Cube
Inputs: side
Formula: V = s³
Best for: equal-sided boxes and blocks
Math Calculators
Volume Calculator
Calculate volume for cubes, boxes, cylinders, spheres, cones, pyramids, and prisms with cubic unit conversions.
Last updated: June 2026
Calculate volume
Choose a shape, enter the dimensions, and calculate volume with instant unit conversions.
Choose a shape
Shortcut cards update the fields, diagram, and formula.
Advanced shapes
All dimensions use this measurement unit.
Unit for the final answer and conversions.
Shape preview
Rectangular prism / box
Formula
V = length x width x height
Required inputs
Length, width, height
Enter dimensions in feet. The main answer appears in cubic feet, with conversions below after calculation.
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. For example, floor area uses square feet, while a box or tank capacity uses cubic feet. Use the Area Calculator when you only need a flat surface measurement.
Volume formulas and shape cards
Rectangular prism / box
Inputs: length, width, height
Formula: V = l × w × h
Best for: boxes, rooms, storage, tanks
Cylinder
Inputs: radius, height
Formula: V = π × r² × h
Best for: round tanks, pipes, cans
Sphere
Inputs: radius
Formula: V = 4/3 × π × r³
Best for: balls and round objects
Cone
Inputs: radius, height
Formula: V = 1/3 × π × r² × h
Best for: cones, funnels, tapered forms
Square pyramid
Inputs: base side, height
Formula: V = 1/3 × s² × h
Best for: square-base pyramids
Rectangular pyramid
Inputs: base length, base width, height
Formula: V = 1/3 × l × w × h
Best for: rectangular-base pyramids
Triangular prism
Inputs: triangle base, triangle height, prism length
Formula: V = 1/2 × b × h × length
Best for: wedges and prism shapes
Hemisphere
Inputs: radius
Formula: V = 2/3 × π × r³
Best for: half-spheres and domes
Capsule
Inputs: radius, straight length
Formula: V = pi x r^2 x h + 4/3 x pi x r^3
Best for: capsules and rounded tanks
Tube / hollow cylinder
Inputs: outer radius, inner radius, length
Formula: V = pi x h x (R^2 - r^2)
Best for: pipes, tubes, hollow forms
Conical frustum
Inputs: top radius, bottom radius, height
Formula: V = 1/3 x pi x h x (R^2 + Rr + r^2)
Best for: buckets, tapered containers
Ellipsoid
Inputs: semi-axes a, b, c
Formula: V = 4/3 x pi x a x b x c
Best for: oval solids and rounded forms
| 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 |
| Capsule | Radius or diameter, straight length | V = pi x r^2 x h + 4/3 x pi x r^3 |
| Tube / hollow cylinder | Outer radius, inner radius, length | V = pi x h x (R^2 - r^2) |
| Conical frustum | Top radius, bottom radius, height | V = 1/3 x pi x h x (R^2 + Rr + r^2) |
| Ellipsoid | Semi-axes a, b, c | V = 4/3 x pi x a x b x c |
Volume units explained
Cubic inches
small objects, packages, product dimensions
Useful when dimensions are measured in inches.
Cubic feet
boxes, rooms, tanks, construction forms
Common for U.S. storage and building estimates.
Cubic yards
concrete, mulch, gravel, sand
Common for bulk construction and landscaping materials.
Cubic centimeters
small metric objects
Often aligns with milliliters for small capacities.
Cubic meters
large metric volumes
Common for tanks, rooms, and larger metric estimates.
Liters
liquids and containers
1 cubic meter equals 1,000 liters.
Milliliters
small liquid volumes
1 milliliter equals 1 cubic centimeter.
Gallons
U.S. liquid capacity
Useful for pools, tanks, 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 milliliter = 1 cubic centimeter.
- 1 cubic inch is about 16.387 cubic centimeters.
Liters and gallons are useful for liquids and containers. Cubic units are useful when you start from shape dimensions. The same volume can be expressed either way after conversion.
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.
Shape-specific volume guides
Box Volume
Formula: V = length × width × height
Inputs needed: length, width, height
Example: A 5 ft × 3 ft × 2 ft storage box has volume 5 × 3 × 2 = 30 ft³.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
Cylinder Volume
Formula: V = π × radius² × height
Inputs needed: radius or diameter, height
Example: A cylinder with radius 2 ft and height 10 ft has volume about 125.66 ft³.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
Sphere Volume
Formula: V = 4/3 × π × radius³
Inputs needed: radius or diameter
Example: A sphere with radius 3 in has volume about 113.1 in³.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
Cone Volume
Formula: V = 1/3 × π × radius² × height
Inputs needed: radius or diameter, height
Example: A cone with radius 3 ft and height 9 ft has volume about 84.82 ft³.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
Pyramid Volume
Formula: V = 1/3 × base area × height
Inputs needed: base dimensions, height
Example: A square pyramid with 6 ft base side and 10 ft height has volume 120 ft³.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
Triangular Prism Volume
Formula: V = 1/2 × triangle base × triangle height × prism length
Inputs needed: triangle base, triangle height, prism length
Example: A 6 ft × 4 ft triangle extended 10 ft has volume 120 ft³.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
Advanced Shape Volume
Formula: Capsules, tubes, frustums, and ellipsoids use radius, length, height, or semi-axis inputs.
Inputs needed: advanced dimensions by shape
Example: Use these for rounded tanks, pipes, tapered containers, and oval solids.
Use the Volume Calculator above to switch shapes, units, and converted results quickly.
