Volume Calculator
Sphere Volume Calculator
Where:
- V = Volume
- r = Radius
- π ≈ 3.14159
Example:
For r = 2m, V ≈ 33.51 m³
Cone Volume Calculator
Where:
- V = Volume
- r = Base radius
- h = Height
- π ≈ 3.14159
Example:
For r = 3m, h = 5m, V ≈ 47.12 m³
Cube Volume Calculator
Where:
- V = Volume
- a = Edge length
Example:
For a = 4m, V = 64 m³
Cylinder Volume Calculator
Where:
- V = Volume
- r = Base radius
- h = Height
- π ≈ 3.14159
Example:
For r = 2m, h = 5m, V ≈ 62.83 m³
Rectangular Tank Volume Calculator
Where:
- V = Volume
- l = Length
- w = Width
- h = Height
Example:
For l=3m, w=4m, h=5m, V = 60 m³
Capsule Volume Calculator
Where:
- V = Volume
- r = Radius
- h = Height of cylinder portion
- π ≈ 3.14159
Example:
For r=2m, h=3m, V ≈ 54.45 m³
Spherical Cap Volume Calculator
Please provide any two values below to calculate.
Where:
- V = Volume
- R = Sphere radius
- h = Cap height
- π ≈ 3.14159
Example:
For R=5m, h=2m, V ≈ 58.64 m³
Conical Frustum Volume Calculator
Where:
- V = Volume
- R = Bottom radius
- r = Top radius
- h = Height
- π ≈ 3.14159
Example:
For R=5m, r=3m, h=4m, V ≈ 193.73 m³
Ellipsoid Volume Calculator
Where:
- V = Volume
- a = Axis 1
- b = Axis 2
- c = Axis 3
- π ≈ 3.14159
Example:
For a=2m, b=3m, c=4m, V ≈ 100.53 m³
Square Pyramid Volume Calculator
Where:
- V = Volume
- a = Base edge length
- h = Height
Example:
For a=5m, h=8m, V ≈ 66.67 m³
Tube Volume Calculator
Where:
- V = Volume
- R = Outer radius (d1/2)
- r = Inner radius (d2/2)
- l = Length
- π ≈ 3.14159
Example:
For d1=6m, d2=4m, l=10m, V ≈ 157.08 m³
Volume refers to the amount of three-dimensional space occupied by a substance or object. The standard unit of volume in the International System (SI) is the cubic meter (m³). Typically, when discussing a container’s volume, we’re referring to its capacity—how much liquid or substance it can hold—rather than the physical space the container itself occupies.
For most basic shapes, volume can be determined using specific geometric formulas. For more complex structures, breaking them into smaller, familiar shapes can make the overall volume easier to calculate. In advanced scenarios, integral calculus may be used when an object’s boundaries can be mathematically defined. For irregular forms, techniques such as the finite element method offer volume estimations. Another approach, when density and mass are known, is using the formula: volume = mass ÷ density.
This calculator helps you find the volume of several commonly encountered shapes.
1. Sphere
A sphere is a perfectly round 3D shape where all points on the surface are equidistant from a center point. The distance from the center to the surface is the radius (r), and the longest straight line through the sphere is the diameter (d).
Volume Formula:
V = (4/3) × π × r³
Example:
A sphere with radius 3 cm.
V = (4/3) × π × (3)³ = 113.097 cm³
2. Cone
A cone tapers smoothly from a circular base to a single apex point. This tool uses the formula for a right circular cone, the most common type.
Volume Formula:
V = (1/3) × π × r² × h
Example:
A cone with radius 2 cm and height 5 cm.
V = (1/3) × π × (2)² × 5 = 20.943 cm³
3. Cube
A cube is a three-dimensional version of a square, where all edges are equal, and faces are squares.
Volume Formula:
V = a³
where a is the edge length.
Example:
A cube with side length 4 cm.
V = (4)³ = 64 cm³
4. Cylinder
A cylinder consists of two parallel circular bases connected by a curved surface. This calculator focuses on right circular cylinders.
Volume Formula:
V = π × r² × h
Example:
A cylinder with radius 3 cm and height 7 cm.
V = π × (3)² × 7 = 197.920 cm³
5. Rectangular Tank
A rectangular tank is like a stretched cube, with three sides of potentially different lengths.
Volume Formula:
V = length × width × height
Example:
A box with dimensions 2 cm × 3 cm × 4 cm.
V = 2 × 3 × 4 = 24 cm³
6. Capsule
A capsule combines a cylinder with two hemispherical ends.
Volume Formula:
V = π × r² × h + (4/3) × π × r³Alternative compact form:
V = π × r² × (h + (4/3) × r)
Example:
A capsule with radius 2 cm and height 5 cm.
V = π × (2)² × 5 + (4/3) × π × (2)³ = 106.810 cm³
7. Spherical Cap
A spherical cap is a slice from a sphere, cut by a plane. It becomes a hemisphere if cut through the center.
Volume Formula:
V = (1/3) × π × h² × (3R – h)
Example:
A spherical cap with sphere radius 4 cm and cap height 2 cm.
V = (1/3) × π × (2)² × (3×4 – 2) = 33.510 cm³
8. Conical Frustum
A conical frustum is what remains when a cone is sliced between two parallel planes, creating top and bottom circular surfaces of different radii.
Volume Formula:
V = (1/3) × π × h × (r² + r × R + R²)
Example:
A frustum with small radius 3 cm, large radius 5 cm, and height 8 cm.
V = (1/3) × π × 8 × ((3)² + (3) × (5) + (5)²) = 301.592 cm³
9. Ellipsoid
An ellipsoid is a stretched or compressed sphere, with three different axis lengths.
Volume Formula:
V = (4/3) × π × a × b × c
where a, b, and c are the semi-axes.
Example:
An ellipsoid with axes 3 cm, 4 cm, and 5 cm.
V = (4/3) × π × 3 × 4 × 5 = 188.495 cm³
10. Square Pyramid
A square pyramid has a square base and four triangular faces meeting at a point.
Volume Formula:
V = (1/3) × a² × h
Example:
A square pyramid with base edge 6 cm and height 10 cm.
V = (1/3) × (6)² × 10 = 120 cm³
11. Tube (Hollow Cylinder)
A tube is a cylindrical shape with an inner hollow section, commonly used to transport liquids or gases.
Volume Formula:
V = (π / 4) × (D² – d²) × l
where d₁ is the outer diameter, d₂ is the inner diameter, and l is the length.
Example:
A tube with outer diameter 6 cm, inner diameter 4 cm, and length 10 cm.
V = (π / 4) × ((6)² – (4)²) × 10 = 94.248 cm³
Common Volume Units
| Unit | Cubic Meters (m³) | Milliliters (mL) |
|---|---|---|
| Milliliter (mL) | 0.000001 | 1 |
| Cubic Inch (in³) | 0.00001639 | 16.39 |
| Pint (pt) | 0.000473 | 473 |
| Quart (qt) | 0.000946 | 946 |
| Liter (L) | 0.001 | 1,000 |
| Gallon (gal) | 0.003785 | 3,785 |
| Cubic Foot (ft³) | 0.028317 | 28,317 |
| Cubic Yard (yd³) | 0.764555 | 764,555 |
| Cubic Meter (m³) | 1 | 1,000,000 |
| Cubic Kilometer (km³) | 1,000,000,000 | 1,015,000,000 |