What is the cylinder volume?
Type the radius and height to get the volume, or type the volume and one measurement to get the other.
- Volume
- 141.4 in³
A cylinder with radius 3 in and height 5 in has a volume of 141.4 in³.
Volume: 141.4 in³. A cylinder with radius 3 in and height 5 in has a volume of 141.4 in³.
How to calculate
Finds the volume of a cylinder from its radius and height (V = πr²h), or the radius or height from the volume.
Example with the default inputs (Radius 3 in, Height 5 in): A cylinder with radius 3 in and height 5 in has a volume of 141.4 in³.
Formula: V = πr²h: the area of the circular base, πr², times the height h.
- The cylinder is a right circular cylinder: two equal circles joined by a straight side. An oblique cylinder with the same base and vertical height has the same volume.
- π is the full-precision value 3.141592653589793….
- The radius and height are in the length units shown next to them, and the volume is in the volume unit shown next to it.
- Each value must be greater than 0.
Worked examples
Each example is checked against the calculator on every build.
- Radius 118.1 in, Height 196.9 in gives Volume 8,627,029 in³.Source: OpenStax Prealgebra 2e, Example 9.53 (141.3 with π ≈ 3.14); hand calculation in content.mdx: π × 3² × 5 = 45π = 141.3717
- Radius 157.5 in, Height 511.8 in gives Volume 39,876,043 in³.Source: OpenStax Prealgebra 2e, Example 9.54 (653.12 with π ≈ 3.14); hand calculation in content.mdx: π × 4² × 13 = 208π = 653.4513
- Volume 61,023,744 in³, Height 393.7 in gives Radius 222.1 in.Source: hand calculation in content.mdx: r = √(1000 ÷ (π × 10)) = 5.6419
- Volume 30,511,872 in³, Radius 196.9 in gives Height 250.6 in.Source: hand calculation in content.mdx: h = 500 ÷ (π × 5²) = 6.3662
How it works
A cylinder is a circle of radius r stretched straight up to a height h. Its volume V is the area of the circle times the height:
V = πr²h
Type any two of the three values and the calculator finds the third:
- volume from radius and height: V = πr²h
- radius from volume and height: r = √(V ÷ (πh))
- height from volume and radius: h = V ÷ (πr²)
Assumptions
- The cylinder is a right circular cylinder. An oblique cylinder with the same base and the same vertical height has the same volume.
- π is the full-precision value 3.141592653589793…. Textbooks that use 3.14 get answers about 0.05% smaller.
- Each value is greater than 0.
- Each box has its own unit. Lengths are converted through metres and volumes through cubic metres (1 in = 0.0254 m and 1 US gallon = 231 in³, both exact). In one length unit, the volume is in that unit cubed: radius and height in inches give cubic inches.
Worked examples by hand
Radius 3, height 5 (OpenStax Example 9.53). V = π × 3² × 5 = 45π = 141.3717. The textbook rounds π to 3.14 and gets 141.3.
Radius 4, height 13 (OpenStax Example 9.54). V = π × 4² × 13 = 208π = 653.4513. With π ≈ 3.14 the textbook gets 653.12.
Volume 1,000, height 10. r = √(1000 ÷ (π × 10)) = √31.8310 = 5.6419.
Volume 500, radius 5. h = 500 ÷ (π × 5²) = 500 ÷ 78.5398 = 6.3662.
Other questions people ask
What is the formula for the volume of a cylinder?
V = πr²h. The base is a circle with area πr², and the cylinder is that circle stacked up to height h. A can with radius 3 in and height 5 in holds π × 9 × 5 = 141.37 in³.
How many gallons does a cylindrical tank hold?
Work out the volume, then switch the volume unit to gallons. A tank 2 ft across (radius 1 ft) and 3 ft tall holds π × 1² × 3 = 9.42 ft³. One US gallon is 231 in³ and one cubic foot is 1,728 in³, so that is 9.42 × 1,728 ÷ 231 = 70.5 gallons.
I know the diameter, not the radius. What do I type?
Halve the diameter and type that as the radius. A pipe 10 cm across has a radius of 5 cm.
How do I find the height from the volume?
Divide the volume by the base area: h = V ÷ (πr²). A 500 cm³ cylinder with radius 5 cm is 500 ÷ 78.54 = 6.37 cm tall.
How do I find the radius from the volume?
Divide the volume by π times the height, then take the square root: r = √(V ÷ (πh)). A 1,000 cm³ (1 liter) cylinder 10 cm tall has a radius of 5.64 cm.
Does the formula work for a slanted (oblique) cylinder?
Yes, if h is the vertical height between the two ends, not the length of the slanted side. Sliding the circular layers sideways does not change how much space they fill.