Regular octagonVEXQOMIRA / GEOMETRY 15
Regular octagon Vexqomira

Formulas, without the guesswork.

Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.

From a side

A = na²/[4 tan(π/n)]; P = na

Inputs: Side a (length units).

Apply this formula ↗

From circumradius

a = 2R sin(π/n)

Inputs: Circumradius R (length units).

Apply this formula ↗

From the apothem

a = 2r tan(π/n)

Inputs: Apothem r (length units).

Apply this formula ↗

From area

a = √[4A tan(π/n)/n]

Inputs: Area A (square units).

Apply this formula ↗

Reading the notation

√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.

A general eight-sided polygon is not determined by one side. These tools apply only to regular octagons.

Reference reading: Regular octagon at Wolfram MathWorld.