Horizontal Cylindrical Tank Volume Calculator
Work out the volume and capacity of a horizontal cylinder tank — one lying on its side — in US gallons, imperial gallons, litres, cubic feet and cubic metres. Enter the diameter and length for the total capacity, or turn on partial fill to find the volume of liquid at a given depth using exact circular-segment math.
Tank volume calculator
How to calculate horizontal cylindrical tank volume
A horizontal cylindrical tank holds exactly the same total volume as the same cylinder stood upright — orientation does not change full capacity. The total volume of a horizontal cylindrical tank is the circular end area multiplied by the length:
where r is the inside radius (half the diameter) and L is the length of the cylinder. So the only thing that makes a horizontal tank different is what happens when it is partially filled.
The horizontal cylindrical tank volume formula (partial fill)
When a cylinder lies on its side, the liquid surface cuts a horizontal chord across the round cross-section. The wetted area is a circular segment, not a simple fraction of the height. For a liquid depth h measured from the bottom of a tank of radius r, the segment area is:
The filled volume of liquid in a horizontal cylinder is then that area multiplied by the length:
The arccosine is evaluated in radians. An equivalent and numerically identical way to write the same segment area is A = ½ r² (θ − sin θ) with θ = 2 · arccos((r − h) / r); the calculator on this page uses that form internally. For the full derivation and the sources behind every formula on this site, see the methodology page.
Worked example
Take a horizontal cylinder tank with a diameter of 4 ft (so r = 2 ft) and a length of 8 ft.
- Total volume: V = π × 2² × 8 = 100.53 ft³. At 7.48052 US gallons per cubic foot, that is about 752 US gallons (≈ 626 imperial gallons, ≈ 2,847 litres).
- Half full (liquid depth = 2 ft = r): a horizontal cylinder is exactly half full at half the diameter, so the volume is precisely half of the total — about 376 US gallons.
- Quarter depth (liquid depth = 1 ft): using the segment formula, A = 2² × arccos((2 − 1) / 2) − (2 − 1) × √(2×2×1 − 1²) = 4 × 1.0472 − 1 × √3 = 4.189 − 1.732 = 2.457 ft². Times the 8 ft length gives 19.66 ft³ ≈ 147 US gallons — noticeably less than a quarter of the full 752 gallons, which is exactly why partial-fill depth and volume are not proportional.
Enter these numbers in the calculator above to confirm the figures and to read off imperial gallons, litres, cubic feet and cubic metres at the same time.
Reading a horizontal tank volume chart
Because the filled volume follows a circular segment, a horizontal tank volume chart — the depth-to-gallons table you read with a dipstick — is curved rather than evenly spaced. Near the bottom and top of the tank, an inch of depth adds relatively little liquid; near the middle, the same inch adds the most. To build a chart for your own tank, enter its diameter and length above, then switch on partial fill and step the liquid level through each depth you care about. This is the same reason heating-oil dipstick charts are non-linear — see our heating oil tank charts for ready-made 275- and 330-gallon tables.
Units and gallons
This is a horizontal tank volume calculator in gallons and every other common unit at once: US gallons, imperial (UK) gallons, litres, cubic feet and cubic metres, plus optional petroleum barrels. One US liquid gallon is 231 cubic inches ≈ 3.785 litres, while one imperial gallon ≈ 4.546 litres, so the calculator shows both to avoid ambiguity. Enter inside dimensions for the closest estimate of liquid capacity.
Vertical instead of horizontal?
If your cylinder stands upright on its end, partial fill is linear and the math is simpler. Use the vertical cylindrical tank volume calculator for that case, or the main tank volume calculator for capsule, rectangular, oval, elliptical and cone-shaped tanks.
Frequently asked questions
How do you calculate the volume of a horizontal cylindrical tank?
For total volume, a horizontal cylinder is the same as any cylinder: V = π × r² × L, where r is the inside radius and L is the length. Orientation does not change the full capacity. What changes is partial fill: when the tank is lying on its side, the liquid forms a circular segment, so you need the segment area times the length rather than a simple proportion of height.
How do I find the volume of liquid in a partially filled horizontal cylinder?
Measure the liquid depth from the bottom of the tank. The filled cross-section is a circular segment with area A = r² × arccos((r − h) / r) − (r − h) × √(2rh − h²), where h is the liquid depth and r is the radius. Multiply that area by the tank length L to get the filled volume. Turn on “Calculate partial fill” above and enter the liquid level — the calculator does this for you and also reports the empty volume.
Why isn’t a horizontal tank half full at half the diameter — wait, isn’t it?
A horizontal cylinder is exactly half full at exactly half the diameter, because the circle is symmetric about its centre line. But that is the only simple point. At one quarter of the diameter the tank holds much less than a quarter of its volume, and at three quarters it holds much more than three quarters. That is why a sight gauge on a horizontal tank is not evenly spaced.
Is a horizontal tank volume chart linear?
No. Because volume changes as a circular segment, a depth-to-volume (dipstick) chart for a horizontal tank is curved: each inch of depth near the middle of the tank adds far more volume than an inch near the top or bottom. This is exactly why printed heating-oil and fuel-tank charts have unevenly spaced rows. You can read a value at any depth using the calculator above.
What units does this horizontal tank calculator output?
Every result is shown at once in US gallons, imperial (UK) gallons, litres, cubic feet and cubic metres, so there is no need to convert. You can also tick “Show petroleum barrels” for oil applications. Enter dimensions in US units (feet and inches) or metric (metres and centimetres) using the unit toggle.
Does it account for dished or hemispherical end caps?
No. This page models a plain horizontal cylinder with flat ends. Real tanks with dished, elliptical or hemispherical heads hold a little more. For a cylinder with hemispherical caps, use the capsule shape on the main tank volume calculator instead.