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Sphere Radius from Diameter, Surface, Volume or Circumference

Sphere Radius from Diameter, Surface, Volume or Circumference. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Radius 3 gives Diameter 6, Circumference 18.849556, Surface area 113.09734, Volume 113.09734, Surface to volume ratio 1.

V = 4πr³/3; A = 4πr²; Cgreat-circle = 2πr; A/V = 3/r

Worked example

Enter these known values and leave the other values blank.

Radius
3 cm
Diameter
6 cm
Circumference
18.85 cm
Surface area
113.1 cm²
Volume
113.1 cm³
Surface to volume ratio
1 1/ cm

Assumptions and limitations

  • This is a sphere with positive radius. Circumference means its great-circle circumference. Surface-to-volume ratio has inverse-length units; a volume-based inverse uses the positive cube root.
  • Select compatible units and enough independent dimensions. Clear unknown values before solving backward. Numeric precision and display rounding do not quantify uncertainty in measured inputs.
  • Arithmetic uses 64 significant digits. Original reference diagrams explain the dimensions and do not follow entered proportions.

Common questions

Which circle does sphere circumference describe?

The great circle lies in a plane through the sphere center and has the same radius as the sphere.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The cubic international mile uses the cube of the exact 1609.344-meter mile, replacing a rounded reciprocal factor.

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