Ellipse perimeter

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)  a2 - b2  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

ellipse sketch

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