Horizontal Tank Volume Calculator
This horizontal tank volume calculator takes the diameter and length of a cylinder lying on its side and gives the liquid volume from the fill depth, or the depth for a given volume. Vertical tanks work too.
Example: Tank orientation: Horizontal cylinder · What to calculate: Volume from fill depth · Inside diameter of the tank 120 cm · Length (horizontal) or height (vertical) 200 cm · Fill depth (e.g. on the dipstick) 40 cm → Result: 660 litres (29.2 % full). Source: Wikipedia – Kreissegment (Segmentfläche A = r²·arccos((r−h)/r) − (r−h)·√(2rh−h²)). Updated: .
How it is calculated
A horizontal tank 120 cm in diameter and 200 cm long holds 2,262 litres; at a depth of 40 cm it contains about 660 litres. In a horizontal tank the volume does not grow evenly with depth.
How it is calculated
In a horizontal cylinder the liquid fills a circular segment of the circle. Its area is A = r² · arccos((r − h)/r) − (r − h) · √(2rh − h²); times the tank length this gives the volume. In a vertical cylinder it is simply V = π · r² · h. The second mode searches the depth that belongs to your volume (bisection) and shows the fill level and the space still free.
In practice
- Measure the inside diameter, not the outside circumference estimated through wall thickness and insulation.
- Read the dipstick or gauge before topping up and use the calculator to find the remaining amount.
- For heating oil, leave room for expansion and never fill to the brim.
Frequently asked questions
How do you calculate the volume in a horizontal tank?
From the area of the circular segment: A = r² · arccos((r − h)/r) − (r − h) · √(2rh − h²), times the tank length. The calculator does it for you.
Why is a horizontal tank half full at half depth but only about 20 % full at a quarter?
Because the cross-section is narrow at the bottom and widens upwards, the volume does not rise linearly with depth.
How do I get the volume from a dipstick reading?
Measure the depth from the lowest point and enter it in the mode “Volume from fill depth”.
Does it work for tanks with domed ends?
It assumes a plain cylinder. The ends add a little volume, which you can add from the manufacturer's data if needed.
Sources and legal basis
- Wikipedia – Kreissegment (Segmentfläche A = r²·arccos((r−h)/r) − (r−h)·√(2rh−h²))
- Wikipedia – Circular segment
- Wikipedia – Zylinder (Geometrie): Volumen
As of: · Editorial policy
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