Sphere Volume

How to Find the Diameter From Sphere Volume

Derive diameter directly from sphere volume using d = ³√(6V / π) with detailed algebraic examples.
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📅 Updated: October 13, 2026
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Finding Diameter Directly from Known Volume

If you need the total width of a sphere whose volume is known, you can either compute the radius and double it, or use the direct diameter inverse equation:

d = ³√[ (6 × V) / π ]

Example Calculation

A spherical meteor has an estimated volume of V = 1,200 cm³. What is its diameter?

  1. Multiply by 6: 6 × 1200 = 7200
  2. Divide by π: 7200 / 3.14159265 ≈ 2291.83
  3. Take cube root: ³√(2291.83) ≈ 13.18 cm

The diameter of the meteor is approximately 13.18 cm.

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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