Horizontal Cylinder Partial Fill Calculator

Method, example, and limits

Formula: Segment area A = r² arccos((r − h)/r) − (r − h)√(2rh − h²); volume = A L.

Inputs and units: r is internal radius, L is cylindrical length, and h is liquid depth from the bottom. Volume and capacity are in cubic units matching the lengths.

Worked example: With radius 1 m, length 5 m, and depth 0.5 m, segment area is about 0.614185 m² and liquid volume is about 3.070924 m³ of a 15.707963 m³ cylinder.

Assumptions: The cylinder is level, has constant circular cross-section and flat ends, and 0 ≤ h ≤ 2r. A depth halfway up the diameter corresponds to half the capacity.

Limits: Excludes end caps, dished heads, internal hardware, tilt, and deformation. Near empty/full levels, small depth measurement errors can create proportionally large volume errors.