Instantly compute area, perimeter, diagonal, height, inradius & circumradius of any regular pentagon. Upload CSV/TXT for bulk processing.
⬠ Launch Calculator ↓Paste hundreds or thousands of side-length values, one per line. Process them all instantly with a single click — no limits.
Drag and drop or browse for your .csv or .txt file. Side lengths are loaded into the bulk processor immediately.
Single-value mode shows all 6 pentagon properties: area, perimeter, diagonal, height, inradius, and circumradius.
Real-time validation catches non-numeric or non-positive inputs and provides helpful inline error messages instantly.
After each bulk calculation, view count, min/max area, and total perimeter in the summary dashboard at a glance.
Copy to clipboard or download a ready-to-use CSV with all side lengths and computed properties in one click.
Enter any positive real number representing the side length of a regular pentagon.
Drag & Drop or click to upload
.csv or .txt · max 5 MB · one side length per line
Or paste side lengths (one per line):
| # | Side (s) | Area | Perimeter | Diagonal | Height | Inradius | Circumradius | Status |
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A pentagon is a polygon with exactly five sides and five interior angles. When all five sides are equal in length and all interior angles are equal (each measuring 108°), it is called a regular pentagon. The sum of interior angles of any pentagon is always 540°, a fact derived from the general polygon formula (n − 2) × 180°, where n = 5. Regular pentagons are among the most studied shapes in geometry, celebrated for their elegant connection to the golden ratio (φ ≈ 1.61803) and their appearance in art, architecture, biology, and engineering.
The area of a regular pentagon with side length s is calculated using the formula: A = (s² / 4) × √(25 + 10√5). This simplifies to approximately A ≈ 1.72047740 × s². Alternatively, you can use the apothem (inradius): A = (5 × s × a) / 2, where a is the apothem. This formula divides the pentagon into five congruent isosceles triangles radiating from the centre. For example, a pentagon with side 6 cm has an area of approximately 1.72047740 × 36 ≈ 61.94 cm².
The perimeter of a regular pentagon is simply five times the side length: P = 5 × s. This is the total boundary length. For an irregular pentagon you would sum all five distinct side lengths. Perimeter is used in fencing problems, construction layouts, and any application requiring the total outer length of a pentagonal boundary.
The height of a regular pentagon is the perpendicular distance from the base to the opposite vertex (apex). Its formula is: H = (s / 2) × √(5 + 2√5), which approximates to H ≈ 1.53884 × s. The diagonal connects two non-adjacent vertices and is related to the side through the golden ratio: d = s × φ = s × (1 + √5) / 2 ≈ 1.61803 × s. This golden-ratio relationship makes the regular pentagon unique among polygons and underlies the construction of the pentagram (five-pointed star).
The inradius (also called the apothem) is the radius of the largest circle that fits inside a regular pentagon, touching every side at its midpoint: r = s / (2 × tan(π/5)) ≈ 0.68819 × s. The circumradius is the radius of the circle passing through all five vertices: R = s / (2 × sin(π/5)) ≈ 0.85065 × s. The ratio R/r = 1/cos(36°) ≈ 1.2361, a constant for all regular pentagons. These two radii are fundamental in computational geometry, circuit-board design, and mosaic tiling.
A regular pentagon obeys several remarkable rules. Each interior angle is 108°; each exterior angle is 72°. The central angle subtended by each side is 72° (360° / 5). Pentagons tile the plane only in conjunction with other shapes — a regular pentagon alone cannot tessellate flat space, unlike triangles, squares, or hexagons. The Penrose tiling, a famous quasi-periodic tiling of the plane, employs two rhombus shapes derived directly from the regular pentagon. In nature, pentagonal symmetry appears in starfish, flowers (many species have 5 petals), and sea urchins.
Our tool operates in two intuitive modes. Single Mode: enter one side length, choose decimal precision (up to 15 places), and click Compute Pentagon. A full properties panel shows area, perimeter, diagonal, height, inradius, circumradius, and derived values including area-to-side ratio and diagonal-to-side ratio. Bulk Mode: paste up to thousands of side lengths (one per line) or upload a .csv or .txt file. The tool validates all input in real time, processes every value instantly, and presents results in a clean sortable table with per-row status badges and a summary statistics dashboard — then lets you copy or download the complete output as a CSV file with one click.
Pentagon geometry is applied across numerous fields. The Pentagon building in Washington D.C. is one of the world's most recognisable architectural uses of pentagonal geometry. In football (soccer), the classic black-and-white ball uses a truncated icosahedron pattern with pentagonal and hexagonal panels. In chemistry, cyclopentane (C₅H₁₀) has a pentagonal ring structure. In crystallography, quasicrystals exhibit five-fold symmetry that was once thought impossible in nature. In graphic design, the regular pentagon underpins the construction of five-pointed stars used in hundreds of national flags, corporate logos, and emblems worldwide.
Interior angle: 108° · Exterior angle: 72° · Sum of angles: 540° · φ = (1+√5)/2 (golden ratio)
Type a single side length or paste a list (one per line). Alternatively drag and drop or upload your .csv / .txt file.
Pick your decimal precision from 2 up to 15 places for maximum accuracy in engineering or academic work.
Click Compute. View the full results table with all 6 properties, then clear, copy to clipboard, or download as CSV.
The area of a regular pentagon with side length s is A = (s² / 4) × √(25 + 10√5) ≈ 1.72048 × s². You can also compute it as A = (5 × s × apothem) / 2, where the apothem (inradius) equals s / (2 × tan(36°)).
For a regular pentagon, simply multiply the side length by 5: P = 5s. For an irregular pentagon, add all five individual side lengths together. The perimeter tells you the total boundary length of the shape.
Height = (s/2) × √(5 + 2√5) ≈ 1.53884 × s. Diagonal = s × (1 + √5) / 2 ≈ 1.61803 × s (the golden ratio times the side). This calculator computes both automatically from the side length you enter.
Yes. Prepare a .csv or .txt file with one positive side-length value per line — no header row needed. Files up to 5 MB are accepted. Upload via drag-and-drop or the file picker. All values are validated and processed instantly in your browser.
The inradius (apothem) r ≈ 0.68819 × s is the radius of the inscribed circle touching all five sides. The circumradius R ≈ 0.85065 × s is the radius of the circumscribed circle passing through all five vertices. Both are computed automatically by this tool.
Completely free, no registration required. All calculations run client-side in your browser using JavaScript — no data is ever transmitted to a server. Your values stay private.
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