End Cap Volume Calculator

Calculate spherical end cap volume, radius or height, plus dome shell and hollow tube weight using dimensions, wall thickness and material density.

Related Calculators

Dome End Cap Weight

Select Dome shell mass and enter the outer base radius R, outer height H and radial wall thickness t. The model uses concentric spherical surfaces, cut at the same base plane, with an open circular rim. Thickness is measured normal to the sphere. It excludes a flat end plate, flange, straight skirt, welds and coating. Choose a density preset or enter the actual material density.

The outer parent-sphere radius is ρ = (R² + H²)/(2H). The inner radius is ρ − t and the inner cap height is H − t. Using V_cap(ρ,H) = πH²(ρ − H/3), shell material volume is outer cap volume minus inner cap volume. The equivalent expression V_shell = πt[2ρH − (ρ + H)t + (2/3)t²] avoids subtracting nearly equal volumes. The open inner rim requires 0 < t < min(H, R²/H).

Mass = shell volume × density. A hemispherical shell with R = H = 1 m and t = 0.1 m has material volume about 0.567581073 m³, giving about 4,455.511421 kg at 7,850 kg/m³. The result reports mass in kg and lb; gravitational weight is a force. This geometric estimate does not validate pressure rating or model ellipsoidal or torispherical heads.

End Cap Volume Formula

The following formula is used to calculate the volume of a domed end cap modeled as a spherical cap, given the base radius and the cap height.

V = (π H (3R² + H²)) / (6)

Variables:

V is enclosed spherical-cap volume, not shell material volume
π is the constant pi (approximately 3.14159)
R is the circular base radius of the end cap, not the radius of the parent sphere
H is the cap height (measured from the base plane to the top of the dome)

To calculate the end cap volume, multiply pi by the cap height and by (3R² + H²), then divide the result by 6.

What is an End Cap?

An end cap is a component used to close off the end of a cylindrical object, such as a pipe or tube. End caps come in multiple geometries (for example, flat, hemispherical, ellipsoidal, and other domed profiles) and are typically made from materials like metal, plastic, or rubber. This page’s volume formula and calculator specifically model a domed end cap as a spherical cap (a “dome”) using the base radius and dome height.

How to Calculate End Cap Volume?

The following steps outline how to calculate the End Cap Volume.

First, determine the base radius of the end cap (R).
Next, determine the cap height of the end cap (H).
Next, calculate the volume using the formula V = πH(3R² + H²) / 6.
Finally, convert the volume to the desired unit. The separate material mode estimates a straight hollow tube only, excluding a dome or plate; its density presets are approximate.
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Radius of the end cap (R) = 5 m

Height of the end cap (H) = 10 m