The Polygon Perimeter from Inner Radius and Number of Sides calculator computes the length of the perimeter of a regular polygon of (n) sides that is inscribed inside a circle of radius (r).
INSTRUCTIONS: Choose units and enter the following:
Polygon Perimeter (P): The calculator return to total perimeter of the regular polygon in meters. However this can be automatically converted to compatible units via the pull-down menu.
P = 2⋅n⋅r⋅tan(π/n)
A regular n-sided polygon is a polygon with n equal length sides and is a polygon which also has n equal angles at the n vertices of the polygon. Because of the symmetries of this construction, a radius of the circle intersects the sides of the polygon at a right angle. As shown in the picture, Figure 1, lines from the vertices to the circle's center form isosceles triangles with the sides of the regular polygon.
A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length . Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side. As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.
The names of polygons vary based on the number of sides as follows:
Polygon Area Calculators:
Polygon Side Calculators
Polygon Perimeter Calculators
Other Polygon Calculators