Sphere - Volume

vCalc Reviewed

V = \frac{4}{3} \cdot π \cdot r^{3}

$V = 4/3 * pi * "r" ^3$

(r) Radius of Sphere

$(r) "Radius of Sphere"$

The Math / Science

The formula for the volume of a sphere is:

V = ⁴/₃•π•r³

where:

V is the volume of a sphere
r is the radius of the sphere

References

Light and Matter(Dr. Benjamin Crowell) Chapter 1.2 Scaling of Area and Volume

The Math

The equation for the volume of a sphere is as follows:

V = 4/3•π•r³

The volume of a sphere is a special case of the Volume of an Ellipsoid (CLICK HERE) where the three semi-axes (a, b, c) are all the same and equal to the radius (r)

V = ⁴/₃ π•a•b•c

One can see that they are algebraically the same.

Ellipsoid Calculator

Ellipsoid - Volume computes the volume of an ellipsoid based on the length of the three semi-axes (a, b, c)
Ellipsoid - Surface Area computes the surface area of an ellipsoid based on the length of the three semi-axes (a, b, c)
Ellipsoid - Mass or Weight computes the mass or weight of an ellipsoid based on the length of the three semi-axes (a, b, c) and the mean density.
Ellipsoid Cap - Volume computes the volume of a section of an ellipsoid.
Oblate Spheroid - Volume computes the volume of an Oblate Spheroid based on the length of the two semi-axes (b, c)
Oblate Spheroid- Surface Area computes the surface area of an Oblate Spheroid based on the length of the two semi-axes (b, c)
Oblate Spheroid- Mass or Weight computes the mass or weight of an Oblate Spheroid based on the length of the two semi-axes (b, c) and the mean density.
Sphere - Volume computes the volume of a sphere based on the length of the radius (a)
Sphere - Surface Area computes the surface area of a sphere based on the length of the radius (a)
Sphere - Mass or Weight computes the mass or weight of a sphere based on the length of the radius (a) and the mean density.
Circular - Volume: Computes the volume of a column with a circular top and bottom and vertical sides.
Circular - Mass: Computes the mass/weight of circular volume based on its dimensions and mean density.
Elliptical Volume: Computes the volume of a column with an elliptical top and bottom and vertical sides.
Elliptical - Mass: Computes the mass/weight of an elliptical volume based on its dimensions and mean density.
Ellipse Vertical Chord from Edge (VE): Computes the length of the vertical chord of an ellipse based on distance from the edge.
Ellipse Vertical Chord from Center (VC): Computes the length of the vertical chord of an ellipse based on distance from the center.
Ellipse Horizontal Chord from Edge (HE): Computes the length of the horizontal chord of an ellipse based on distance from the edge.
Ellipse Horizontal Chord from Center (HC): Computes the length of the vertical chord of an ellipse based on distance from the center.
Common Mean Density: Provides a lookup function to find the mean density of hundreds of materials (woods, metals, liquids, chemicals, food items, soils, and more)

Sphere Calculators

Sphere Surface Area based radius (r)
Sphere Surface Area from Volume
Sphere Volume from Radius
Sphere Volume from Circumference
Sphere Volume from Surface Area
Sphere Volume from Mass and Density
Sphere Radius from Volume
Sphere Radius from Surface Area
Sphere Weight (Mass) from volume and density
Sphere Density
Area of Triangle on a Sphere
Distance between Two Points on a Sphere
Sphere Cap Surface Area
Sphere Cap Volume
Sphere Cap Weight (Mass)
Sphere Segment Volume
Sphere Segment Weight (Mass)
Sphere Segment Wall Surface Area (without the circular top and bottom ends)
Sphere Segment Full Surface Area (with the top and bottom circles, aka ends)
Volume of Spherical Shell
Mass of Spherical Shell

Volume is a three dimensional measurement of the amount of space taken up by an object. Volume units are cubic measurements for solid objects such as cubic inches and cubic meters. Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel.

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape. Many such calculations are available in the following list of calculators.

In many cases, the calculators are for a column with a geometric shaped base and vertical sides. One basic formula for volume is area times a Height when the volume has vertical sides.