A simple form for finding the volume of a cylinder oriented vertically or horizontally.
Units of measure are inches (yielding gallons US) or centimeters (yielding Liters).
How it works.

Orientation of the Cylinder:   Horizontal   Vertical Round Answer
to Decimal:
Unit of Measure:    Inches      Centimeters
Enter Cylinder Length
Enter Cylinder Diameter
Enter liquid Depth

The fluid surface area (circle portion) is
The Units³ are
The Cylinder Volume is
The Rounded Volume is

As a request I created an MS Excel® and OpenOffice® spread sheet to list volumes at depth intervals. It is a simple form and not pretty but functional. It calculates volume in gallons (US), barrels of oil and Liters. Down load MS Excel® 2000 file here , MS Excel® 2000 in Metric Units here or the OpenOffice® file here
Updated June 30, 2006

Another resource for volume calculations is: ABE Volume Calculator Page

The most FAQ is :'What about inclined cylinder?'
The math for this problem is beyond my abilities, but for those of you who really want to inflict brain damage on your self I found a site that can help you: Inclined Cylinder Calculator

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How it works.
All units of measure must be the same, i.e., a tank with a length of 10 ft. and a diameter of 4 ft. and liquid depth of 36 inches would have the dimensions entered : Inches (checked), length = 120", diameter = 48", liquid depth = 36". This yields cubic inches which is converted to gallons by the ratio: 231 in3/gal.
The calculation for a cylinder oriented vertically is quite simple, area of the circle x length. This gives the cubic units, inches or centimeters depending on your unit of measure.
However, calculating the volume of liquid in a tank oriented horizontally is more difficult as the area of the liquid on the ends of the tank changes with depth as the shape of the area changes as illustrated in the images.

The images below hopefully will illustrate the geometry used in solving the problem.

tank viewTotal view of horizontal tank. Assumptions made: tank is level, ends are flat, measurements are ID and must be in like units.

The calculation for the horizontal cylinder is based on the formula:

[(r2 acos (r-df) / r) - (r - df) * sqrt(2rdf - df2)] x L
Where   r = radius , df = depth of fluid , angles are in radians and L = length
acos = inverse cosine, arccosine, or cos-1

This yields the section area. Area x Length = Volume

graphic of formula

Below are some graphics to help explain the geometry. (pardon the crude graphics)

circle sector     minus     minus triangle    leaving    resulting liquid level   bottom segment.
top section

For fluid levels that are > r, the volume is:   (area of the circle  -  top segment) x length.

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If you find this script useful and would like to have a copy, you can down load the Cylinder file in Zip format here.

If you have any comments, suggestions, or problems with the script, contact

This page has been viewed times since September, 2002.

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