Volume Calculator
Volume is the amount of three-dimensional space occupied by an object
or shape. It is commonly measured in cubic units such as cubic meters
(m³), cubic centimeters (cm³), cubic feet (ft³), and cubic inches (in³).
Different three-dimensional shapes use different mathematical formulas
to calculate their volume. The calculators above allow you to enter the
required measurements, select the appropriate units, and calculate the
volume quickly and accurately.
Sphere
A sphere is a perfectly round three-dimensional shape in which
every point on its surface is the same distance from its center.
This distance is called the radius.
Sphere Volume Formula
V = 4/3 × π × r³
Where:
- V = Volume of the sphere
- r = Radius of the sphere
- π ≈ 3.14159
Example
If a sphere has a radius of 5 meters:
V = 4/3 × π × 5³ = 523.60 m³
Therefore, the volume of the sphere is
523.60 m³.
Cone
A cone is a three-dimensional shape with a circular base that
gradually tapers to a single point called the apex or vertex.
Its volume is calculated using the radius of the circular base
and the height of the cone.
Cone Volume Formula
V = 1/3 × π × r² × h
Where:
- V = Volume of the cone
- r = Radius of the circular base
- h = Height of the cone
- π ≈ 3.14159
Example
If a cone has a radius of 3 meters and a
height of 5 meters:
V = 1/3 × π × 3² × 5 = 47.12 m³
Therefore, the volume of the cone is
47.12 m³.
Cube
A cube is a three-dimensional shape with six equal square faces.
All of its edges have the same length. The length of one edge is
used to calculate the volume of a cube.
Cube Volume Formula
V = s³
Where:
- V = Volume of the cube
- s = Length of one side
Example
If a cube has a side length of 4 meters:
V = 4³ = 64 m³
Therefore, the volume of the cube is
64 m³.
Cylinder
A cylinder is a three-dimensional shape with two parallel,
circular bases connected by a curved surface. Its volume is
calculated using the radius of its circular base and its height.
Cylinder Volume Formula
V = π × r² × h
Where:
- V = Volume of the cylinder
- r = Radius of the circular base
- h = Height of the cylinder
- π ≈ 3.14159
Example
If a cylinder has a radius of 3 meters and a
height of 5 meters:
V = π × 3² × 5 = 141.37 m³
Therefore, the volume of the cylinder is
141.37 m³.
Rectangular Tank
A rectangular tank is a three-dimensional rectangular shape with
a length, width, and height. Its volume is calculated by multiplying
these three measurements together.
Rectangular Tank Volume Formula
V = l × w × h
Where:
- V = Volume of the rectangular tank
- l = Length
- w = Width
- h = Height
Example
If a rectangular tank has a length of 6 meters,
a width of 4 meters, and a height of
3 meters:
V = 6 × 4 × 3 = 72 m³
Therefore, the volume of the rectangular tank is
72 m³.
Capsule
A capsule is a three-dimensional shape made up of a cylindrical
section with two hemispherical ends. Its volume is calculated
using the radius of the hemispherical ends and the cylindrical
length.
Capsule Volume Formula
V = π × r² × l + 4/3 × π × r³
Where:
- V = Volume of the capsule
- r = Radius of the hemispherical ends
- l = Cylindrical length
- π ≈ 3.14159
Example
If a capsule has a radius of 2 meters and a
cylindrical length of 5 meters:
V = π × 2² × 5 + 4/3 × π × 2³ = 96.34 m³
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Therefore, the volume of the capsule is
96.34 m³.
Spherical Cap
A spherical cap is the portion of a sphere cut off by a plane.
Its volume depends on the radius of the sphere and the height
of the cap.
Spherical Cap Volume Formula
V = 1/3 × π × h² × (3r − h)
Where:
- V = Volume of the spherical cap
- r = Radius of the sphere
- h = Height of the cap
- π ≈ 3.14159
Example
If a spherical cap has a sphere radius of 5 meters
and a cap height of 2 meters:
V = 1/3 × π × 2² × (3 × 5 − 2) = 54.45 m³
Therefore, the volume of the spherical cap is
54.45 m³.
Conical Frustum
A conical frustum is the portion of a cone that remains after
the top is cut off by a plane parallel to its base. It has a
larger radius, a smaller radius, and a height.
Conical Frustum Volume Formula
V = 1/3 × π × h × (R² + Rr + r²)
Where:
- V = Volume of the conical frustum
- R = Larger radius
- r = Smaller radius
- h = Height of the frustum
- π ≈ 3.14159
Example
If a conical frustum has a larger radius of 5 meters,
a smaller radius of 3 meters, and a height of
4 meters:
V = 1/3 × π × 4 × (5² + 5 × 3 + 3²) = 205.25 m³
Therefore, the volume of the conical frustum is
205.25 m³.
Ellipsoid
An ellipsoid is a three-dimensional shape similar to a stretched or
compressed sphere. It has three semi-axis lengths, usually represented
by a, b, and c.
Its volume is calculated using these three semi-axis lengths.
Ellipsoid Volume Formula
V = 4/3 × π × a × b × c
Where:
- V = Volume of the ellipsoid
- a = Length of semi-axis a
- b = Length of semi-axis b
- c = Length of semi-axis c
- π ≈ 3.14159
Example
If an ellipsoid has semi-axis lengths of
3 meters, 4 meters, and
5 meters:
V = 4/3 × π × 3 × 4 × 5 = 251.33 m³
Therefore, the volume of the ellipsoid is
251.33 m³.
Tube
A tube is a hollow cylindrical shape with an outer radius and an inner
radius. The space between the two cylindrical surfaces forms the
material of the tube. Its volume is calculated using the outer radius,
inner radius, and length of the tube.
Tube Volume Formula
V = π × h × (R² − r²)
Where:
- V = Volume of the tube
- R = Outer radius
- r = Inner radius
- h = Length of the tube
- π ≈ 3.14159
Example
If a tube has an outer radius of 5 meters,
an inner radius of 3 meters, and a length of
4 meters:
V = π × 4 × (5² − 3²) = 201.06 m³
Therefore, the volume of the tube is
201.06 m³.
Disclaimer
The Volume Calculator on SmartMyTools is provided for general
informational and educational purposes only. While we strive to
provide accurate calculations, the results should not be considered
a substitute for professional advice or precise measurements.
SmartMyTools does not guarantee the accuracy, completeness, or
suitability of the results for any particular purpose. Users are
responsible for verifying calculations and measurements before
using them for construction, engineering, manufacturing, or other
practical applications.
