Method #1 – Face diagonal from the length of one side
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Formula – How to calculate the face diagonal of a cube from the length of one side
Face Diagonal = √(Side2 x 2)
Example
A cube has a side length of 10
Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421
Method #2 – Face diagonal from the volume
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Formula – How to calculate the face 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 face diagonal from the length of one side
Face Diagonal = √(Side2 x 2)
Example
A cube has a volume of 1,000
Side = 3√1000 = 10
Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421
Method #3 – Face diagonal from the surface area
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Formula – How to calculate the face 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 face diagonal from the length of one side
Face Diagonal = √(Side2 x 2)
Example
A cube has a surface area of 600
Side = √(600 ÷ 6) = √100 = 10
Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421
Method #4 – Face diagonal from the perimeter
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Formula – How to calculate the face 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 face diagonal from the length of one side
Face Diagonal = √(Side2 x 2)
Example
A cube has a perimeter of 120
Side = 120 ÷ 12 = 10
Face Diagonal = √(102 x 2) = √(100 x 2) = √200 = 14.1421
Method #5 – Face diagonal from the interior diagonal
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Formula – How to calculate the face diagonal of the cube from the interior diagonal
Step 1 – Find the length of one side from the interior diagonal
Side = Diagonal ÷ √3
Step 2 – Find the face diagonal from the length of one side
Face Diagonal = √(Side2 x 2)
Example
A cube has an interior diagonal of 14
Side = 14 ÷ √3 = 14 ÷ 1.4422 = 9.7074
Face Diagonal = √(9.70742 x 2) = √(94.2336 x 2) = √188.4672 = 13.7283