Volume Calculator
Fast, accurate 3D volume calculations with step-by-step mathematical substitution, live geometric diagrams, and instant US customary & metric unit conversions.
The base of a right cylinder is a flat circular disk with area equal to π multiplied by the radius squared.
Multiplying the circular base area by the perpendicular height yields the 3D interior volume.
Volume measures the quantity of three-dimensional space enclosed by an object. For standard rectangular prisms, volume is Length × Width × Height. For cylinders, it is π × r² × h. For cones and pyramids, volume is one-third of the base area times height (⅓ × Base × Height). For spheres, volume is ⁴⁄₃ × π × r³. One cubic foot holds 7.48 US liquid gallons.
All Volume Calculators by Shape & Project
Cans, rods, pipes, vertical tanks
Boxes, crates, rooms, aquariums
Funnels, conical piles, party hats
Balls, globes, spherical tanks
Equal-sided blocks, dice, containers
Square, rectangular, triangular bases
Ramps, wedges, roof attics
Domes, bowls, igloos, end caps
Propane tanks, pills, pressure vessels
Tapered buckets, flower pots, cups
Horizontal & vertical liquid tanks
Slabs, footings, Sonotubes, bags
What is Volume? Definitions, Units & Physical Principles
In geometry and physics, volume is the scalar quantity that describes how much three-dimensional space is bounded by a closed surface. Everything with physical mass in the universe displaces volume.
1D: Length
One-dimensional straight distance along an edge (inches, feet, meters).
2D: Surface Area
Two-dimensional surface boundary enclosing the shape (sq ft, cm², m²).
3D: Volume
Total three-dimensional internal space enclosed (cubic feet, gallons, liters).
Universal Volume Units & Conversion Factors (NIST SP 811)
Exact mathematical conversion constants verified against the National Institute of Standards and Technology Special Publication 811.
| Starting Unit | Symbol | Equivalent in Cubic Meters (m³) | Equivalent in US Gallons |
|---|---|---|---|
| Cubic Meter (SI Base) | m³ | 1.0 m³ (exact) | 264.172 gal |
| Liter (Metric Accepted) | L | 0.001 m³ (exact) | 0.264172 gal |
| Cubic Foot (US Customary) | ft³ | 0.0283168 m³ | 7.48052 gal |
| Cubic Yard | yd³ | 0.764555 m³ | 201.974 gal |
| US Liquid Gallon | gal | 0.0037854 m³ | 1.0 gal (231 in³) |
| Cubic Inch | in³ | 0.000016387 m³ | 0.004329 gal |
Volume Formulas Reference Cheat Sheet
| 3D Shape | Mathematical Formula | Variables Key | Calculator |
|---|---|---|---|
| Cylinder | V = π r² h | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Rectangular Box | V = L × W × H | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Cone | V = ⅓ π r² h | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Sphere | V = ⁴⁄₃ π r³ | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Cube | V = s³ | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Pyramid | V = ⅓ A_base h | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Triangular Prism | V = ½ b h_t L | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Hemisphere | V = ⅔ π r³ | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Capsule | V = π r² a + ⁴⁄₃ π r³ | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
| Frustum | V = ⅓ π h (R² + r² + Rr) | r=radius, h=height, s=side, L=length, W=width | Open Tool → |
Worked Calculation Examples
Example 1: Sizing a Garden Raised Bed (Box / Rectangular Prism)
A raised garden bed measures 8 feet long, 4 feet wide, and 1.5 feet deep.
Example 2: Liquid Capacity of a Cylindrical Water Rain Barrel
A rain collection barrel has a 24-inch diameter (radius = 12 in) and stands 36 inches tall.
Example 3: Volume of a Spherical Tank
A spherical gas storage vessel has a radius of 2.0 meters.
How to Measure the Volume of Irregular 3D Objects
Physical objects such as rocks, tools, sculptures, and fasteners do not conform to tidy geometric formulas. The universally accepted scientific method for measuring irregular volume is Archimedes’ Water Displacement Method:
- Take a container with marked volume gradations (such as a graduated cylinder or measuring cup) and fill it with sufficient water to fully submerge the object.
- Record the initial baseline water level (V_initial).
- Gently lower the dry object completely underwater, ensuring no air bubbles cling to its crevices.
- Record the elevated water level (V_final).
- Calculate volume: V_object = V_final - V_initial. (e.g., 500 mL water rising to 680 mL indicates an object volume of 180 cm³ / 180 mL).
Frequently Asked Questions About Volume
What is volume and how is it measured?▼
How do you calculate the volume of any 3D shape?▼
How many gallons are in a cubic foot of water?▼
What is the difference between volume and capacity?▼
How do you convert cubic inches to US gallons?▼
How many cubic feet are in a cubic yard?▼
How do you measure the volume of an irregular object?▼
Why does doubling an object’s dimension increase its volume by eight times?▼
What is the formula for the volume of a cylinder?▼
How do you find the volume of a box?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- The International System of Units (SI Brochure, 9th edition) — Bureau International des Poids et Mesures (BIPM). Verified 2026-10-01.
International metric definitions for derived units of volume (cubic meter and non-SI unit accepted for use: liter).
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.