Hemisphere Volume Formula: Calculating Half-Spheres Accurately

How to calculate the volume of a hemisphere using V = 2/3πr³, with applications for bowls, domes, and igloos.

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📅 Updated: October 13, 2026

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Calculating the Volume of a Hemisphere

Because a hemisphere is formed by cutting a sphere into two identical halves, its volume is exactly one-half of a complete sphere:

V_hemisphere = (1/2) × (4/3 π r³) = 2/3 × π × r³

A planetarium dome is built in the shape of a hemisphere with internal radius r = 12 meters. What volume of air does it contain?

V = 2/3 × π × (12)³ = 2/3 × π × 1728 = 1152π ≈ 3,619.11 m³

Sphere Volume Formula

V = (4/3) × π × r³

Where V = Volume • r = Radius • π ≈ 3.14159265

V Volume of the sphere — The three-dimensional space enclosed within the spherical surface, measured in cubic units (e.g., cm³, m³, in³, ft³).
r Radius of the sphere — The straight-line distance from the exact center to any point on the outer surface (r = d / 2).
π Pi (π) — The mathematical circle constant, approximately 3.14159265 (or 22/7).
4/3 Geometric Constant (4/3) — The rational coefficient derived from spherical calculus integration.
r³ Radius Cubed (r³) — The radius multiplied by itself three times (r × r × r), measuring 3D volume.

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