A calculator for drawing small arcs of large circles

arc of a circle

Not infrequently in designing furniture I need to lay out a very gentle arc with a given length and height — a curve too long and shallow to sketch easily or construct precisely. This calculator takes the width and height of an arc and generates a table of coordinates of points on that arc, say every inch or half-inch, which can be connected by hand to cut a template or used to build a form to bend a batten. In the diagram, the arc is shown in blue, and the coordinates for point P are labeled x (the distance along the baseline from center) and y (the height of the arc at distance x from center).

To use the calculator, input the width and height of your arc, the horizontal interval (along the baseline) between the points you want to plot, and the desired precision. The coordinates will be generated in ordinary fractions of an inch, to the desired precision (up to 1/64 inch). If desired, you can also see decimal values. You can even bookmark the results page for reference.

For more about this calculator and the math behind it, read my blog post.


Width and height of arc
  1. inches
  2. inches
  1. inch
  2. inch