About this Volume Calculator
Volume measures the amount of 3D space an object occupies. Whether you are calculating how much water fits in a tank (cylinder), measuring a package (prism), or solving a geometry problem, this tool provides the volume for the most common 3D shapes.
Who this calculator is for
- Students solving geometry and mensuration problems for 3D solids.
- Homeowners, builders, and planners estimating capacity or fill volume.
- Anyone comparing inside space against outside coverage with surface area.
When to use it
- Use this calculator when you need the capacity or interior space of a standard 3D shape.
- Use it to estimate container size, shipping box volume, or liquid capacity.
- Use it after finding circle or area values for bases that feed into cylinder, cone, or sphere volume problems.
Key assumptions
- All dimensions are entered in the same linear unit, and the result is returned in cubic units.
- Dimensions are treated as non-negative geometric lengths.
- This calculator returns geometric volume only and does not convert capacity into weight without a separate density value.
Accuracy and testing
Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.
How this calculator works
Different shapes use specific formulas based on their dimensions:
* Cylinder: $\pi \times r^2 \times h$ (Area of base × Height)
* Sphere: $\frac{4}{3} \times \pi \times r^3$
* Cone: $\frac{1}{3} \times \pi \times r^2 \times h$
* Cube: $side^3$
* Rectangular Prism: $Length \times Width \times Height$
Inputs explained
Shape
Select the geometric object you are measuring.
Radius (r)
The distance from the center to the outer edge of a circular base.
Height (h)
The vertical distance from the base to the top.
Length/Width
The horizontal dimensions of the object.
Understanding your results
The result is in cubic units (e.g., $in^3, m^3, ft^3$). Be consistent with your input units—if you enter inches, the volume is in cubic inches.
Example scenarios
Water Tank
Shape: Cylinder. Radius: 2ft. Height: 5ft. Volume ≈ 62.83 cubic feet.
Shipping Box
Shape: Rectangular Prism. Length: 10, Width: 8, Height: 5. Volume = 400.
Key Features
- Instant Calculation
- Private & Secure
- Mobile Optimized
Tips & Best Practices
- To convert cubic feet to gallons (for water), multiply the result by **7.48**.
- Volume grows very fast. Doubling the radius of a sphere increases its volume by 8 times ($2^3$).
Glossary of Terms
- Radius
- A straight line from the center to the circumference of a circle or sphere.
- Pi ($\pi$)
- The ratio of a circle's circumference to its diameter, approx 3.14159.
- Prism
- A solid object with two identical ends and flat sides.