How to use this calculator
- Identify the measurements labelled Surface area S. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
Surface area S = 314.159265359
Worked example
For Surface area S = 314.159265359 cm², applying the displayed relationship gives radius ≈ 5 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
A central plane cuts the sphere in a great circle of radius r. Surface area is 4πr² and enclosed volume is 4πr³/3. These are ideal spherical relationships, not formulas for an ellipsoid.
A hollow shell’s material volume requires an inner radius as well as an outer radius; this tool models a solid ball. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.