How to estimate volume for irregular objects
For small waterproof objects, water displacement can estimate volume when no simple shape formula fits.
- Fill a container with enough water.
- Record the starting water level.
- Submerge the object fully if it is safe and waterproof.
- Record the new water level.
- The difference is the object volume.
Avoid this method for objects that dissolve, absorb water, float, or should not get wet.
Real-life uses
Boxes and storage
Estimate how much space a box, bin, shelf, or storage container can hold.
Tanks and containers
Use cylinder or rectangular prism volume, then convert to liters or gallons.
Concrete forms
Estimate slabs, post holes, footings, and forms before using construction-specific tools.
Mulch, gravel, and sand
Use volume with depth to plan bulk landscaping material estimates.
Classroom geometry
Check formulas, units, and worked examples for common 3D shapes.
Using volume for concrete, mulch, gravel, and sand
Volume is often the first step for material planning, but project calculators can add depth, waste, bags, tons, and cubic yard context. Try the Concrete Calculator, Concrete Bags Calculator, Mulch Calculator, Sand Calculator, or Gravel Calculator. For bulk unit planning, use the Cubic Yard Calculator or Square Feet to Cubic Yards Calculator.
A practical measure-to-order workflow
Measure the flat footprint with the Square Footage Calculator when needed, add the planned depth with the Square Feet to Cubic Yards Calculator, then choose the material-specific calculator before ordering.
Treat the result as a planning estimate. Material density, compaction, waste, supplier specifications, delivery limits, and local site conditions can change the quantity you need.
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.
- Treating geometric volume as the final order quantity without checking depth, compaction, waste, and supplier specifications.
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. You can also estimate area-and-depth projects with the Square Feet to Cubic Yards Calculator, Mulch Calculator, or Sand Calculator.
For a room, wall, bed, or other flat footprint, start with the Square Footage Calculator. For bulk stone, use the Gravel Calculator; for small pours, use the Concrete Bags Calculator.
Volume calculator guides
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.
1
Choose the shape you want to calculate.
2
Select the input unit and enter the required dimensions.
3
Choose radius or diameter for round shapes.
4
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 area for rectangles, squares, triangles, circles, trapezoids, parallelograms, and ellipses with formulas and square units.
Calculate Area
Square Footage Calculator
Calculate area for rooms, walls, flooring, paint, concrete, gravel, and material estimates before converting to volume.
Calculate Sq Ft
Unit Converter
Convert between various measurement units.
Convert Units
Cubic Yard Calculator
Calculate cubic yards from length, width, and depth for gravel, sand, concrete, mulch, topsoil, fill, and material orders.
Use Calculator
Square Feet to Cubic Yards Calculator
Convert area plus depth into cubic yards and cubic feet for gravel, sand, concrete, mulch, topsoil, and bulk materials.
Use Calculator
Concrete Calculator
Estimate concrete cubic yards, cubic feet, bags, cost, and overage for slabs, footings, post holes, and small pours.
Estimate Concrete
Concrete Bags Calculator
Estimate 40 lb, 60 lb, 80 lb, and other concrete bag counts for slabs, posts, footings, patios, and walkways.
Estimate Bags
Gravel Calculator
Estimate gravel cubic yards, tons, depth, overage, and cost for driveways, paths, patios, drainage, and landscaping.
Estimate Gravel
Mulch Calculator
Estimate mulch cubic yards, cubic feet, bags, depth, and cost for garden beds, tree rings, paths, and landscaping.
Estimate Mulch
Sand Calculator
Estimate sand cubic yards, tons, bags, depth, and cost for pavers, patios, sandboxes, pool bases, landscaping, and fill.
Estimate Sand
Related Guides
Background reading and explanations related to Volume Calculator.
Volume Calculator Guide: Shapes, Formulas, Units, and Examples
Learn how to use a volume calculator for boxes, cylinders, spheres, cones, prisms, pyramids, and unit checks.
Read Guide
How to Use a Volume Calculator
Follow the step-by-step workflow for choosing a shape, entering dimensions, checking units, and reading cubic results.
Read Guide
Volume Calculator Formulas for Common Shapes
Reference volume formulas for cubes, boxes, cylinders, spheres, cones, prisms, pyramids, and tanks.
Read Guide
How to Calculate Volume Step by Step
Learn manual volume calculation steps with matching units, worked examples, and calculator checks.
Read Guide
Volume of Solids, Tanks, Prisms and Pyramids
Understand practical volume estimates for solids, tanks, containers, prisms, pyramids, and material spaces.
Read Guide
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.
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.
How do I calculate cylinder volume in gallons?
Calculate cylinder volume first, then convert the cubic result to gallons. One cubic foot is about 7.48 US gallons.
How do I find the volume of an L-shaped room?
Split the L shape into two rectangular prisms, calculate each volume separately, then add the results.
How do I calculate swimming pool volume?
Use length, width, and average depth for rectangular pools, or a cylinder-style estimate for round pools. Convert cubic feet to gallons if needed.
How do I convert cubic feet to gallons?
Multiply cubic feet by about 7.48 to estimate US gallons. For example, 10 cubic feet is about 74.8 gallons.
What is the volume of the Earth?
Earth volume is usually estimated with the sphere formula, but Earth is not a perfect sphere. It is about 1.08 trillion cubic kilometers.
How do I find the volume of an irregular object?
For small waterproof objects, water displacement can estimate volume. For larger objects, split the shape into simpler sections.
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.