Octagon Calculator

Your details

Pick the measurement you already know; the calculator derives everything else.
All length inputs and outputs use this unit.
The length of one of the eight equal edges.
in
Calculate how many tiles or boards are needed and the total material cost for the octagon floor.
Currency
Area
695.2935
Area unitin²
Perimeter96
Short diagonal (d1)22.1731
Medium diagonal (d2)28.9706
Long diagonal (d3)31.3575
Circumradius (R)15.6788
Apothem (r)14.4853
Side length (a)12
Interior angle135deg
Total diagonals20

Side 12 in: area 695.29 in², perimeter 96 in.

  • The area is 2(1+sqrt(2)) x a^2, approximately 4.8284 times the side squared, so doubling the side quadruples the area.
  • Across opposite vertices the octagon spans 31.358 in (the long diagonal), which is also the diameter of the circumscribed circle.
  • The apothem of 14.485 in is the radius of the largest circle that fits inside the shape, and the ratio apothem/circumradius is always about 0.9239 regardless of size.
  • Interior angles are always 135 degrees and exterior angles are 45 degrees; that is why two octagon roof sections meet a square perfectly at a corner.

Next stepUse the circumradius (15.679 in) to draw the octagon by stepping eight vertices around a circle, or use the apothem to fit the shape snugly inside one.

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