Solve regular polygon measurements from flexible values. Review perimeter, area, angles, diagonals, and practical examples. Built for classes, projects, estimations, checks, reports, and revisions.
| Polygon | Sides | Known Side | Perimeter | Area |
|---|---|---|---|---|
| Triangle | 3 | 6 cm | 18 cm | 15.5885 cm² |
| Square | 4 | 5 cm | 20 cm | 25.0000 cm² |
| Hexagon | 6 | 8 cm | 48 cm | 166.2769 cm² |
| Octagon | 8 | 4 cm | 32 cm | 77.2548 cm² |
Perimeter: P = n × s
Area: A = (P × a) ÷ 2
Area from side: A = n × s² ÷ (4 × tan(π ÷ n))
Apothem from side: a = s ÷ (2 × tan(π ÷ n))
Circumradius from side: R = s ÷ (2 × sin(π ÷ n))
Interior angle: ((n - 2) × 180) ÷ n
Exterior angle: 360 ÷ n
Diagonals: n × (n - 3) ÷ 2
A regular polygon has equal sides and equal angles. That symmetry makes formulas reliable and fast. This calculator helps students, teachers, engineers, and designers measure shapes without repetitive manual work.
Many geometry tasks start with a regular polygon. Floor plans, tiling layouts, logos, machine parts, and classroom problems often use triangles, pentagons, hexagons, and other equal sided figures. When one value is known, the missing dimensions can be derived with trigonometry. This page handles that process in one place.
The tool calculates perimeter and area first. It also returns apothem, circumradius, central angle, exterior angle, interior angle, and diagonal count. These values help with drafting, estimating material use, checking dimensions, and verifying textbook exercises. Because the calculator supports multiple input modes, you can start from side length, apothem, or circumradius.
A regular polygon can be divided into congruent isosceles triangles that meet at the center. That idea turns a complex shape into simple pieces. The perimeter equals the number of sides multiplied by one side length. The area can then be found from one half of the perimeter multiplied by the apothem. Trigonometric relations connect side length, apothem, and circumradius through the central angle.
Use the perimeter result for edge length totals, trim estimates, fencing, or border design. Use the area result for coverage, surface planning, or comparisons between shapes. The angle outputs are helpful when drawing precise polygons or checking geometric proofs. The diagonal count is useful for combinatorics and shape analysis.
Always confirm the side count before calculating. A small mistake in side number changes every result. Keep units consistent and choose a precision level that matches your task. For classroom work, four decimal places are usually enough. For planning or fabrication, use the precision that your drawing or measurement standard requires. Clear labels also improve saved reports and exported tables. Good documentation reduces mistakes later. In advanced work, compare results from two input modes to catch typing errors early and strengthen confidence before modeling, fabrication, printing, or instruction.
A regular polygon has equal side lengths and equal interior angles. Common examples include the equilateral triangle, square, pentagon, and hexagon.
Yes. The calculator uses the side length and side count to derive the apothem and circumradius, then computes area and perimeter automatically.
The apothem is the distance from the center of a regular polygon to the midpoint of any side. It is useful in the area formula.
The circumradius is the distance from the center of the regular polygon to any vertex. It helps describe polygons inscribed in circles.
Units keep the result meaningful. Perimeter uses linear units, while area uses square units. Consistent units prevent reporting mistakes.
Every formula changes with the side count. A wrong value alters the side relationships, angles, perimeter, area, and diagonal total.
Use higher precision for drafting, modeling, fabrication, or detailed checks. Lower precision is usually enough for learning, quick estimates, and simple reports.
It shows how many line segments can connect nonadjacent vertices. This is useful in geometry lessons, pattern analysis, and polygon structure studies.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.