3. Storage Tank Volume Calculations: Measurement Notes

Measurement Notes

This article provides a way to measure tank volumes for the common case of a partly filled tank mounted horizontally or vertically. It can be used for tanks with flat ends (a classic cylinder), spherical ends such as are used to store propane and natural gas, and elliptical ends, that is, ends that are curved but not fully spherical. This page can also be used for spherical tanks — tanks with no cylindrical section.

The mathematical methods described in this article should provide results of high accuracy (but read this disclaimer) if the tank has been measured accurately. In order to compute volume, the methods require three tank dimensions described below, plus one content height measurement. Remember when measuring a tank that it is the inside dimensions that determine the tank's volume. Some measurements will need to be corrected for the tank's wall thickness, therefore knowing that thickness is important for best accuracy.

All measured tank dimensions must be expressed in the same units of length (and when using the provided online calculators, they can be expressed in centimeters, meters, inches, or feet). The volume result can be expressed in a number of different ways, the only limitation is that the tank dimension set must be internally consistent.

Use this table to guide your measurement activity, and refer to the horizontal and vertical pages for graphic depictions of the variables:

Variable name Description Notes

L The length of the cylindrical section. This measurement can be made without any correction for wall thickness. Many tanks have a weld line that separates the cylindrical section from the end caps. The L value is simply the linear distance between the weld lines.

R The radius of the cylinder and the major radius of the elliptical end caps. There are a number of ways to get this measurement. One way is to measure the tank's diameter and divide by 2. For some tanks, it will be easier ot measure the tank's circumference and divide by 2 π (6.283...). But remember to subtract the tank's wall thickness from the measured value as a final step.

r The minor radius of the elliptical end caps. If the tank has spherical end caps, simply use the R value acquired above for this measurement (because for a sphere all radii are equal). If the tank is cylindrical (flat end plates), set this value to zero. For tanks with curved but not spherical end caps, and for greatest volume accuracy, this measurement needs to be performed carefully. Again, even though it is not easy to make this measurement directly, there are a number of ways to get a reasonable value. One way is to measure the overall tank length, subtract the previously measured L value, and divide by 2. Another way is to use a plumb line and make marks on the ground (horizontal tank), repeat this at the weld line, and take the difference. Remember to subtract the wall thickness before using the value.

y The height of the tank's contents. This value is normally acquired with integrated measurement equipment like a floating sensor or dipstick. This is the most frequently entered variable — it can be entered in the calculator display on this page, or it can be compared to a permanent table of values created with the provided volume computer.

Here is a list of tank types and how they are specified to the volume computer:

Cylinder (flat ends). Set variable r to zero, R to the radius of the cylinder, and L to the length of the cylinder.
Cylinder with spherical end caps. Set R to the radius of the tank's cylindrical section, set r = R, set L to the length of the cylindrical section.
Cylinder with curved but not spherical end caps. Set R to the radius of the tank's cylindrical section, set r to the perpendicular radius (see the graphic depiction on each of the volume computer pages and see the measurement notes above), set L to the length of the cylindrical section.
Spherical tank. Set both R and r to the radius of the sphere, set L to zero.

Here are some notes on the numerical range of the variables:

By looking at the tank images for each solution page, you can see that some of the variables have a very specific range, within which they produce meaningful results, and outside which they may produce error messages.
Variable R, the tank radius, and variable L, the tank cylindrical length, don't have any innate limitations apart from the fact that they must be greater than or equal to zero.
Variable r should fall in the range between zero and the value given to R, e.g. 0 <= r <= R.
Variable y should fall in the range:
- Horizontal Tank: between zero and 2R inclusive, that is, it should not exceed the diameter of the tank (0 <= y <= 2R).
- Vertical Tank: between zero and L+2r inclusive, that is, it should not exceed the overall height of the tank (0 <= y <= L+2r).
An error message will be printed if these ranges are exceeded.

Most of the variable values, and the chosen input and output units, are preserved between visits to this page.

Note on the volume computer output format:

Each volume computer (horizontal, vertical) has two output modes, HTML table and CSV (comma separated values) database. The HTML table is suitable for perusing by eye or for exporting as part of an HTML page. The CSV output can be exported into a spreadsheet program for graphing or further processing, or it can be pasted into a database. The CSV output format is an industry standard portable data format that is accepted by many programs and database applications.
To copy the contents of the generated database, click the output display with your mouse, press Ctrl+A to select the entire table, then Ctrl+C to copy it to the system clipboard.

Variable name	Description	Notes
L	The length of the cylindrical section.	This measurement can be made without any correction for wall thickness. Many tanks have a weld line that separates the cylindrical section from the end caps. The L value is simply the linear distance between the weld lines.
R	The radius of the cylinder and the major radius of the elliptical end caps.	There are a number of ways to get this measurement. One way is to measure the tank's diameter and divide by 2. For some tanks, it will be easier ot measure the tank's circumference and divide by 2 π (6.283...). But remember to subtract the tank's wall thickness from the measured value as a final step.
r	The minor radius of the elliptical end caps.	If the tank has spherical end caps, simply use the R value acquired above for this measurement (because for a sphere all radii are equal). If the tank is cylindrical (flat end plates), set this value to zero. For tanks with curved but not spherical end caps, and for greatest volume accuracy, this measurement needs to be performed carefully. Again, even though it is not easy to make this measurement directly, there are a number of ways to get a reasonable value. One way is to measure the overall tank length, subtract the previously measured L value, and divide by 2. Another way is to use a plumb line and make marks on the ground (horizontal tank), repeat this at the weld line, and take the difference. Remember to subtract the wall thickness before using the value.
y	The height of the tank's contents.	This value is normally acquired with integrated measurement equipment like a floating sensor or dipstick. This is the most frequently entered variable — it can be entered in the calculator display on this page, or it can be compared to a permanent table of values created with the provided volume computer.