Icosahedron Calculator (V ≈ 2.1817a³)

The calculator applies the exact formula V = 5(3 + √5)/12·a³ ≈ 2.1817·a³, A = 5√3·a². Worked example: a = 2 cm → V = 17.45 cm³, A = 34.64 cm². Keep every input in one unit system and the result follows in cubic units (m³, ft³, liters); full precision is kept until the final rounding. Radius fields expect radii — halve any diameter before entering it.

1. 1

   Enter the measurements

   Type the values required by the formula for icosahedron volume and area.

2. 2

   Check the units

   One unit system throughout — cm, m, ft or in.

3. 3

   Read the result

   The calculator substitutes, evaluates and rounds only at the end.

• 1

  Volume scales with the cube of linear dimensions

• 2

  Convert results: 1 m³ = 1000 L, 1 ft³ = 7.48 US gal

• 3

  π ≈ 3.14159 — precision kept to the last step

• Mixing units (cm radius with m height)

• Entering a diameter where the formula wants a radius

• Forgetting the solid must be closed — check h > 0