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Cylinder Volume Calculator

Cylinder volume measures the three-dimensional interior liquid or storage capacity of any cylindrical vessel. This free Cylinder Volume Calculator com

Mathematics
Formula & Methodology
Volume = π × Radius² × Height = πr²h In terms of Diameter: Volume = (π × Diameter² × Height) ÷ 4

To compute cylinder volume: 1. Measure the radius (half the diameter) and square it: r². 2. Multiply by π (approx 3.14159) to find the area of the circular base. 3. Multiply the base area by the cylinder's height (h) to find total internal cubic capacity.

Cylinder Volume

226.1947

Overview

Cylinder volume measures the three-dimensional interior liquid or storage capacity of any cylindrical vessel. This free Cylinder Volume Calculator computes cubic volume from radius and height, providing instant conversions into US gallons and metric liters.

Whether determining hot water tank storage, sizing beer brewing kegs, measuring industrial pipe flow capacities, or verifying chemical drum contents, this tool provides exact volumetric answers.

Worked Examples

Example 1: Tank with Radius = 3 ft, Height = 8 ft

Inputs: Radius = 3, Height = 8

  1. Base Area: π × 3² = 9π ≈ 28.27 sq ft.
  2. Volume: 28.27 × 8 = 226.19 cu ft.
  3. Gallons: 226.19 × 7.48 ≈ 1,692 gallons.
Final Answer: 226.19 cu ft

Example 2: 55-Gallon Drum (Radius 11.5 in, Height 34.5 in)

Inputs: Radius = 11.5, Height = 34.5

  1. Volume: π × (11.5)² × 34.5 ≈ 14,332 cu in.
  2. Gallons: 14,332 ÷ 231 = 62.0 gross gallons.
Final Answer: 14,332 cu in

Example 3: Pipe Section (Radius 1 m, Length 5 m)

Inputs: Radius = 1, Height = 5

  1. Volume = π × 1² × 5 = 5π ≈ 15.708 m³.
  2. Liters = 15.708 × 1,000 = 15,708 liters.
Final Answer: 15.708 cu m

How to Use This Calculator

  1. Enter the internal radius of the cylinder.
  2. Enter the vertical height or length of the cylinder.
  3. Click "Calculate" to view the total volume.
  4. Review the cubic units and fluid conversions below.
  5. Click "Reset" to compute volume for another cylinder.

Reference Table

Radius (r)Height (h)FormulaCubic Volume
11π(1)(1)3.14
24π(4)(4)50.27
38π(9)(8)226.19
410π(16)(10)502.65
512π(25)(12)942.48

Frequently Asked Questions

What is the formula if I only know the diameter?
Divide the diameter by 2 to get the radius (r = d/2), or use V = (π × d² × h) / 4.
How do you convert cubic inches to gallons?
Divide cubic inches by 231 (1 US liquid gallon = 231 cu in).
How do you convert cubic feet to gallons?
Multiply cubic feet by 7.4805 (1 cu ft ≈ 7.48 gallons).
Does the orientation of the cylinder matter (horizontal vs vertical)?
For a completely full cylinder, orientation makes no difference to total volume. For a partially filled cylinder, horizontal tanks require specialized segment calculus.
What happens if you double the radius versus doubling the height?
Doubling the height doubles the volume (2×), but doubling the radius quadruples the volume (4×) because radius is squared.

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Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Computed via exact circular cylinder integration algorithms.