P = ns
Perimeter
Perimeter equals the number of sides multiplied by side length.
NUT ENGINEERING TOOLS
Regular Polygon Solver
See It. Solve It. Understand It.
Enter the number of sides and one known dimensional measurement. Nut solves the complete regular polygon geometry and shows how the relationships work.
Live Geometry
Live Geometry changes with the number of sides.
Enter What You Know
Number of sides is required. Then enter one dimensional measurement and leave the remaining measurements blank.
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Calculated Results
Complete regular polygon geometry from the measurements entered.
Number of Sides
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Side Length
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Perimeter
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Apothem
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Circumradius
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Area
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Interior Angle
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Exterior Angle
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Your Solution
Nut shows the equations and values used to solve the polygon.
Enter the number of sides and one known measurement to see the solution.
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How It Works
A regular polygon has equal sides and equal interior angles.
a = s ÷ [2 tan(π ÷ n)]
Apothem
The apothem is the perpendicular distance from the center to the midpoint of a side.
R = s ÷ [2 sin(π ÷ n)]
Circumradius
Circumradius is the distance from the center to a vertex.
A = Pa ÷ 2
Area
Area equals one-half the perimeter multiplied by the apothem.
Exterior = 360° ÷ n
Exterior Angle
The exterior angles of a regular polygon total 360 degrees.
Interior = 180° − Exterior
Interior Angle
Each interior angle is supplementary to its exterior angle.
Nut Industries V2 — Development Preview