Method #1 – Interior diagonal from the length of one side
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Formula – How to calculate the interior diagonal of a cube from the length of one side
Interior Diagonal = √3 x Side
Example
A cube has a side length of 10
Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205
Method #2 – Interior diagonal from the volume
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Formula – How to calculate the interior diagonal of the cube from the volume
Step 1 – Find the length of one side from the volume
Side = 3√Volume
Step 2 – Find the interior diagonal from the length of one side
Interior Diagonal = √3 x Side
Example
A cube has a volume of 1,000
Side = 3√1000 = 10
Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205
Method #3 – Interior diagonal from the surface area
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Formula – How to calculate the interior diagonal of a cube from the surface area
Step 1 – Find the length of one side from the surface area
Side = √(Surface Area ÷ 6)
Step 2 – Find the interior diagonal from the length of one side
Interior Diagonal = √3 x Side
Example
A cube has a surface area of 600
Side = √(600 ÷ 6) = √100 = 10
Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205
Method #4 – Interior diagonal from the perimeter
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Formula – How to calculate the interior diagonal of the cube from the perimeter
Step 1 – Find the length of one side from the perimeter
Side = Perimeter ÷ 12
Step 2 – Find the interior diagonal from the length of one side
Interior Diagonal = √3 x Side
Example
A cube has a perimeter of 120
Side = 120 ÷ 12 = 10
Interior Diagonal = √3 x 10 = 1.73205 x 10 = 17.3205
Method #5 – Interior diagonal from the face diagonal
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Formula – How to calculate the interior diagonal of the cube from the face diagonal
Step 1 – Find the length of one side from the face diagonal
Side = √(Diagonal2 ÷ 2)
Step 2 – Find the interior diagonal from the length of one side
Interior Diagonal = √3 x Side
Example
A cube has an face diagonal of 14
Side = √(142 ÷ 2) = √(196 ÷ 2) = √98 = 9.89949
Interior Diagonal = √3 x 9.89949 = 1.73205 x 9.89949 = 17.1464