Horizontal Cylinder volume formula
Total volume, exact partial fill, derivation, worked example and a copy-ready fill table.
V = πr²LV(h) = [r²·acos((r−h)/r) − (r−h)·√(2rh−h²)] · Lseg(r,h) = r²·acos((r−h)/r) − (r−h)·√(2rh−h²). All closed-form — spreadsheet-implementable with ACOS and SQRT.Derivation
The wetted cross-section at liquid depth h is a circular segment. Its area follows from the sector swept by the chord (angle θ = 2·acos((r−h)/r), area ½r²θ) minus the triangle above the chord — simplifying to the closed form shown. Multiply by length because every slice along the tank is identical.
Worked example
Take D = 48 in, L = 96 in. Total capacity: 752 gal. At a stick reading of 19.2 in (40% of the 48 in maximum depth), the filled volume is 280.9 gal — 37.4% of capacity. Check it live on the calculator.
| Depth | Volume |
|---|---|
| 5% | 1.9% |
| 10% | 5.2% |
| 15% | 9.4% |
| 20% | 14.2% |
| 25% | 19.6% |
| 30% | 25.2% |
| 35% | 31.2% |
| 40% | 37.4% |
| 45% | 43.6% |
| 50% | 50% |
| 55% | 56.4% |
| 60% | 62.6% |
| 65% | 68.8% |
| 70% | 74.8% |
| 75% | 80.4% |
| 80% | 85.8% |
| 85% | 90.6% |
| 90% | 94.8% |
| 95% | 98.1% |
Need the full inch-by-inch table for specific dimensions? The dip chart generator prints it as a laminate-ready PDF.
FAQ
What is the formula for a horizontal cylinder volume?
Total: V = πr²L. Partial fill at depth h: V(h) = [r²·acos((r−h)/r) − (r−h)·√(2rh−h²)] · L. Derivation and a worked example are above.
Is the fill-ratio table exact?
Yes — computed by the same engine as our calculators (any horizontal cylinder (curve is proportion-independent)), verified by the automated test suite described on the methodology page.
Can I use this in a spreadsheet?
Yes — the formulas are closed-form (acos and sqrt only). Copy the 5%-step table for quick interpolation, or implement the formula directly for exact values.