Ellipses are far more aesthetically pleasing than “racetrack”-shaped tables. They also have fascinating — and somewhat complicated — geometry.
I created this calculator for two purposes:
(1) Commission elliptical tables from furniture-makers not using CNC machines (who thus need to draw the shape using the string method)
(2) Scale table designs to ensure desired seating capacity (as opposed to guessing based on racetrack tables, as furniture showrooms do)
Perimeter of an elliptical table
Major axis - centerpoint to most distant edge of table (a) | inches | |||
Minor axis - centerpoint to closest edge of table (b) | inches | |||
Distance from centerpoint to each of the two foci (f) | √ a^{2} - b^{2} | 26 | inches | |
Length of string to draw the ellipse | 2a | 72 | inches | |
Table perimeter | π [3(a+b) - √ (3a+b)(a+3b) ] | 193 | inches | |
Number of people at the table | inches | |||
Table frontage per person | 24 | inches | ||
Compare to a racetrack-shaped table (circle of radius b, plus rectangular insert for expansion): | ||||
Circumference of circular table, without insert | 2πb | 157 | inches | |
Table frontage per person, without insert | 20 | inches | ||
Width of insert (d) | inches | |||
Perimeter of table, with insert | 2πb+2d | 197 | inches | |
Table frontage per person, with insert | 25 | inches |