Math Calculators
Volume Calculator
Calculate volume for cubes, boxes, cylinders, spheres, cones, pyramids, and prisms with cubic unit conversions.
Enter the values and review the result.
Calculate volume
Choose a shape, enter the dimensions, and calculate volume with instant unit conversions.
Choose a shape and enter positive dimensions to calculate volume.
The result will show the formula, step-by-step substitution, primary cubic result, and unit conversions.
What is volume?
Volume measures the three-dimensional space inside or occupied by an object. It is useful for boxes, tanks, packages, concrete forms, containers, and classroom geometry problems.
Volume vs area
Area measures a flat surface in square units, such as square feet. Volume measures three-dimensional space in cubic units, such as cubic feet or cubic meters.
Volume formulas table
| Shape | Inputs needed | Formula |
|---|---|---|
| Cube | Side | V = s³ |
| Rectangular prism / box | Length, width, height | V = l × w × h |
| Cylinder | Radius or diameter, height | V = π × r² × h |
| Sphere | Radius or diameter | V = 4/3 × π × r³ |
| Hemisphere | Radius or diameter | V = 2/3 × π × r³ |
| Cone | Radius or diameter, height | V = 1/3 × π × r² × h |
| Square pyramid | Base side, height | V = 1/3 × s² × h |
| Rectangular pyramid | Base length, base width, height | V = 1/3 × l × w × h |
| Triangular prism | Triangle base, triangle height, prism length | V = 1/2 × b × h × length |
Volume units explained
Cubic inches are useful for small objects and packages.
Cubic feet are common for boxes, storage, tanks, and construction estimates.
Cubic yards are common for concrete, mulch, gravel, and bulk materials.
Cubic centimeters are useful for small metric measurements.
Cubic meters are common for larger metric volume estimates.
Liters are often used for liquid capacity and containers.
- 1 cubic foot = 1,728 cubic inches.
- 1 cubic yard = 27 cubic feet.
- 1 cubic meter = 1,000 liters.
- 1 liter = 1,000 cubic centimeters.
- 1 cubic inch is about 16.387 cubic centimeters.
Worked examples
Box: A 5 m × 2 m × 3 m box has volume = 5 × 2 × 3 = 30 cubic meters.
Cylinder: Radius 2 ft and height 10 ft gives volume = 3.1416 × 2² × 10 = 125.66 cubic feet.
Sphere: Radius 3 in gives volume = 4/3 × 3.1416 × 3³ = 113.10 cubic inches.
Cone: Radius 3 ft and height 9 ft gives volume = 1/3 × 3.1416 × 3² × 9 = 84.82 cubic feet.
Square pyramid: Base side 6 ft and height 10 ft gives volume = 1/3 × 6² × 10 = 120 cubic feet.
Real-life uses
Volume calculations help with storage boxes, shipping packages, tanks and containers, concrete forms, landscaping or material estimates, and classroom geometry.
Common mistakes
- Mixing inches and feet in the same calculation.
- Using diameter as radius for cylinders, spheres, hemispheres, or cones.
- Confusing area with volume.
- Forgetting cubic units in the final answer.
- Using outside dimensions when inside capacity is needed.
- Rounding too early before converting units.
Related calculators
Use the Area Calculator for flat shapes, the Unit Converter for basic conversions, or the Cubic Yard Calculator and Concrete Calculator for construction-style material estimates.
Quick answers
What this calculator answers
- Result: Calculate volume for common 3D shapes and convert between cubic units and liters.
- Formulas: Supports cubes, boxes, cylinders, spheres, hemispheres, cones, pyramids, and triangular prisms.
- Best use: Use it for geometry homework, boxes, tanks, containers, concrete forms, and material estimates. cubic yard calculator
Transparency note
Accuracy and limitations
Calzivo tools are built for practical estimates, conversions, and checks. Some tools use standard formulas or simplified assumptions, and results can be affected by input accuracy, rounding, units, local rules, or changing official requirements.
Results depend on the values you enter and any simplified assumptions used by the tool. Verify important results before making decisions or submitting official information.
How to Use This Tool
Use these steps to enter the right inputs and interpret the result correctly.
Choose the shape you want to calculate.
Select the input unit and enter the required dimensions.
Choose radius or diameter for round shapes.
Review the formula, substitution, primary result, and unit conversions.
Related Tools
Other helpful tools for volume, geometry, unit conversion, and material estimates.
Area Calculator
Calculate the area of any geometric shape.
Unit Converter
Convert between various measurement units.
Cubic Yard Calculator
Calculate cubic yards from length, width, and depth for gravel, sand, concrete, mulch, topsoil, fill, and other bulk materials.
Square Feet to Cubic Yards Calculator
Convert area and depth into cubic yards and cubic feet for gravel, sand, concrete, mulch, topsoil, and bulk materials.
Concrete Calculator
Estimate concrete in cubic yards, cubic feet, cubic meters, and bags for slabs, footings, post holes, and small pours.
Scientific Calculator
A full-featured scientific calculator in your browser.
Related Guides
Background reading and explanations related to Volume Calculator.
Frequently Asked Questions
Common questions about Volume Calculator and how to read the result.
What is the formula for volume?
The formula depends on the shape. For a box it is length × width × height, while cylinders, cones, spheres, pyramids, and prisms use their own formulas.
Why is volume measured in cubic units?
Volume measures three-dimensional space, so each result combines length, width, and height into units like cubic feet or cubic meters.
What is the difference between area and volume?
Area measures a flat surface in square units. Volume measures space inside or occupied by a 3D object in cubic units.
How do I calculate the volume of a box?
Choose rectangular prism and enter length, width, and height. The formula is volume = length × width × height.
How do I calculate cylinder volume from diameter?
Choose cylinder, select diameter, and enter the diameter and height. The calculator divides diameter by 2 to get radius before using π × radius² × height.
How do I convert cubic feet to cubic yards?
Divide cubic feet by 27 because 1 cubic yard equals 27 cubic feet.
Which shape should I choose for a tank?
Choose cylinder for a round tank, rectangular prism for a box-shaped tank, or another shape that best matches the inside capacity.
Which shape should I choose for a box?
Use rectangular prism for most boxes and packages. Use cube only when all sides are the same length.
Can this calculator be used for concrete or mulch estimates?
Yes for basic volume math. For project-specific ordering, use the concrete, cubic yard, or square feet to cubic yards calculators.
Are the results exact?
The arithmetic is precise for the values entered, but real objects can have rounded edges, wall thickness, fill limits, or measurement error.