Horizontal Cylindrical Tank Volume Calculator

This calculator works out the volume of a horizontal cylindrical tank from the tank’s diameter and length, plus the depth of the liquid inside. Enter those three measurements, and you get the volume of liquid in the tank in your choice of units, along with the percentage of the tank’s total capacity that is filled.

Formula

The liquid volume in a horizontal cylindrical tank is calculated using the formula for the area of a circular segment, multiplied by the tank length. In symbols:

V = L × (r² × (θ − sin θ))

where:

• V = volume of liquid (cubic meters, cubic feet, liters, gallons, etc.)
• L = length of the cylindrical tank (same linear unit as r)
• r = radius of the tank (half the diameter, in the same unit as L)
• θ = the central angle of the liquid segment, in radians, calculated as θ = 2 × arccos((r − h) / r), where h is the liquid depth

An equivalent form that uses diameter and depth directly is:

V = L × ( (d/2)² × ( arccos(1 − 2h/d) − sin( arccos(1 − 2h/d) ) ) )

Here d is the tank diameter, h is the liquid depth, and the angle is in radians. If you prefer degrees, convert: θ (radians) = θ (degrees) × π / 180.

Worked Example

Using the default values from the calculator above: tank diameter d = 2.0 m, length L = 4.0 m, liquid depth h = 0.8 m.

1. Radius r = d/2 = 1.0 m.
2. Compute the ratio 2h/d = 2 × 0.8 / 2.0 = 0.8.
3. Compute the angle: arccos(1 − 0.8) = arccos(0.2) ≈ 1.3694 radians.
4. Compute sin of that angle: sin(1.3694) ≈ 0.9798.
5. Area of the segment = r² × (θ − sin θ) = 1.0² × (1.3694 − 0.9798) = 0.3896 m².
6. Volume = L × area = 4.0 × 0.3896 = 1.5584 m³.

The calculator rounds to three decimals, so it shows 1.558 m³. The fill percentage is (h/d) × 100 = (0.8/2.0) × 100 = 40%.

When to Use This Calculator

Horizontal cylindrical tanks are common in fuel storage, water tanks on trucks, chemical processing, and many industrial settings. This calculator is for a tank that lies on its side, with a circular cross-section. It is the right tool when you need to know how much liquid is currently in the tank (for inventory or transfer) or how much space remains before overflow.

If the tank is vertical (standing on end), the volume is simply the area of the circle times the liquid height — no segment geometry needed. This calculator does not apply to elliptical, rectangular, or spherical tanks.

How to Measure the Inputs

Accurate measurements are essential for a correct volume. Here are the key points:

• Diameter (d): Measure the inside diameter of the tank, not the outside, if the walls are thick. For a typical steel tank, the difference can be several centimeters. If you only have the outside diameter, subtract twice the wall thickness.
• Length (L): Use the internal length between the two end caps. If the tank has dished or elliptical heads, this formula only covers the cylindrical section; the heads add a small extra volume that is not included here.
• Liquid depth (h): Measure from the bottom of the tank to the liquid surface. Use a dipstick or a level sensor. For a tank that is not perfectly level, take the measurement at the center or use an average.

All three measurements must be in the same unit. If you mix meters and centimeters, the result will be off by a factor of 100 or more.

Common Mistakes and How to Avoid Them

The most frequent error is using the diameter instead of the radius in the segment area formula. Always halve the diameter first.

Another common mistake is forgetting that the angle in the formula must be in radians when using a calculator or spreadsheet. If you use degrees, the result will be nonsense. Most scientific calculators have a mode switch; make sure it is set to radians.

Also, the formula assumes the tank is exactly horizontal. If the tank is tilted, the liquid surface is not a flat segment, and this calculation will be inaccurate. For tilted tanks, you need a more complex model that accounts for the slope.

Finally, remember that the formula gives the volume of the liquid, not the total capacity. To get the total capacity, set h = d in the formula. The result will be π × r² × L, the standard cylinder volume.

Units and Conversions

The calculator works with any consistent unit set. If you enter meters, the volume is in cubic meters. If you enter feet, the volume is in cubic feet. To convert to more practical units:

• 1 cubic meter = 1000 liters = 264.172 US gallons
• 1 cubic foot = 7.48052 US gallons = 28.3168 liters
• 1 liter = 0.264172 US gallons

For example, the worked example above gives 1.558 m³, which is 1558 liters or about 411.7 US gallons.

Limitations of the Formula

This formula is exact for a perfect horizontal cylinder with flat ends. Real tanks often have curved or dished heads, which add volume beyond the cylindrical section. The extra volume can be significant for short tanks with large diameter. If you need extreme accuracy, you must add the head volume separately.

Also, the formula assumes the liquid surface is flat and horizontal. In a moving vehicle or a tank that is being filled or drained, waves and turbulence can make the depth measurement unreliable. For such situations, use a stilling well or take the measurement after the liquid has settled.

Temperature changes can affect liquid volume, especially for fuels and chemicals. The calculator gives the volume at the current temperature; if you need the volume at a standard temperature, you must apply a thermal expansion correction.

Frequently Asked Questions

How do I calculate the total capacity of a horizontal cylinder?

Set the liquid depth equal to the diameter (h = d). The formula then simplifies to the full cylinder volume: V = π × r² × L. For the default example, that would be π × 1² × 4 = 12.566 m³.

What if my tank has elliptical or dished heads?

This calculator only covers the cylindrical section. To include the heads, you need to add the volume of the two heads. For a standard 2:1 elliptical head, the volume of one head is approximately (π/6) × d³. For a hemispherical head, it is (π/12) × d³. Add these to the cylindrical volume for total capacity.

Can I use this for a vertical cylindrical tank?

No. For a vertical tank, the volume is simply the circular area times the liquid height: V = π × r² × h. That is a much simpler calculation and does not require the segment formula.

Why does the volume not increase linearly with depth?

Because the cross-section of a horizontal cylinder is a circle. Near the bottom, the width of the liquid surface is small, so adding a centimeter of depth adds little volume. Near the middle, the width is large, so the same centimeter adds much more volume. This is why the fill percentage in the calculator is not proportional to the depth.

How accurate is the dipstick method for measuring depth?

It depends on the tank shape and the stick. For a horizontal cylinder, a dipstick reading is accurate to a few millimeters if the tank is level and the stick is straight. That translates to a small volume error, but it can be larger if the tank has internal baffles or is not perfectly round.

Related

• Oblique Rectangular Prism Volume Calculator
• Bearing to Angle Calculator: Convert Bearings to Angles
• Sheets Grade Calculator: How to Use It

in d | Tank diameter | m | 2.0 | 0
in l | Tank length | m | 4.0 | 0
in h | Liquid depth | m | 0.8 | 0
out vol | Liquid volume | m³ | l * (0.5 * (d/2)^2 * (acos(1 - 2*h/d) - sin(acos(1 - 2*h/d)))) | 3
out pct | Fill percentage | % | (h / d) * 100 | 1