Hollow Cylinder Volume Calculator

A hollow cylinder (tube or pipe) has material between an outer and inner radius.

How the Math Works

The volume of a hollow cylinder is calculated using the formula V = πh(R² - r²), where R is the outer radius, r is the inner radius, and h is the height. This formula subtracts the volume of the empty inner cylinder from the total volume of the solid outer cylinder. First, we square both radii and find their difference, which gives the cross-sectional area of the 'walled' portion. Multiplying by π and the height gives the complete volume. The units for all measurements should be consistent (e.g., all in inches or all in centimeters) to ensure the result is accurate.

Practical Applications

To use this calculator practically, measure the outer and inner diameters of your pipe or hollow cylinder, then divide each by 2 to get the radii. Measure the height or length of the cylinder as well. Enter these three measurements into the calculator. This is commonly used in construction when determining how much material (like concrete, metal, or plastic) is needed for a cylindrical structure, or when calculating the capacity of pipes and tubes for fluid transport.

Day-to-Day Use

This calculation helps in everyday situations like determining how much water a garden hose can hold, calculating the amount of concrete needed for a cylindrical foundation, or figuring out how much material is required for DIY projects involving pipes. It's also useful for comparing insulation efficiency between different pipe thicknesses, or when upgrading plumbing systems to ensure new pipes can handle the required flow volume. Students also use this when working on geometry homework or science fair projects involving volume calculations.

Worked example

Outer 5, inner 3, height 10 → π·10·(25 − 9) ≈ 502.65.

FAQ