Volume Calculator (All Shapes)
Calculate volume for any 3-D shape — rectangular prism, cylinder, cone, sphere, pyramid — with unit conversion between cubic feet, yards, meters, gallons, and liters.
Volume Calculator (All Shapes)
Enter project dimensions below — results update instantly. Switch units freely.
Estimates assume typical industry density and waste factors. Always verify with your supplier and local building code before purchasing material.
Why Volume Is Trickier Than Area
Area is 2D: length × width. Volume is 3D: length × width × depth — but that only works for boxes. For cylinders, spheres, cones, and irregular shapes, the formulas get more involved.
Common construction 3-D shapes and their formulas:
- Rectangular prism / box: V = L × W × H (slabs, walls, beams)
- Cylinder: V = π × r² × h (sonotubes, columns, tanks, pipes)
- Cone: V = (1/3) × π × r² × h (gravel piles, funnels)
- Pyramid: V = (1/3) × L × W × H (hip roof voids, pyramidal forms)
- Sphere: V = (4/3) × π × r³ (spherical tanks, dome volumes)
- Hemisphere: V = (2/3) × π × r³ (domes, round-bottom tanks)
For irregular 3-D shapes, decompose into combinations of these primitives.
Volume Formula Cheat Sheet
Cylinder: V = π × r² × h
Cone: V = (1/3) × π × r² × h
Sphere: V = (4/3) × π × r³
Pyramid: V = (1/3) × L × W × H
Construction volume conversions:
- 1 ft³ = 7.48 US gallons = 28.32 liters
- 1 yd³ = 27 ft³ = 202 US gallons = 765 liters
- 1 m³ = 1.308 yd³ = 35.3 ft³ = 264 gallons
- 1 gallon = 0.134 ft³ = 3.785 liters
| Shape | Formula | Example (5-unit dims) | Volume (units³) |
|---|---|---|---|
| Cube | s³ | 5³ | 125 |
| Rectangular prism | L × W × H | 5 × 5 × 5 | 125 |
| Cylinder | π × r² × h | π × 2.5² × 5 | 98.17 |
| Cone | (1/3) × π × r² × h | (1/3) × π × 2.5² × 5 | 32.72 |
| Sphere | (4/3) × π × r³ | (4/3) × π × 2.5³ | 65.45 |
| Hemisphere | (2/3) × π × r³ | (2/3) × π × 2.5³ | 32.72 |
| Pyramid (square base) | (1/3) × s² × h | (1/3) × 5² × 5 | 41.67 |
| Frustum (truncated cone) | (π × h) × (r1² + r1r2 + r2²) / 3 | — | varies |
For truncated cones (frustums): V = (π × h / 3) × (R² + R × r + r²) where R = large radius, r = small radius.
| From | To ft³ | To yd³ | To m³ | To gallons (US) |
|---|---|---|---|---|
| 1 in³ | 0.000579 | 0.0000214 | 0.0000164 | 0.004329 |
| 1 ft³ | 1 | 0.03704 | 0.02832 | 7.481 |
| 1 yd³ | 27 | 1 | 0.7646 | 201.97 |
| 1 m³ | 35.31 | 1.308 | 1 | 264.17 |
| 1 gallon (US) | 0.1337 | 0.00495 | 0.003785 | 1 |
| 1 liter | 0.03531 | 0.001308 | 0.001 | 0.264 |
US gallons differ from UK gallons (1 UK gallon = 1.2 US gallons). Always specify units internationally.
Real-World Example Calculations
Rectangular Pool 10 × 20 × 5 ft
Small rectangular in-ground swimming pool water capacity.
- Length × Width
- 20 × 10 ft
- Depth (avg)
- 5 ft
Takeaway: Straightforward box calculation. Pool water treatment dosing scales with gallons.
Cylindrical Water Tank 6 ft dia × 10 ft tall
Residential water storage tank volume.
- Diameter
- 6 ft
- Height
- 10 ft
Takeaway: π × 3² × 10 = 282.7 ft³. Used for rural off-grid water storage, irrigation tanks.
Gravel Pile (Cone) 12 ft dia × 6 ft tall
Cone-shaped pile of delivered gravel after dumping.
- Diameter
- 12 ft
- Height
- 6 ft
Takeaway: (1/3) × π × 6² × 6 = 226 ft³. Common method for estimating remaining gravel in a pile from known dimensions.
Frequently Asked Questions
How do I calculate volume of a cylinder?
V = π × r² × h. Radius is half the diameter. Example: 8-in diameter × 3-ft sonotube: radius = 4 in = 0.333 ft, volume = π × 0.333² × 3 = 1.05 ft³.
How do I calculate volume of a sphere?
V = (4/3) × π × r³. Example: 6-ft diameter sphere: radius = 3 ft, volume = (4/3) × π × 27 = 113 ft³. Spheres have the largest volume per surface area of any shape.
How many gallons in a cubic foot?
7.48 US gallons per cubic foot. Reverse: 1 gallon = 0.134 ft³. Useful for pool, tank, and irrigation calculations.
How do I calculate volume of a cone?
V = (1/3) × π × r² × h. A cone has exactly 1/3 the volume of a cylinder with the same radius and height. For gravel pile estimating: measure diameter, measure height, apply formula.
How many cubic feet in a cubic meter?
One cubic meter = 35.31 cubic feet. One cubic yard = 0.7646 m³. Always specify units when working with metric plans from international sources.
What's the volume of an irregular container?
Two approaches: (1) Decompose into simple shapes — boxes, cylinders, cones — and sum. (2) Water displacement — fill with water, measure water volume (for smaller containers up to 5-10 gallons). Scale-model pool or tank estimates often use both.
How accurate do volume calculations need to be?
For bulk materials (concrete, aggregate, mulch): ±2-3% accuracy. For tanks and pressure vessels: ±0.5-1%. For engineered structures: per spec, often ±0.1-0.5%. More precision requires more careful measurement of dimensions.