Checked example
Worked calculation
Result: For r = 1 m, L = 3 m and y = 1 m, the tank is half full: V = 1.5π ≈ 4.71239 m³.
01 • Guide
The fill curve is nonlinear
Equal increases in depth do not add equal volumes. Near the bottom the liquid is narrow; near mid-depth it spans almost the full diameter. The live graph shows this S-shaped relation.
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
Endpoint handling
At depth zero the result is exactly empty. At depth 2r it is exactly full. The implementation handles those endpoints directly and clamps tiny floating-point roundoff inside the square root and arccosine.
The calculator validates physical limits before displaying a result. Blank or impossible inputs never produce a stale value, NaN or Infinity.
03 • Guide
Assumptions to verify
The tank must be level, have a constant circular section and use internal measurements. Elliptical sections, dished heads and tilted installation need a vessel-specific calibration chart.
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.