# 10 degree(s) length, length of 10 degrees?

In my paper, I want to describe the length of a interval of 10 degrees. But what is the correct way to say it?

1. 10 degrees length
2. 10 degrees span
3. 10 degrees' length
4. length of 10 degrees ...

The reason I'm asking, is that MS Word reports error for 10 degrees length. So I want to know, what is the correct expression?

Also, I think this question is very simple, is there any way I can search for it? So I don't need to post it here to bother someone again in the future.

Context:

The dataset that I'm working store the data (angular) into 0, 10, 20, 30 .. 350. I want to expresss the length of the interval. How to do it?

I now write it as the interval has a length of 10 degrees

• "Degree" and "length" are incompatible. If you mean angular degrees you would say "subtending 10 degrees", if temperature then "range of 10 degrees". Jun 30 '16 at 14:26
• Are you referring to the Y axis markers being in multiples of 10, or to the way your data has a spike extending every 10 degrees? (Although, either way, I'd probably phrase it as "10-degree intervals" or "at intervals of 10 degrees".) Jun 30 '16 at 15:02
• @Hellion that's very good. seems like I made up the `length` concept. But isn't interval length a solid concept? Jun 30 '16 at 15:16
• In technical work, length should only be used to reference a term having units of length to the first power. If it contains other units, or length raised to a power different from 1, it isn't referred to as a length. As others have pointed out, an angle is nondimensional. Degrees of arc is the scale you are using for angles. 10 degrees is the interval you have divided the circle into. So you might say "divided into 10 degree intervals", or "evaluated at 10 degree intervals" or "calculated every 10 degrees". Jun 30 '16 at 17:13
• "at intervals of 10 degrees" seems clear and simple. Jun 30 '16 at 18:32

## 3 Answers

the interval has a span of 10 degrees

Astronomers measure angular separation of objects in degrees......

....your hands and fingers are a remarkably accurate (and convenient) measuring tool [for small angles]. When you hold your hand at arm’s length, you can estimate angles like this:

•Stretch your thumb and little finger as far from each other as you can. The span from tip to tip is about 25 degrees

Also, see Wikipedia, Vision span

The visual field of the human eye spans approximately 120 degrees of arc

To answer the question in the OP's last sentence, how to search: I just entered span, degrees into Google.

I don't think any of your examples are correct. A degree is dimensionless, and one cannot apply "length" to something without dimension.

I think you are looking for an angle of 10 degrees.

This picture has an arc of S. The arc does have a length. So does the radius r. Both might be measured in inches or centimeters.

The angle θ does not have a length. It is measured in degrees or radians.

• Perhaps he is making a chart, and one axis has temperatures, measured in degrees. And he wants to talk about a certain interval along that axis. Jun 30 '16 at 14:20
• Thanks, and that's why I'm posting here. I really have no idea how to express it correctly. I have update the context. I hope you can take a look at it. Jun 30 '16 at 14:58

You are referring to the angles between the radial lines formed by the dataset.

A radial is one of the rays that diverge from the centre.

The sentence would refer to the angular difference between the radials.
I see no reason why you couldn't refer to the angular interval especially if it is repeatable or a de-facto standard.

The reason MS Word flagged your term is that "degrees" and "length" failed the grammar checker "compatible words" feature in the word processor.

• In your paper, you will have an issue to identify one radial from another. If your data reveals a sampling bias, the overall pattern would be quite intriguing.
– Stan
Jun 30 '16 at 16:17