Vertical Cylinder volume formula
Total volume, exact partial fill, derivation, worked example and a copy-ready fill table.
V = πr²HV(h) = πr²hseg(r,h) = r²·acos((r−h)/r) − (r−h)·√(2rh−h²). All closed-form — spreadsheet-implementable with ACOS and SQRT.Derivation
Every horizontal slice is the same full circle, so volume is exactly linear in depth — the one tank where gallons-per-inch is a single constant: πr²/231 in inch units.
Worked example
Take D = 48 in, H = 72 in. Total capacity: 564 gal. At a stick reading of 28.8 in (40% of the 72 in maximum depth), the filled volume is 225.6 gal — 40% of capacity. Check it live on the calculator.
| Depth | Volume |
|---|---|
| 5% | 5% |
| 10% | 10% |
| 15% | 15% |
| 20% | 20% |
| 25% | 25% |
| 30% | 30% |
| 35% | 35% |
| 40% | 40% |
| 45% | 45% |
| 50% | 50% |
| 55% | 55% |
| 60% | 60% |
| 65% | 65% |
| 70% | 70% |
| 75% | 75% |
| 80% | 80% |
| 85% | 85% |
| 90% | 90% |
| 95% | 95% |
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 vertical cylinder volume?
Total: V = πr²H. Partial fill at depth h: V(h) = πr²h. Derivation and a worked example are above.
Is the fill-ratio table exact?
Yes — computed by the same engine as our calculators (any vertical cylinder (linear)), 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.