How to layout an oval or true ellipse?

There are a number of geometric methods but the fastest is the "pins and string" string method. Then the question becomes, How do I make the ellipse the size I want it?
The answer is relatively simple but is not always right at our finger tips.

Given a and b, half the height and the width, the distance from the center to one pin is:

c = sqrt( b² - a² )

Then the length of the string is:

String Length = 2b + 2c

A slightly simpler formula was provided by Rob Curry. Given the Width is greater than the Height:

Pin Distance = sqrt(Width² - Height²)

String Length = Pin Distance + Width

To make it REALLY easy I've written a little Javascript program. Given the Height and the Width it provides the pin distance 2c and the string length as shown in the diagram above.

Height (2a)
Width (2b)
Pin Distance (2c)
String Length

anvilfire graphic (c) 1998 Patrick Dempsey

Copyright © 1997, 2004, 2007

Cones calc counter

Geometric Method

A major and minor circle are drawn to match the major and minor dimensions of the ellipse. Lines are drawn from the center out. These may be equally divided or not.

Then descenders are drawn on the X and Y axis from where each of the radial line cross the circles. Where they meet is a point on an ellipse. This method is best done on a drawing board with squares or a drafting machine but some of us can do this freehand.