How it’s calculated
Vertical cylinders and rectangular tanks fill linearly: the liquid volume is the base area times the depth. A horizontal cylinder does not, because the liquid's cross-section is a circular segment.
Example (horizontal): r = 1 m, L = 3 m, depth 0.5 m. A = 1 × arccos(0.5) − 0.5 × √(1 − 0.25) = 1.0472 − 0.4330 = 0.6142 m², so V = 1.8426 m³ ≈ 1,843 L, only 19.5% of the 9,425 L capacity even though it is 25% of the depth.
Real tanks may have domed or dished ends, internal fittings or sloped bottoms. Treat results as estimates.
Frequently asked questions
Why is a horizontal tank half full at half depth, but not a quarter full at quarter depth?
The tank is narrow at the bottom and widest in the middle, so each inch of depth near the bottom holds less liquid than an inch near the centre. Only at exactly half depth is it half full.
How do I measure liquid depth?
Lower a clean stick or tape to the bottom of the tank through the fill opening, then read the wet mark.
Does this include domed tank ends?
No. It assumes flat ends. Domed or elliptical heads add extra volume; check the manufacturer’s capacity chart for exact figures.
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Sources
- Horizontal Cylindrical Segment — Wolfram MathWorld
- Circular Segment — Wolfram MathWorld
- Prealgebra 2e, 9.6 Solve Geometry Applications: Volume and Surface Area — OpenStax
- NIST Handbook 44, Appendix C: Units of Measurement — U.S. National Institute of Standards and Technology
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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