Cone-Bottom Tank volume formula
Total volume, exact partial fill, derivation, worked example and a copy-ready fill table.
V = πr²Hcone/3 + πr²Hcylh≤Hcone: V = π(r·h/Hcone)²·h/3 | h>Hcone: V = Vcone + πr²(h−Hcone)seg(r,h) = r²·acos((r−h)/r) − (r−h)·√(2rh−h²). All closed-form — spreadsheet-implementable with ACOS and SQRT.Derivation
Inside the cone the wetted radius grows linearly with depth, so volume grows with the cube of depth — which is why the bottom of a cone tank holds almost nothing. Above the knuckle it switches to plain cylinder math. At 40% depth this representative tank holds only 25.9% of its volume.
Worked example
Take D = 48 in, Hcyl = 60 in, Hcone = 24 in. Total capacity: 532.7 gal. At a stick reading of 33.6 in (40% of the 84 in maximum depth), the filled volume is 137.9 gal — 25.9% of capacity. Check it live on the calculator.
| Depth | Volume |
|---|---|
| 5% | 0.1% |
| 10% | 0.5% |
| 15% | 1.7% |
| 20% | 4% |
| 25% | 7.9% |
| 30% | 13.5% |
| 35% | 19.7% |
| 40% | 25.9% |
| 45% | 32.1% |
| 50% | 38.2% |
| 55% | 44.4% |
| 60% | 50.6% |
| 65% | 56.8% |
| 70% | 62.9% |
| 75% | 69.1% |
| 80% | 75.3% |
| 85% | 81.5% |
| 90% | 87.6% |
| 95% | 93.8% |
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 cone-bottom tank volume?
Total: V = πr²Hcone/3 + πr²Hcyl. Partial fill at depth h: h≤Hcone: V = π(r·h/Hcone)²·h/3 | h>Hcone: V = Vcone + πr²(h−Hcone). Derivation and a worked example are above.
Is the fill-ratio table exact?
Yes — computed by the same engine as our calculators (cone height = D/2, shell = 1.25×D), 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.