Calculators

Hemisphere Volume Calculator

Calculate the volume, curved surface area, base area, and total surface area of a hemisphere.
👤 By Administrator
📅 Updated: October 13, 2026
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Hemisphere Volume & Surface Area Calculator

A hemisphere represents exactly half of a full sphere. This tool calculates volume V = 2/3πr³, curved dome area A = 2πr², base disc area A = πr², and total solid surface area A = 3πr².

Hemisphere Formulas
Volume: V = 2/3 × π × r³
Total Area (Solid): A = 3 × π × r²
Curved Area (Dome): A = 2 × π × r²

Practical Calculation Steps

  1. Radius: Identify hemisphere radius r.
  2. Volume: Cube the radius, multiply by 2, and divide by 3 (then multiply by π).
  3. Surface Area: If solid, remember to add the circular base (πr²) to the dome (2πr²), giving 3πr².
Sphere Volume Formula

Sphere Volume Formula

V = (4/3) × π × r³
Where V = Volume • r = Radius • π ≈ 3.14159265

Essential Mathematical Notation

  • 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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