Calculate the perimeter of any regular polygon from side length, area, apothem, or circumradius. Also computes area, interior angle, diagonals, and more with visual comparisons.
<p>The <strong>Regular Polygon Perimeter Calculator</strong> computes the perimeter of any regular polygon given the number of sides and one known measurement—side length, area, apothem, or circumradius. It also derives every other key property: area, apothem, circumradius, interior and exterior angles, sum of interior angles, and diagonal count.</p> <p>Knowing the perimeter of a regular polygon is essential for fencing, edging, framing, and material estimation in construction, landscaping, and crafts. Whether you're building an octagonal gazebo, cutting a hexagonal tile border, or fencing a pentagonal garden bed, this calculator gives you the total edge length immediately—plus all the geometry you might need.</p> <p>Four flexible input modes make the calculator versatile. If you measured a side, enter it directly. If you know the area from a blueprint, enter that instead. Architects often work with the apothem (inradius) or circumradius—those modes are available too. The calculator converts between all representations using standard trigonometric identities, so you only need one measurement plus the number of sides.</p> <p>A comparison bar chart shows how perimeter scales with side count (for unit side length), a dimension bar chart compares side length, apothem, and circumradius, and a full reference table lists properties for regular polygons from 3 to 12 sides. Eight presets let you jump to common shapes instantly.</p>
Perimeter is the number people usually need first when a polygon becomes a physical object. It tells you how much trim to buy for an octagonal frame, how much fencing surrounds a many-sided garden bed, or how much edge banding a decorative panel will require. The difficulty is that real plans do not always give you a side length directly. Sometimes you start from an area target, an apothem from a blueprint, or a circumradius from a radial layout.
This calculator turns any one of those inputs into the full set of polygon measurements. That makes it useful for estimating material, checking homework, and comparing which regular shape gives the boundary length or area you need without manually rearranging trigonometric formulas every time.
Perimeter = n × s. From apothem: s = 2a tan(π/n). From circumradius: s = 2R sin(π/n). From area: s = √(4A tan(π/n) / n). Interior Angle = (n−2) × 180° / n.
Result: Perimeter = 36, Area ≈ 93.53, Apothem ≈ 5.20
A regular hexagon with s = 6 has perimeter = 6 × 6 = 36. Apothem = 6 / (2 tan 30°) ≈ 5.20. Area = ½ × 36 × 5.20 ≈ 93.53.
Every regular polygon perimeter problem reduces to $P = ns$, but the real work is often finding the side length from a different measurement. If you know the area, apothem, or circumradius, you have enough information to reconstruct the side through trigonometry. That is why this calculator asks for the number of sides first: once the polygon type is fixed, the missing side length and perimeter follow from a consistent set of formulas.
Regular polygons with the same side length do not all behave the same way. As the number of sides increases, the perimeter grows linearly because you are adding more equal edges, while the shape itself becomes visually closer to a circle. That comparison matters in design problems where you want a certain appearance or footprint but need to control total edge length for materials such as molding, fencing, LED strips, or border stones.
A common mistake is entering a value in the wrong mode and interpreting the result as if it came from a side length. For example, an apothem of 8 and a circumradius of 8 produce different polygons even with the same side count. When checking your work, confirm the input mode, then compare the derived side length and area cards to see whether the geometry matches your expectation. If you are solving by hand, this is also a good way to catch an incorrect trig function before it affects the final perimeter.
The perimeter is the total length of all sides. For a regular polygon with n sides each of length s, perimeter = n × s.
Yes, if you also know n. The calculator derives the side length from the area using s = √(4A tan(π/n) / n), then computes perimeter = n × s.
The polygon approaches a circle. The perimeter approaches 2πR (circumference), and the area approaches πR².
Yes. Irregular polygons have unequal sides, so you would need to measure and sum each side individually.
The apothem goes from the center to the midpoint of a side (inradius). The circumradius goes from the center to a vertex (outer radius). The circumradius is always larger.
Enter the number of sides and your desired side length. The perimeter gives you the total fence length needed. Add extra for overlaps and gates.