Box and Sphere Dimensions with Same Volume Calculator

Calculate Box & Sphere Dimensions
Select Answer Mode	Lbox Wbox Hbox øsph V
Set Units Shortcut	mm cm m in ft
Length of Box [?]
⟳ Select length unit millimetres (mm) centimetres (cm) inches (in) feet (ft) yards (yd) metres (m) yoctometres (ym) zeptometres (zm) attometres (am) femtometres (fm) picometres (pm) nanometres (nm) micrometres (µm) millimetres (mm) centimetres (cm) decimetres (dm) metres (m) decametres (dam) hectometres (hm) kilometres (km) megametres (Mm) gigametres (Gm) terametres (Tm) petametres (Pm) exametres (Em) zettametres (Zm) yottametres (Ym) thousandths of an inch (thou) inches (in) feet (ft) yards (yd) miles (mi) nautical miles (nmi) astronomical units (au) light-years (ly) parsecs (pc) kiloparsecs (kpc) megaparsecs (Mpc) gigaparsecs (Gpc)
Width of Box [?]
⟳ Select width unit millimetres (mm) centimetres (cm) inches (in) feet (ft) yards (yd) metres (m) yoctometres (ym) zeptometres (zm) attometres (am) femtometres (fm) picometres (pm) nanometres (nm) micrometres (µm) millimetres (mm) centimetres (cm) decimetres (dm) metres (m) decametres (dam) hectometres (hm) kilometres (km) megametres (Mm) gigametres (Gm) terametres (Tm) petametres (Pm) exametres (Em) zettametres (Zm) yottametres (Ym) thousandths of an inch (thou) inches (in) feet (ft) yards (yd) miles (mi) nautical miles (nmi) astronomical units (au) light-years (ly) parsecs (pc) kiloparsecs (kpc) megaparsecs (Mpc) gigaparsecs (Gpc)
Height of Box [?]
⟳ Select height unit millimetres (mm) centimetres (cm) inches (in) feet (ft) yards (yd) metres (m) yoctometres (ym) zeptometres (zm) attometres (am) femtometres (fm) picometres (pm) nanometres (nm) micrometres (µm) millimetres (mm) centimetres (cm) decimetres (dm) metres (m) decametres (dam) hectometres (hm) kilometres (km) megametres (Mm) gigametres (Gm) terametres (Tm) petametres (Pm) exametres (Em) zettametres (Zm) yottametres (Ym) thousandths of an inch (thou) inches (in) feet (ft) yards (yd) miles (mi) nautical miles (nmi) astronomical units (au) light-years (ly) parsecs (pc) kiloparsecs (kpc) megaparsecs (Mpc) gigaparsecs (Gpc)
Diameter of Sphere [?]
⟳ Select diameter unit millimetres (mm) centimetres (cm) inches (in) feet (ft) yards (yd) metres (m) yoctometres (ym) zeptometres (zm) attometres (am) femtometres (fm) picometres (pm) nanometres (nm) micrometres (µm) millimetres (mm) centimetres (cm) decimetres (dm) metres (m) decametres (dam) hectometres (hm) kilometres (km) megametres (Mm) gigametres (Gm) terametres (Tm) petametres (Pm) exametres (Em) zettametres (Zm) yottametres (Ym) thousandths of an inch (thou) inches (in) feet (ft) yards (yd) miles (mi) nautical miles (nmi) astronomical units (au) light-years (ly) parsecs (pc) kiloparsecs (kpc) megaparsecs (Mpc) gigaparsecs (Gpc)
Volume [?]
L m³ cm³ US gal ft³ in³ Select volume unit cu centimetres (cc, cm³) millilitres (mL) cu inches (in³) litres (L) gallons (gal, usa liq) gallons (gal, imp) cu feet (ft³) cu metres (m³) cu nanometres (nm³) cu micrometres (µm³) cu millimetres (mm³) cu centimetres (cc, cm³) millilitres (mL) teaspoons (tsp, metric) tablespoons (Tbsp, metric) cups (metric) litres (L) cu metres (m³) kilolitres (kL) megalitres (ML) cu kilometres (km³) cu thous (thou³) cu inches (in³) fluid ounces (fl oz, imp) pints (pt, imp) gallons (gal, imp) cu feet (ft³) cu yards (yd³) cu miles (mi³) cu nautical miles (nmi³) cu thous (thou³) teaspoons (tsp, usa) tablespoons (Tbsp, usa) cu inches (in³) fluid ounces (fl oz, usa) cups (usa) pints (pt, usa liq) gallons (gal, usa liq) cu feet (ft³) barrels (bbl, oil) cu yards (yd³) cu miles (mi³) cu nautical miles (nmi³) yoctolitres (yL) zeptolitres (zL) attolitres (aL) femtolitres (fL) picolitres (pL) nanolitres (nL) microlitres (µL) millilitres (mL) centilitres (cL) decilitres (dL) litres (L) decalitres (daL) hectolitres (hL) kilolitres (kL) megalitres (ML) gigalitres (GL) teralitres (TL) petalitres (PL) exalitres (EL) zettalitres (ZL) yottalitres (YL) cu yoctometres (ym³) cu zeptometres (zm³) cu attometres (am³) cu femtometres (fm³) cu picometres (pm³) cu nanometres (nm³) cu micrometres (µm³) cu millimetres (mm³) cu centimetres (cm³) cu decimetres (dm³) cu metres (m³) cu decametres (dam³) cu hectometres (hm³) cu kilometres (km³) cu megametres (Mm³) cu gigametres (Gm³) cu terametres (Tm³) cu petametres (Pm³) cu exametres (Em³) cu zettametres (Zm³) cu yottametres (Ym³) cu astronomical units (au³) cu light-years (ly³) cu parsecs (pc³) cu kiloparsecs (kpc³) cu megaparsecs (Mpc³) cu gigaparsecs (Gpc³)

Related Tools

• Box and Cylinder dimensions calculator
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• Box volume calculator
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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:

L_box = π · ø_sph³ / (6 · W_box · H_box)

W_box = π · ø_sph³ / (6 · L_box · H_box)

H_box = π · ø_sph³ / (6 · L_box · W_box)

ø_sph = ∛(6 · L_box · W_box · H_box / π)

V = L_box · W_box · H_box
V = π · ø_sph³ / 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…

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. The volume will be calculated as soon as all the dimensions for either the box or the sphere have been fully entered. If all dimension inputs have values, then the dimensions of the box will be used to calculate the volume. If you would like to use the dimension for the sphere rather than the box, simply clear one of the box dimensions, and the tool will automatically allow the sphere diameter to be entered instead.