Calculators

Sphere Radius Calculator

Solve backwards to calculate the radius of a sphere given its known volume or surface area.
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📅 Updated: October 13, 2026
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Sphere Radius Calculator (Reverse Geometry)

Determine the exact radius of a sphere when only the total volume or surface area is known by applying inverse algebra: r = ³√(3V / 4π) or r = √(A / 4π).

Inverse Radius Formulas
From Volume: r = ³√[ (3 × V) / (4 × π) ]
From Surface Area: r = √[ A / (4 × π) ]

Step-by-Step Inversion

  1. Multiply volume V by 3.
  2. Divide by 4π (≈ 12.56637).
  3. Take the cube root of the quotient.
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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