How to use this calculator
- Identify the measurements labelled Total surface area S, Radius r. 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
Total surface area S = 188.495559215; Radius r = 3
Worked example
For Total surface area S = 188.495559215 cm², Radius r = 3 cm, applying the displayed relationship gives radius ≈ 3 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Unrolling the lateral surface gives a rectangle with height h and width 2πr. This explains the lateral area 2πrh. Volume is the base area πr² multiplied by the perpendicular height.
Total surface area here includes two bases. Slanted cylinders and open containers need different surface models. 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.