What This Calculator Does
This tool estimates how much heating oil sits inside a horizontal cylindrical tank — the most common shape for residential basement and outdoor oil tanks. By measuring the depth of oil with a dip stick (the "stick reading") and knowing the tank's diameter and length, you can convert that depth into US gallons without draining or guessing.
How to Use It
Enter three measurements in inches: the tank diameter (the full height of the round end), the tank length (end to end), and the oil fill depth read from your dip stick. The calculator returns gallons in the tank, the total volume in cubic inches and liters, the tank's full capacity, and the percent full.
The Formula Explained
A horizontal cylinder filled partway forms a "circular segment" cross-section. With radius \(r = \text{diameter} \div 2\) and fill depth \(h\), the segment area is \(r^{2}\cdot\arccos\!\left(\frac{r-h}{r}\right) - (r-h)\cdot\sqrt{2rh-h^{2}}\). Multiply by the length \(L\) to get cubic inches, then divide by 231 (cubic inches per US gallon) for gallons. The angle term uses the inverse cosine, which is why a simple "depth ÷ diameter × capacity" estimate is inaccurate near the top and bottom.
$$V_{gal} = \frac{L\left[r^{2}\arccos\!\left(\frac{r-h}{r}\right) - (r-h)\sqrt{2rh - h^{2}}\right]}{231}$$
Worked Example
Suppose a tank is 44 in in diameter, 60 in long, and the oil depth is exactly 22 in (half full). Here \(r = 22\) and \(h = 22\), so \(r-h = 0\). The area becomes $$22^{2}\cdot\arccos(0) = 484\cdot\left(\frac{\pi}{2}\right) = 760.27\ \text{in}^{2}.$$ Times length 60 = 45{,}616 in³, divided by 231 ≈ 197.5 gallons — exactly half of the ~395-gallon full capacity.
FAQ
Why divide by 231? One US liquid gallon is defined as 231 cubic inches.
My tank is oval, not round. This formula assumes a true circular cross-section; oval ("obround") tanks need a different equation and will read slightly off.
Does temperature matter? Oil expands slightly with heat, so volume readings can vary by a percent or two between cold and warm conditions — this calculator reports geometric volume only.
