Volume Calculator
11 shapes · Formulas · Liters · m³ · Gallons
📦 Choose a shape and enter dimensions to compute volume.
Core Volume Formulas
Volume measures three dimensional space. For solids with known geometry, closed form formulas give exact results once every length uses the same unit.
Sphere and cylinder
Cone and square pyramid
What This Calculator Includes
- 11 shapes: sphere, cube, box, cylinder, cone, square pyramid, capsule, frustum, ellipsoid, tube, spherical cap
- Unit picker: mm, cm, m, in, ft for inputs
- Conversions: m³, liters, cm³, in³, ft³, US gallons
- Formula strip and step by step substitution
- Chart comparing scaled unit values
What Is a Volume Calculator?
A volume calculator finds how much space a three dimensional object occupies or how much a container can hold. The SI unit is the cubic meter. Everyday work also uses liters, cubic centimeters, cubic inches, cubic feet, and gallons.
Students use it for geometry homework. Builders and shoppers use it for tanks, packing, concrete, and shipping. The same formulas appear in science labs whenever density and mass are related through volume.
How to use this tool
- Select a shape tab.
- Choose the length unit for your measurements.
- Enter every required dimension (radius, height, edges, and so on).
- Read the volume in your unit cubed, then scan the conversion table.
Worked examples
Cylinder with r = 3 cm and h = 5 cm: V = π×3²×5 = 45π ≈ 141.372 cm³ ≈ 0.141 liters.
Sphere with r = 2 in: V = (4/3)π×8 ≈ 33.510 in³. Convert with 1 in³ ≈ 16.387 cm³ if you need metric output.
Box 4 ft × 3 ft × 2 ft: V = 24 ft³. One cubic foot is about 28.317 liters, so this holds roughly 679 liters of capacity if used as a tank.
Shape formula reference
| Shape | Formula |
|---|---|
| Sphere | V = (4/3)πr³ |
| Cube | V = a³ |
| Rectangular box | V = lwh |
| Cylinder | V = πr²h |
| Cone | V = (1/3)πr²h |
| Square pyramid | V = (1/3)a²h |
| Capsule | V = πr²h + (4/3)πr³ |
| Conical frustum | V = (1/3)πh(r² + rR + R²) |
| Ellipsoid | V = (4/3)πabc |
| Tube | V = π(D² − d²)L/4 |
| Spherical cap | V = (1/3)πh²(3R − h) |
Common unit conversions
1 m³ = 1,000 L. 1 L = 1,000 cm³. 1 ft³ ≈ 28.3168 L. 1 US gallon ≈ 3.785 L. This page converts through cubic meters using standard length factors (1 in = 0.0254 m, 1 ft = 0.3048 m).
Sphere, cube, and box details
A sphere uses only the radius. Doubling the radius multiplies volume by eight because the formula cubes r. A cube uses one edge. A rectangular box (also called a rectangular prism or tank) multiplies three independent edges.
Example: a cube with edge 10 cm has volume 1,000 cm³, which is exactly one liter. That link between cm³ and liters is why metric kitchen and lab measuring is convenient.
Cylinder, cone, and pyramid
Right circular cylinders appear as cans, pipes (when solid), and tanks. Cones appear as funnels and party hats. Square pyramids appear in architecture models and packaging. The shared one third factor for cones and pyramids is easy to forget on tests.
Example: cylinder r = 4, h = 10 → V = 160π. Matching cone → V = (160π)/3. The cone holds one third as much as the cylinder.
Capsule, frustum, ellipsoid, tube, and cap
A capsule joins a cylinder with two hemispheres, equal to one full sphere plus the cylinder. A conical frustum is a truncated cone, common for buckets and lampshades. An ellipsoid generalizes the sphere with three semi axes. A tube subtracts an inner cylinder from an outer one. A spherical cap is the slice cut from a sphere by a plane.
Density link
When density is uniform, mass = density × volume. After you know volume in m³ or cm³, multiply by density in matching units to estimate mass. This page does not solve density problems directly, but the volume result is the starting point.
How to calculate volume manually
Identify the solid. Write the matching formula. Substitute numbers with consistent units. Multiply powers carefully (r² means r times r). Then convert if needed: for example divide cm³ by 1,000 to get liters.
Common mistakes
- Using diameter where the formula needs radius (divide diameter by 2 first)
- Mixing units inside one calculation
- Forgetting the 1/3 factor on cones and pyramids
- Treating a hollow tube as a solid cylinder
- Entering a spherical cap height larger than the sphere diameter
Practical scenarios
Garden soil bags are often sold by cubic feet or liters. A raised bed that is 8 ft long, 4 ft wide, and 1 ft deep needs 32 ft³ of fill before settling. Convert with this calculator by choosing the box shape and feet as the unit.
A water cooler jug near 5 US gallons is about 0.019 m³. A workshop dust collection pipe can be modeled as a tube once you know outer diameter, inner diameter, and run length. Classroom labs often ask for sphere and cylinder volumes back to back so students see how the formulas differ by only a height factor or a 4/3 factor.
When this calculator is useful
Use it for tanks, pipes, packaging, 3D print estimates, classroom geometry, and quick capacity checks. Pair it with the Triangle Calculator, Square Footage Calculator, and Conversion Calculator when area or unit conversion is the next step.
When results may not fit
Irregular solids without a known formula need displacement methods, CAD mesh volume, or calculus. Tapered real world tanks may only approximate a frustum. Always verify which radius or diameter a drawing labels.
Calculation Methodology
- Read the selected shape and length unit.
- Convert every input length to meters.
- Apply the closed form volume formula in cubic meters.
- Convert m³ to the display unit cubed and to liters, cm³, in³, ft³, and US gallons.
- Show the algebraic formula with your substituted numbers.
Quick Capacity Examples
| Object | Inputs | Volume |
|---|---|---|
| Sphere | r = 5 cm | ≈ 523.6 cm³ |
| Cube | a = 10 cm | 1,000 cm³ = 1 L |
| Cylinder | r=3, h=5 cm | ≈ 141.4 cm³ |
| Cone | r=3, h=6 cm | ≈ 56.5 cm³ |
Live results update as you change tabs and inputs.
Frequently Asked Questions
Sources & References
- NIST — SI Units: Volume / Liter relationships via meter definitions
- Standard solid geometry texts for sphere, cylinder, cone, pyramid, frustum, and ellipsoid formulas
- NIST Handbook / common conversion: 1 in = 0.0254 m exactly; 1 L = 0.001 m³
Last reviewed for methodology: 2026. Formulas assume ideal right circular and right square based solids unless noted.