3D ShapesV = 4/3 × π × r³

Sphere Volume Calculator

Calculate volume, total surface area, and hemisphere capacity from radius, diameter, or circumference.

Sphere Volume & Area Solver

Multi-way bi-directional • Caps & shells • Instant

Presets:

1. Geometry Type

Radius (r)

Diameter (d)

2. Sphere Volume (V)Calculated

Volume

3. Surface Area & Perimeter

Total Surface Area (A)

283.53 sq in

Equatorial Circumference (C)

29.85 in (75.8 cm)

Formulas, calculation steps & FAQs below↓

Formulas & Calculation Guide

Sphere Geometry & Derivation

A sphere is defined as the set of all points in three-dimensional space equidistant from a central point. The distance from the center to any surface point is the radius r.

Key Mathematical Formulas

Volume (V): V = (4/3) × π × r³ = (π × d³) / 6
Surface Area (A): A = 4 × π × r² = π × d²
Circumference (C): C = 2 × π × r = π × d
Hollow Spherical Shell Volume: V_shell = (4/3) × π × (R_outer³ - r_inner³)

Spherical tank – calculation example

Let’s calculate the volume of a spherical gas storage pressure vessel with diameter 10 meters (radius 5 meters):

Spherical radius: radius = 5 m.
Compute surface area: surface area = 314.16 m².
The calculation results are available for you: tank volume = 523.60 m³ (138,322 US gallons / 523,598 Liters).
Circumference around equator: circumference = 31.42 m.

💡 Archimedes proved in 225 BC that a sphere possesses exactly two-thirds the volume and surface area of a cylinder enclosing it with diameter and height equal to 2r.

Frequently Asked Questions

Expert answers to common calculations, unit conversions, and dimensional requirements.

What is the formula to calculate the volume of a sphere?↓

The volume of a sphere is given by V = (4/3) · π · r³, where r is the radius. When given the diameter d, the formula becomes V = (π · d³) / 6.

How do you calculate the surface area of a sphere?↓

The total surface area of a sphere equals four times the area of its great circle: A = 4 · π · r² = π · d².

How do you calculate the volume of a spherical cap (dome)?↓

For a spherical cap of height h cut from a sphere of radius r, the volume is V_cap = (π · h² / 3) · (3r - h). Alternatively, if only the base radius of the cap a and height h are known: V_cap = (1/6) · π · h · (3a² + h²).

What is the volume of a hemisphere?↓

A hemisphere is exactly half of a full sphere: V_hemi = (2/3) · π · r³. The total surface area of a solid hemisphere with a flat base is A = 3 · π · r² (2πr² curved surface + 1πr² circular flat base).