Checked example
Worked calculation
Result: Volume 603.185789 cm³ and height 12 cm give r = √(603.185789/(12π)) = 4 cm.
01 • Guide
Use the positive root
Algebra produces a squared radius, but physical radius is nonnegative. A positive volume and height yield one positive radius; negative dimensions have no geometric meaning.
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
Other routes to radius
Diameter gives r = d/2, circumference gives r = C/(2π), and base area gives r = √(A/π). Choose the directly measured quantity with the best accuracy.
The calculator validates physical limits before displaying a result. Blank or impossible inputs never produce a stale value, NaN or Infinity.
03 • Guide
Round-trip verification
A useful check is to substitute the derived radius back into πr²h. It should recover the original volume within floating-point and measurement tolerance.
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.