Checked example
Worked calculation
Result: With radius 2 cm and total area 150.796 cm², the derived height is 10 cm and volume is 125.664 cm³.
01 • Guide
Two valid inverse modes
If radius is known, isolate h with a linear rearrangement. If height is known, solve the quadratic in r. The calculator offers both modes and rejects a surface area too small to contain the two circular ends.
Keep the full precision of intermediate values and round only the final display. This avoids compounding error when a derived radius or converted unit is used in another step.
02 • Guide
Total versus lateral area
Total surface area includes both bases and the curved side. A label or open pipe may specify lateral area only, 2πrh; substituting that into the total-area formula gives the wrong dimensions.
The calculator validates physical limits before displaying a result. Blank or impossible inputs never produce a stale value, NaN or Infinity.
03 • Guide
Why one number is insufficient
Many cylinders share the same total surface area. A short wide cylinder and a tall narrow cylinder can use equal material while holding different volumes, so a second measurement is essential.
Interpretation
How to use the result responsibly
The answer models an ideal geometric cylinder. Manufacturing tolerances, wall thickness, rounded ends, deformation, tank tilt and measurement uncertainty can all shift a real value. Use inside dimensions for capacity and outside dimensions for occupied space. For safety, compliance, dosing, structural or purchasing decisions, compare the estimate with drawings, calibration data or a qualified professional.
Dimensional checks help catch mistakes: a volume result must carry cubic units, an area result square units and a derived radius or height linear units. If changing one unit alters the represented physical size, a conversion step was missed.