Math
Sphere volume and surface area
Find the surface area and volume of a sphere.
Calculators / Math / Spherical shell
Spherical shell calculator
Find the material volume between two concentric spherical surfaces.
On this page
Shell volume255.52units³
Outer surface area314.16units²
Wall thickness1units
Calculator controls
How to calculate
Find the material volume between two concentric spherical surfaces.
Shell volume =
4*pi*(R^3-r^3)/3 units³Outer surface area =
4*pi*R^2 units²Wall thickness =
R-r unitsWorked example
- Outer radius: 5
- Inner radius: 4
- Shell volume: 255.52 units³
- Outer surface area: 314.16 units²
- Wall thickness: 1 units
Assumptions and limits
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. Inner radius must be smaller than outer radius.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the material volume between two concentric spherical surfaces. Use concentric inner and outer radii; a displaced cavity cannot be described by this uniform-thickness model.
When this tool is useful
Use concentric inner and outer radii; a displaced cavity cannot be described by this uniform-thickness model.
Understanding your inputs
| Input | Example |
|---|---|
Outer radius R | 5 |
Inner radius r | 4 |
Frequently asked questions
Which assumptions matter for this result?
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. Inner radius must be smaller than outer radius.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.