Radius of an arc

      Formulas for determining the radius of an arc, or "eyebrow"

I would like to know the formula for determining the radius of an arc, or "eyebrow", in cabinetmakers terms. I know it starts with a line connecting two points of the arc and the amount of "rise" within that segment.

Forum Responses
I looked for this formula for a long time and found it in a book called "Pocket Ref" by Thomas J. Glover.

Here is the formula if the line connecting the to points is "A" and the distance from a to the edge of the circle is b (at a 90 degree angle to a)
then (^2 equals "squared"):
(((a/2)^2)+(b^2))/2*b =radius
or half a squared plus b squared divided by 2 times b.
I think the degrees are (atan(a/2)/(r-b))*2

I just draw the horizontal line and then the rise from the midpoint, create a 3 point arc, then ask ACAD what the radius is.

Here is another way:

Square 1/2 of span.
Divide by rise.
Add rise.
Divide by 2.

Rise squared plus half the width squared divided by twice the rise.

The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).

Comment from contributor A:
Another way:

C= chord length
M= distance from chord to edge of circle

C squared divided by 8M + M/2 = R

Comment from contributor B:
To calculate radius of a circle where:
r = radius and is unknown
C = chord length (a line the crosses any two points on a circle)
B = length of perpendicular line from midpoint of chord to edge of circle

r=((4*Bsquared + Csquared)/8B)

Would you like to add information to this article?
Interested in writing or submitting an article?
Have a question about this article?

Have you reviewed the related Knowledge Base areas below?
  • KnowledgeBase: Architectural Millwork

  • KnowledgeBase: Architectural Millwork: Custom Millwork

  • KnowledgeBase: Business

  • KnowledgeBase: Business: Project Management

  • KnowledgeBase: Cabinetmaking

  • KnowledgeBase: Computerization

  • KnowledgeBase: Furniture

  • KnowledgeBase: Furniture: Custom Furniture

  • KnowledgeBase: Solid Wood Machining

  • KnowledgeBase: Woodworking Miscellaneous

  • KnowledgeBase: Woodworking Miscellaneous: Bending Wood

  • KnowledgeBase: Knowledge Base

    Would you like to add information to this article? ... Click Here

    If you have a question regarding a Knowledge Base article, your best chance at uncovering an answer is to search the entire Knowledge Base for related articles or to post your question at the appropriate WOODWEB Forum. Before posting your message, be sure to
    review our Forum Guidelines.

    Questions entered in the Knowledge Base Article comment form will not generate responses! A list of WOODWEB Forums can be found at WOODWEB's Site Map.

    When you post your question at the Forum, be sure to include references to the Knowledge Base article that inspired your question. The more information you provide with your question, the better your chances are of receiving responses.

    Return to beginning of article.

    Refer a Friend || Read This Important Information || Site Map || Privacy Policy || Site User Agreement

    Letters, questions or comments? E-Mail us and let us know what you think. Be sure to review our Frequently Asked Questions page.

    Contact us to discuss advertising or to report problems with this site.

    To report a problem, send an e-mail to our Webmaster

    Copyright © 1996-2021 - Woodweb.com
    All rights reserved. No part of this publication may be reproduced in any manner without permission of the Editor.
    Review Woodweb.com's Copyright Policy.

    The editors, writers, and staff at Woodweb.com try to promote safe practices. What is safe for one woodworker under certain conditions may not be safe for others in different circumstances. Readers should undertake the use of materials and methods discussed at Woodweb.com after considerate evaluation, and at their own risk.

    865 Troxel Road
    Lansdale, PA 19446

    Contact Us

  • WOODWEB - the leading resource for professional woodworkers

      Home » Knowledge Base » Knowledge Base Article