Calculate the volume of a cylinder by entering the radius (or diameter) and height. Results appear instantly in cubic feet, cubic yards, cubic meters, and liters.
The volume of a right circular cylinder is:
V = π × r² × h
Where:
- r = radius of the circular base
- h = height (perpendicular distance between the two bases)
- π ≈ 3.14159
If you know the diameter (d = 2r), the formula becomes:
V = π × (d / 2)² × h
Worked Example
Problem: A cylindrical water tank has a diameter of 10 ft and a height of 8 ft. What is its volume?
Solution:
- Radius = 10 / 2 = 5 ft
- V = π × 5² × 8 = π × 25 × 8 = π × 200
- V ≈ 628.32 ft³
Converting:
- 628.32 ft³ ÷ 27 ≈ 23.27 yd³
- 628.32 × 0.02832 ≈ 17.80 m³
- 628.32 × 28.317 ≈ 17,794 L
Radius vs Diameter
In practice, it is often easier to measure the diameter of a cylinder (the full width across) than the radius. This is especially true for pipes, tanks, and circular containers — you simply run a tape measure across the widest point.
The calculator accepts both: enter the radius and the diameter fills automatically (d = 2r), or enter the diameter and the radius updates (r = d/2).
Common Cylinder Volumes
| Object | Typical Dimensions | Approximate Volume |
|---|
| Standard soup can | d = 2.6 in, h = 4.1 in | 21.8 in³ (0.013 ft³) |
| 55-gallon drum | d = 22.5 in, h = 33.5 in | 13,340 in³ (7.35 ft³) |
| Residential water tank | d = 2 ft, h = 5 ft | 15.71 ft³ (≈ 117 gal) |
| Cylindrical grain silo | d = 18 ft, h = 40 ft | 10,179 ft³ |
Frequently Asked Questions
What is the formula for the volume of a cylinder?
Volume = π × r² × h, where r is the radius of the circular base and h is the height (or length) of the cylinder. Using diameter instead: Volume = π × (d/2)² × h = π × d² × h / 4.
How do I calculate cylinder volume from diameter?
Divide the diameter by 2 to get the radius, then apply the formula: V = π × (d/2)² × h. For example, a cylinder with diameter 10 ft and height 8 ft: r = 5 ft, V = π × 25 × 8 ≈ 628.32 ft³. The calculator does this automatically — just enter the diameter directly.
How many gallons does a cylinder hold?
Multiply the volume in cubic feet by 7.48052 to convert to US gallons. For example, 10 ft³ × 7.48052 ≈ 74.8 gallons. For liters, the calculator already shows the liter result — then multiply by 0.264172 to get US gallons.
How do I find the height of a cylinder given the volume and radius?
Rearrange the formula: h = V / (π × r²). For example, if V = 500 ft³ and r = 4 ft: h = 500 / (π × 16) = 500 / 50.265 ≈ 9.95 ft.
What units can I use in this calculator?
Each dimension accepts feet, inches, yards, centimeters, or meters independently. The calculator converts all values to feet before computing, then displays results in ft³, yd³, m³, and liters.