Regular Polygon Calculator

Area, perimeter, angles, circumradius and inradius

Quick Answer

Regular Polygon Calculator: Area, perimeter, angles, circumradius and inradius. Area A = n·a² ÷ (4·tan(π/n)) = perimeter × apothem ÷ 2.

Enter any one value, the rest auto-solve

Sides n

Side length s

Perimeter Pauto

Area Aauto

Circumradius Rauto

Inradius rauto

Diagram (updates live with input)

Step-by-step

半中心角 = π/n = 180°/6 = 30.0000°

P = ns = 6 × 10.0000 = 60.0000

A = ns²/(4·tan(π/n)) = 259.8076

R = s/(2·sin(π/n)) = 10.0000，r = s/(2·tan(π/n)) = 8.6603

内角 = (n−2)×180°/n = 120.0000°，外角 = 360°/n = 60.0000°

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How to Use

Enter known values: fill sides, radius or angles in the Regular Polygon Calculator.
Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
See formula and steps: the result panel shows the formula used and the substitution.
Try another case: change any known value to solve again.

Key Points

Regular Polygon Calculator is a free online geometry tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Area, perimeter, angles, circumradius and inradius.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Regular polygon (side a, n sides)

Area A = n·a² ÷ (4·tan(π/n)) = perimeter × apothem ÷ 2

Interior angle = (n−2)×180° ÷ n · Exterior = 360° ÷ n

Circumradius R = a ÷ (2sin(π/n)) · Inradius r = a ÷ (2tan(π/n))

FAQ

How do I use the Regular Polygon Calculator?

Open the page and fill in the input fields — results update automatically. Area, perimeter, angles, circumradius and inradius.

Are the results accurate?

Yes. Standard formulas and conversion factors are used and verified.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. Everything runs locally in your browser.

Related Guides

Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated: 2026-08-07

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Regular Polygon Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/polygon

Results provided by this tool are for reference only and do not constitute professional advice.