Cuboid Calculator
Calculator and formulas for calculating the volume and surface of a cuboid
This function calculates the volume, the surface area and the diagonal of a cuboid. A cuboid is a polyhedron with six rectangles as faces. The opposite faces are parallel and of equal size.
To perform the calculation, enter the length of the three sides and click the 'Calculate' button.
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Properties of a cuboid
A cuboid is a geometric figure consisting of six rectangles, two of which are parallel and opposite each other. The size of a cuboid is always clearly determined by three details.
Formulas for a cuboid
Volume (\(\small{V}\))
The volume of a cuboid is calculated from the product of length, width and height:\[ V=a · b · c\]
Surface area (\(\small{S}\))
The surface area of a cuboid is the sum of the areas of all six sides:\[S= 2 ·((a · b) + (a · c) + (b · c)) \]
Diagonal (\(\small{d}\))
The diagonal of a side of the cuboid is the diagonal that extends from one corner of the cuboid to the opposite corner of the same side. It can be calculated using the Pythagorean theorem:\[ d=\sqrt{a^2 · b^2}\]
Diagonal (\(\small{e}\))
The spatial diagonal of a cuboid is the diagonal that extends from one corner of the cuboid to the opposite corner. It can be calculated using the Pythagorean theorem:\[ e=\sqrt{a^2 · b^2 · c^2}\]
Perimeter of the base area
The perimeter of the base area (rectangle) of a cuboid is calculated from the sum of the side lengths:\[ U_{Grund}=2 · (a+b)\]
Example:
Given a cuboid with the dimensions:
- Length \(a=4 \ \text{cm}\)
- Width \(b=3 \ \text{cm}\)
- Height \(c=2 \ \text{cm}\)
Calculations:
Volume:
\[V=4×3×2=24 \ \text{cm} \]Surface:
\[O=2×(4×3+4×2+3×2)=2×(12+8+6)=2×26=52 \ \text{cm} \]Diagonal of the room:
\[d= \sqrt{4^2 + 3^2 + 2^2} =\sqrt{16+9+4}= \sqrt{29} ≈5.39 \ \text{cm} \]Perimeter of the base area:
\[ U_{Grund}=2×(4+3)=2×7=14 \ \text{cm} \]
Cuboid
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Square Pillar
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Antiprism
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Hexagonal prism
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Triangular prism
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Regular prism
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Oblique prism
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Ramp
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Anticube
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Wedge
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Right Wedge
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Rhombohedron
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Parallelepiped
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Tetrahedron, irregular
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Tetragonal Trapezohedron
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Pentagonal Trapezohedron
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Prismatoid
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Stellated Octahedron
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Stellated Dodecahedron
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Great Stellated Dodecahedron
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Great Dodecahedron
Tetrahedron • Cube • Octahedron • Dodecahedron • Icosahedron
Tetrahedron • Cube • Octahedron • Dodecahedron • Icosahedron
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