Volume Calculator
Find the volume of 3D geometric shapes including spheres, cylinders, rectangular boxes, and cones. Get accurate measurements for any 3D shape instantly.
Result
- Shape
- -
- Volume
- 0 cubic units
Formula & Guide
Formulas
V
Rectangular Box
V = L × W × H
Multiply length, width, and height
V
Sphere
V = (4/3) × π × r³
Four-thirds times π times radius cubed
V
Cylinder
V = π × r² × h
π times radius squared times height
V
Cone
V = (1/3) × π × r² × h
One-third of cylinder volume
Formula Variables
V
Volume
The amount of 3D space occupied by the shape, measured in cubic units
L, W, H
Length, Width, Height
The three dimensions of a rectangular box
r
Radius
The distance from center to edge (for sphere, cylinder, cone)
h
Height
The vertical dimension (for cylinder and cone)
π
PI
Mathematical constant approximately 3.14159
Step-by-Step Scenario
Example Scenario
Length
6 units
Width
4 units
Height
3 units
1
Identify the Dimensions
- Length = 6, Width = 4, Height = 3 (all in same units)
Make sure all measurements use the same units
2
Apply the Formula
- Volume = Length × Width × Height
- Volume = 6 × 4 × 3
- Volume = 24 × 3
Additional Examples
Sphere
Radius: 3 units
Volume
(4/3) × π × 3³ ≈ 113.1
Cylinder
Radius: 2 units
Height: 5 units
Volume
π × 2² × 5 ≈ 62.83
Characteristics of Volume
Three-Dimensional
Volume measures 3D space, requiring three dimensions (length, width, height) or equivalent measurements like radius and height.
Cubic Units
Volume is always expressed in cubic units (e.g., cubic meters, cubic feet) because it represents space in three dimensions.
Practical Applications
Used in construction, manufacturing, shipping, storage, fluid capacity, and any field involving 3D space calculations.
Mathematical Relationships
Cone volume is 1/3 of cylinder volume with same base and height. Sphere volume uses the radius cubed, showing exponential growth.
Important Notes
- Volume is always expressed in cubic units (e.g., cubic meters, cubic feet) based on the units of the input measurements.
- For shapes involving π (sphere, cylinder, cone), the result will be an approximation since π is an irrational number.
- All measurements must use the same units. Mixing units will give incorrect results.
- The cone volume formula includes 1/3 because a cone is one-third the volume of a cylinder with the same base and height.
- For rectangular boxes, the order of dimensions doesn't matter - length × width × height gives the same result as width × length × height.
Frequently Asked Questions
Find answers to common questions about volume calculations.
Volume is the amount of 3D space occupied by an object. It's measured in cubic units (e.g., cubic meters, cubic feet). Volume represents how much space a 3D shape takes up.
Box volume = Length × Width × Height. Multiply all three dimensions together. For example, a box with dimensions 5×4×3 has volume = 5 × 4 × 3 = 60 cubic units.
Sphere volume = (4/3) × π × radius³. For example, a sphere with radius 3 has volume = (4/3) × π × 27 ≈ 113.1 cubic units.
Cylinder volume = π × radius² × height. First square the radius, multiply by π, then multiply by height. For example, radius 2 and height 5: π × 4 × 5 ≈ 62.83 cubic units.
Cone volume = (1/3) × π × radius² × height. It's one-third of the cylinder volume with the same base and height. The 1/3 factor accounts for the cone's tapering shape.
You can use any units (meters, feet, inches, etc.) as long as all measurements use the same unit. Volume will be in cubic units (e.g., cubic meters, cubic feet) of that measurement.