Horizontal tank
Volume of Horizontal Cylinder Calculator
A tank lying on its side needs segment maths, not a simple π r² h. Enter the liquid depth and get the true volume and fill percentage.
A cylinder lying on its side does not fill evenly, so you cannot use π r² h for a partly full one. This volume of horizontal cylinder calculator uses the correct circular-segment maths: enter the liquid depth and it returns the true volume and the fill percentage.
Horizontal tanks are common for fuel and water precisely because they are stable and easy to dip, but that convenience hides awkward geometry: the same rise in depth adds very different volumes near the bottom, middle and top.
The formula behind it
The volume of a cylinder is:
V = π r² hA worked example
Worked example. Take a cylinder with a diameter of 10 cm (so a radius of 5 cm) and a height of 25 cm. The base area is π × 5² = 78.54 cm², and multiplying by the height gives a volume of about 1.96 litres (1,963 cm³ · 0.52 US gallons).
This assumes flat ends and a level tank. Dished (curved) heads add a small amount of extra volume, so the flat-end result is slightly conservative.
Conversions use standard factors: 1 US gallon = 231 in³, 1 Imperial gallon = 4.54609 L, 1 litre = 1000 cm³.
How to work it out
- Measure the inside diameter and the length of the tank.
- Measure the liquid depth straight down from the surface to the bottom.
- The tool finds the filled circular-segment area from that depth.
- It multiplies the segment area by the length for the liquid volume.
- Read the fill percentage and remaining space.
Getting an accurate measurement
Take the depth straight down from the liquid surface to the bottom of the tank. Keep every measurement in the same system, and let the tool convert between units for you.
After you have your answer
Most jobs need one or two more things once the volume lands. The common follow-ups, with the numbers you need, are below:
Does it handle dished ends?
This assumes flat ends. Tanks with curved heads hold a little more, so treat the flat-end figure as a close, slightly conservative estimate.
How do I convert a dip reading to volume?
Measure the depth from the liquid surface to the bottom of the tank and enter it as the liquid depth; the tool converts that dip into a volume using the circular-segment area.
Why isn't half the depth half the volume?
Because a round tank is widest in the middle. At the halfway depth you are at exactly 50%, but above and below that the relationship curves, which is why a chart or this tool is needed.
What is the full capacity?
The result shows both the liquid volume at your depth and the full pi r squared times length capacity, so you can see exactly how much room is left.
Common mistakes to avoid
Two cautions with side-lying tanks: do not assume the depth-to-volume relationship is linear, and take the depth straight down to the lowest point. Curved tank ends hold marginally more than the flat-end estimate.
Getting the number in the unit you need
Showing every unit at once is about speed and safety: you see the answer in litres, gallons and cubic feet side by side, so there is no chance of applying the wrong conversion factor. Change the output unit at the top to make any of them the headline figure, switch the precision to exact if you want the value in terms of pi, and use copy-result to paste a tidy summary wherever you need it.
What to work out next
Once you have your answer you may also want to work in tank capacity gallons hollow tube & pipe. These related calculators pick up where this one leaves off:
Common uses
People reach for this in a range of situations:
- Dipping a horizontal fuel tank and converting depth to volume
- Gauging a side-lying water tank between deliveries
- Estimating remaining product in a cylindrical vessel
In short: measure the width and the height, keep them in the same unit, and the tool turns them into a volume you can read in litres, gallons, cubic feet or anything else, with the working shown so you can trust it. If a result ever looks off, re-enter the measurement you are least sure of, or switch to the diameter input and let the tool halve it for you, which catches the most common error before it matters.
Questions people ask
Why can't I use π r² h for a horizontal tank?
How do I measure the liquid depth?
Does this include dished ends?
What is the formula for the volume of a cylinder?
V = π r² h — the area of the circular base (π r²) multiplied by the height (h). If you have the diameter instead of the radius, halve it first: r = d ÷ 2.