cube radius: 5³ = 125.
  2. Multiply: (4/3) × π × 125 ≈ 523.5988 cm³.
  3. Surface area: 4 × π × 25 ≈ 314.16 cm².
Final Answer: Volume: 523.60 cu units, SA: 314.16

Example 2: Basketball (Diameter = 9.5 inches, Radius = 4.75 in)

Input: Radius = 4.75

  1. Radius cubed: 4.75³ = 107.1719.
  2. Volume: (4/3) × π × 107.1719 ≈ 448.92 cubic inches.
Final Answer: 448.92 cu in

Example 3: Sphere with Radius = 10 meters

Input: Radius = 10

  1. Volume: (4/3) × π × 1000 ≈ 4,188.79 m³.
Final Answer: 4,188.79 cu m

How to Use This Calculator

  1. Enter the sphere radius into the input field.
  2. Click "Calculate" to determine the volume.
  3. Review the surface area, diameter, and fluid capacity conversions below.
  4. Click "Reset" to compute volume for another sphere.

Reference Table

Radius (r)Diameter (2r)Surface Area (4πr²)Volume (4/3 πr³)
1212.574.19
2450.2733.51
36113.10113.10
510314.16523.60
10201256.644188.79

Frequently Asked Questions

Why does the sphere volume formula include 4/3?
Archimedes proved (and calculus confirms via triple integration in spherical coordinates) that a sphere occupies exactly 2/3 the volume of its circumscribed cylinder (V = 2/3 × (πr² × 2r) = 4/3 πr³).
How do you find the radius if you already know the volume?
Rearrange the formula: Radius = ³√[ (3 × Volume) ÷ (4π) ]. Take the cube root of 3V / 4π.
Why are pressure vessels often shaped like spheres?
A sphere minimizes surface area for any given volume, distributing internal pressure equally in all directions without stress-concentrating corners.
What happens to volume if you double the radius?
Because volume depends on r³, doubling the radius multiplies the volume by 2³ = 8 times (800% of original).
How do you calculate half of a sphere (hemisphere)?
Divide the sphere volume by 2: Hemisphere Volume = (2/3) πr³.

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Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Computed via exact spherical volume triple integration.