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Box and Sphere Dimensions with Same Volume Calculator

Select Answer Mode
Vbox = Vsph
Box
Sphere
Set Units Shortcut
Calculate Box & Sphere Dimensions
Length of Box [?]
Width of Box [?]
Height of Box [?]
Diameter of Sphere [?]
Volume [?]

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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

Contents

  • User Guide
    • Formulas
      • Same Volume Mode (Vbox = Vsph)
      • Box Mode
      • Sphere Mode
      • Symbols
    • Parameters
      • Length of Box
      • Width of Box
      • Height of Box
      • Diameter of Sphere
      • Volume

User Guide

Box and Sphere with Same VolumeThis 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 (Vbox = Vsph)

Lbox = π · øsph3 / (6 · Wbox · Hbox)

Wbox = π · øsph3 / (6 · Lbox · Hbox)

Hbox = π · øsph3 / (6 · Lbox · Wbox)

øsph = ∛(6 · Lbox · Wbox · Hbox / π)

Box Mode

Lbox = V / (Wbox · Hbox)

Wbox = V / (Lbox · Hbox)

Hbox = V / (Lbox · Wbox)

V = Lbox · Wbox · Hbox

Sphere Mode

øsph = ∛(6 · V / π)

V = π · øsph3 / 6

Symbols

  • Lbox = Length of box
  • Wbox = Width of box
  • Hbox = Height of box
  • øsph = 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.

Primary Sidebar

Tool Sections

  • Area
  • Chemical Quantities
  • Circular Shapes
  • Density
  • Diameter & Radius
  • Energy & Power
  • Electrical & Electromagnetic
  • Flow
  • Force, Load & Torque
  • Length & Distance
  • Liquid Depth & Level
  • Mass & Weight
  • Movement & Motion
  • Pressure
  • Pricing & Quantities
  • Rectangular Shapes
  • Sensors & Instruments
  • Speed & Acceleration
  • Temperature & Heat
  • Time & Frequency
  • Travel & Transportation
  • Volumetric

Tool Feedback

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