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How to Find the Diameter of a Circle

We all know what circles are don&#;t we? We are surrounded by circular objects, from wheels to aerosol cans. But if you needed to find the diameter of a circle would you be able to? In this post we provide a reminder of basic school mathematics and look at why its useful to know how to figure out circle dimensions.

Online Shopping Fails

Most of us will have read some amusing stories of people who have made online purchases which, when they arrived, turned out to be entirely the wrong size. The COVID-19 pandemic has fuelled an explosion in online shopping with many people using e-commerce for the very first time. But even experienced online shoppers can be caught out by not checking sizes.

In some cases, advertisements have purposely mislead shoppers by omitting dimensions. For example, Fleur Webb paid £60 for what appeared to be a bargain patio furniture set, on sale from what she thought was a trusted Amazon vendor. Images showed the furniture in a garden setting, surrounded by candles, with champagne on the table. But when the patio set arrived it turned out to be miniature furniture for a doll&#;s house. In this case the advertisement was clearly an intentional con but Fleur acknowledged that she should have spotted the dubious absence of dimensions.

There are many circumstances in which customers must determine and confirm the dimensions they need before placing their product orders. Making mistakes in measuring and calculating what&#;s needed can be expensive for both the customer and supplier and will inevitably lead to delays and disappointment.

What Does Diameter of a Circle Mean?

The Anti Climb Spiked Collars for Poles and Pipes, available from our online store, are an example of products for which its necessary to provide the correct dimensions when placing an order.

For example, our Spiked Anti Climb Collars for Round Poles are specified for poles of various diameters from 76mm (3 inches) up to 272mm (10.75 inches.) When placing orders for these products its therefore important to get the size right.

Circles - Circumference - Diameter - Radius

 If you cast your mind back to school days hopefully you will recall how the diameter of a circle is the distance from side to side, via the centre point. Half the distance is called the radius and the distance around the circle is the circumference.

How to Calculate the Diameter of a Circle

Its often possible to measure the diameter of a circle simply by using a tape measure or ruler. But this requires the measuring tape to be laid across the circle, via the centre point, which isn&#;t possible for in-situ poles.

A caliper tool can potentially be used to get an accurate diameter measurement. But what most people need to know is is how to calculate the diameter of a circle from the circumference.

Measuring the circumference of a pole, with a measuring tape, is easy. Armed with this single dimension, along knowledge of the ratio between a circle&#;s diameter and its circumference, is all you need to calculate the pole diameter.

Formulae for Calculating Circumference from Radius or Diameter

As shown, the circumference of a circle can be calculated by multiplying the diameter (d) by the constant, pi (π). Pi is generally approximated to 3.14 or 3.142, which is adequately accurate for most practical applications. Therefore, if the circumference of a circle is known then the diameter can be simply calculated by dividing this measurement by pi.

The following table lists the round pole diameters for which various off-the-shelf anti climb collar products are available from our store alongside their corresponding pole circumferences.

Circumference mm  Circumference inches  Diameter mm  Diameter inches    239  9.4  76  3  280  11  89  3.5  315  12.6  100  4  359  14.2  114  4.5  437  17.3  139  5.5  528  20.4  168  6.5  607  23.6  193  7.5  689  26.7  219  8.5  858  33.8  273  10.75

Note: all circumference dimensions have been rounded.

For example, if you have measured the circumference of a pole on which you need to install anti-climb protection and the measurement is 345mm, dividing this by pi (3.14) provides a diameter of 109.9mm. Therefore the anti climb pole collar suitable for poles with diameters up to 114mm (4.5 inches) would fit as required.

 

Products Requiring Circle Dimensions

As noted, our anti climb spiked pole collars are just one example of products from our online store for which accurate pole dimensions are needed when placing orders. Other examples include:

The old saying &#;measure twice and cut once&#;, generally applied to woodworking, can potentially be adapted for online shopping to: &#;measure twice and order once&#;, highlighting how getting the required dimensions right-first-time will prevent disappointment and the often costly need to return goods and re-order the right size.

If you have any questions about the dimensions of products you need or if you have any special requirements remember we are here to help. Give us a call on and we&#;ll provide you with free, expert advice.

This message was added on Thursday 20th January

Eastloong contains other products and information you need, so please check it out.

Is a diameter the distance between two points? Or is a diameter the average circle diameter?

(This tip is compliant only with ISO &#; ISO -2:)

Recently, following a failure, I was asked the question: what is a diameter?

A problem was found of parts not mating. When re-measured, the results were different from the values in the original measurement report. After examination, it was discovered that the values reported in the original measurement for the diameter requirement were the average (Least Squares) circle size, and in the repeat measurement, distances were measured between opposing points, and that was the reason for the difference. The supplier claimed that &#;That is the way to measure by CMM, and no special control requirements have been given&#;&#; Hence the question, what is a diameter?

It is important to remember that according to the latest approach of ISO, a drawing is a specification of requirements applied to the finished part! The drawing specifies what should be, and not how to produce or how to check it (unless otherwise stated explicitly).

And regarding the Question &#; What is a Diameter?
According to ISO, the default definition, unless otherwise specified, is:
&#;Diameter is the length of a straight line connecting two points, in a section perpendicular to the axis of a circular body, which passes through the center of the cross section.&#;
In other words, real distances should be reported, not average values!!!

It therefore follows that the claim &#;that is the way to measure by CMM&#; is unsatisfactory, and the value that was reported is not the value required!!!
In addition, the definition of a diameter contains two requirements, which are not simple; the standard provides a solution on how to find them:

• diameter shall be measured perpendicular to the axis! &#; a real part is does not have a perfect form; it has a center line, it has no axis (a theoretical straight line).
• The length of the straight line connecting the points, which passes through the center of the circle! &#; the section line is not a perfect circle, so what is the center?

The following illustrations show how a cylinder diameter is defined according to ISO GPS standards:

• What is the axis to which the measurement is perpendicular?
• What is the center through which the measurement must pass?

In Figure 1, the blue surface represents a sample of a cylinder envelope. The numbered elements are:

1. An average (LSQ &#; Least Squares) cylinder of sampling points from the real envelope of the feature.
2. The axis of the average cylinder (the cylinder is a theoretical geometric form, so its axis is straight).
3. Section planes perpendicular to the axis of the average (LSQ) cylinder.
4. The average (LSQ) circle.

Figure 1

Figure 2 shows a section perpendicular to the axis, and the numbered elements are:

Figure 2

1.  The section line of the measurements in a section plane perpendicular to the axis.
2.  The average (LSQ) circle of the points, in the section plane.
3.  The dimensions of the diameter are the distances between opposing points, with the straight line connecting them passing through the center of the LSQ circle in the cross section.

It is important to note that the average (LSQ) circle center in the cross section is not necessarily on the axis of the average cylinder.
The average cylinder is used to define the measuring direction.
The average circle in the cross section is used to find the center of the cross section.
The maximum and minimum dimensions must be reported (verify that there is no deviation in the envelope from the dimension&#;s defined tolerance).

In summary

The default definition in ISO for a diameter dimension is the real distance between two points in a section perpendicular to the axis that passes through the center of the cross section.
If we want a different definition, it must be noted explicitly!!!

Specifying a standard in the drawing defines the rules according to which the drawing should be interpreted, and prevents disputes!!!

Questions? Ideas? Suggestions?
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If you are looking for more details, kindly visit Diameter Measuring Equipment.