Select Answer Mode | |
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V_{box} = V_{sph} | |
Box | |
Sphere | |
Set Units Shortcut |
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Related Tools
- Box and Cylinder dimensions calculator
- Cylinder and Sphere dimensions calculator
- Box 1 and Box 2 dimensions calculator
- Cylinder 1 and Cylinder 2 dimensions calculator
- Box volume calculator
- Sphere volume calculator
User Guide
This tool will calculate the measurement of a selected dimension for one of the shapes, which is necessary to ensure a rectangular box and a sphere have the same volume.
Experiment with different dimensions of each shape whilst maintaining an equal volume for both.
Formulas
The formulas used by this box and sphere dimensions with same volume calculator to determine each individual parameter are as follows:
Same Volume Mode (V_{box} = V_{sph})
L_{box} = π · ø_{sph}^{3} / (6 · W_{box} · H_{box})
W_{box} = π · ø_{sph}^{3} / (6 · L_{box} · H_{box})
H_{box} = π · ø_{sph}^{3} / (6 · L_{box} · W_{box})
ø_{sph} = ∛(6 · L_{box} · W_{box} · H_{box} / π)
Box Mode
L_{box} = V / (W_{box} · H_{box})
W_{box} = V / (L_{box} · H_{box})
H_{box} = V / (L_{box} · W_{box})
V = L_{box} · W_{box} · H_{box}
Sphere Mode
ø_{sph} = ∛(6 · V / π)
V = π · ø_{sph}^{3} / 6
Symbols
- L_{box} = Length of box
- W_{box} = Width of box
- H_{box} = Height of box
- ø_{sph} = Diameter of sphere
- V = Volume of box or sphere
- π = Pi = 3.14159…
Parameters
Length of Box
This is the length of the longest horizontal dimension of the rectangular box.
Width of Box
This is the length of the shortest horizontal dimension of the rectangular box.
Height of Box
This is the length of the vertical dimension of the rectangular box.
Diameter of Sphere
This is the diameter of the spherical object.
Volume
This is the volume of the rectangular or spherical shaped object.