How to calculate volume: core mathematical formulas
Volume measures the three-dimensional space occupied by a solid object or liquid container. The formula depends directly on the geometric shape:
| Shape | Standard Volume Formula | Required Measurements | Example (Inputs: 10, 5, 4 ft) |
|---|---|---|---|
| Rectangular Prism / Box | V = Length × Width × Height | Length, Width, Height | 10 × 5 × 4 = 200 ft³ |
| Cylinder | V = π × r² × Height | Radius, Height | π × 3² × 8 = 226.19 ft³ |
| Sphere | V = (4/3) × π × r³ | Radius | (4/3) × π × 5³ = 523.60 m³ |
| Cone | V = (1/3) × π × r² × Height | Base Radius, Height | (1/3) × π × 3² × 6 = 56.55 ft³ |
| Square / Rectangular Pyramid | V = (1/3) × L × W × Height | Base Length, Base Width, Height | (1/3) × 6 × 6 × 9 = 108 ft³ |
Common volume unit conversion cheat sheet
When measuring spaces, units often need to be converted between solid measurements (cubic feet, cubic yards) and liquid capacities (liters, gallons):
- 1 Cubic Foot (ft³) = 1,728 cubic inches (in³) = 0.03704 cubic yards (yd³) = 28.3168 Liters = 7.4805 US Gallons.
- 1 Cubic Yard (yd³) = 27 cubic feet (ft³) = 764.55 Liters = 201.97 US Gallons. (Essential for ordering ready-mix concrete, gravel, and bulk topsoil).
- 1 Cubic Meter (m³) = 1,000 Liters = 35.3147 cubic feet = 264.172 US Gallons.
- 1 US Gallon = 231 cubic inches = 0.13368 cubic feet = 3.7854 Liters.
Frequently asked questions about calculating volume
How do I find the volume if I only have diameter instead of radius?
The radius is always half of the diameter (r = Diameter ÷ 2). For example, if a cylindrical tank has an internal diameter of 6 feet, its radius is 3 feet. Plug 3 feet into the cylinder volume equation: π × 3² × Height.
How do I calculate the volume of an irregular shape?
For complex architectural rooms or landscaping beds, break the shape down into smaller rectangular sections, calculate the volume of each individual box, and sum them together. For irregular solids in science, use the water displacement method: submerge the object in a graduated cylinder and measure the volume change in milliliters.
How many bags of concrete or soil make 1 cubic yard?
One cubic yard equals 27 cubic feet. If using standard 2 cubic foot bags of soil, you need 14 bags (13.5 rounded up). For 60 lb bags of concrete (which yield approx 0.45 ft³), you need 60 bags to yield one cubic yard.
Created and formula-tested by Velour Trends · Updated 9 November 2026. Certified geometric standards. Report a calculation issue.