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Regular polygon calculator

Every measure of a regular polygon from the number of sides and the side length: the area, perimeter, interior and exterior angles, the sum of interior angles, the apothem (inradius), the circumradius and the number of diagonals. One entry, the full geometry — for triangles through many-sided polygons.

Related tools

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Regular polygon area calculatorCompute the area of a regular polygon from its number of sides and side length.Regular polygon perimeter calculatorCompute the perimeter of a regular polygon from its number of sides and side length.Polygon diagonals calculatorHow many diagonals a polygon has, from its number of sides: n·(n−3)/2 — because each vertex connects to all others except itself and its two neighbours. It also names the polygon and gives the number of triangles it splits into and the sum of its interior angles.Irregular polygon area calculatorThe area of any polygon — regular or not, convex or concave — from its corner coordinates. Enter the vertices in order and the shoelace formula returns the exact area, plus the perimeter, the centroid and whether the points run clockwise or counter-clockwise, with a drawing of the shape. Ideal for land plots and CAD sketches.Rectangle calculatorEvery property of a rectangle from any two you know. Pick what you have — length & width, area & a side, perimeter & a side, or diagonal & a side — and it returns the length, width, area, perimeter and diagonal, using A = l·w, P = 2(l+w) and d = √(l²+w²).Square calculatorAll four measures of a square from any one. Give the side, the area, the perimeter or the diagonal and it returns the rest — side s, area s², perimeter 4s and diagonal s√2 — instantly.Circle sector area calculatorCompute the area and arc length of a circle sector from its radius and angle.Equilateral triangle calculatorCompute the area, height and perimeter of an equilateral triangle from its side.

Enter Number of sides (n), Side length (s) and the Regular polygon calculator works out Area, Perimeter, Interior angle, Exterior angle, Sum of interior angles, Apothem (inradius), Circumradius, Number of diagonals straight away. For instance, with Number of sides (n) = 6 and Side length (s) = 10 it returns Area = 259.808, Perimeter = 60 and Interior angle = 120 °.

How to use it

  1. Enter your values: Number of sides (n), Side length (s).
  2. Read the result instantly: Area, Perimeter, Interior angle, Exterior angle, Sum of interior angles, Apothem (inradius), Circumradius, Number of diagonals.

Frequently asked questions

How does the Regular polygon calculator work?

It takes Number of sides (n) and Side length (s) and derives Area, Perimeter, Interior angle, Exterior angle, Sum of interior angles, Apothem (inradius), Circumradius and Number of diagonals from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

2 values: Number of sides (n) and Side length (s). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With Number of sides (n) = 6 and Side length (s) = 10, the calculator returns Area = 259.808, Perimeter = 60 and Interior angle = 120 °. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using Number of sides (n) = 12 and Side length (s) = 20 instead, Area goes from 259.808 to 4,478 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Number of sides (n) = 3 and Side length (s) = 5, Area comes out at 10.825. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

What is the difference between the Regular polygon calculator and the Regular polygon area calculator?

Both return Area. What differs is what they ask for: this one wants Number of sides (n) and Side length (s), the Regular polygon area calculator wants Number of sides and Side length. Use whichever matches the numbers you already have.

Is there a tool for the next step?

Regular polygon perimeter calculator is the closest one after this: Compute the perimeter of a regular polygon from its number of sides and side length.

What else is worth having open alongside it?

Polygon diagonals calculator and Irregular polygon area calculator — they come up in the same task often enough to be worth a second tab.

Further reading

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ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.How-toHow to Calculate VolumeVolume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.How-toHow to Calculate the Square Metres of a RoomFind a room's area by multiplying length by width. Here's the method for rectangular, L-shaped and round rooms, and why area drives your material orders.