Area of a Regular Polygon Calculator: Sides, Perimeter, Apothem, Circumradius

Q: What is the formula for the area of a regular polygon with side length?

A common formula is A = n a^2 / (4 tan(pi/n)) , where n is the number of sides and a is the side length.

Q: How do you find the area of a regular polygon from the perimeter and apothem?

Use A = P r / 2 , where P is the perimeter and r is the apothem.

Q: What is the classic regular polygon area formula?

The classic formula is A = n × a × r / 2 , where n is the number of sides, a is the side length, and r is the apothem.

Q: How do you find the area of a regular polygon from the circumradius?

Use A = n R^2 sin(2pi/n) / 2 , where R is the circumradius and n is the number of sides.

Area of a Regular Polygon Calculator: calculate regular polygon area from the number of sides and the side length, perimeter and apothem, apothem, or circumradius. Works for pentagons, hexagons, octagons, and more.

This regular polygon area calculator finds the area from the number of sides and the values you know. You can work from the side length, from the perimeter and apothem, from the apothem, from the circumradius, or from the classic side-and-apothem formula.

The calculator is useful for regular pentagons, hexagons, octagons, and other regular polygons. It also works in reverse from the area to the selected measure while keeping the number of sides fixed.

Regular polygon area can be written in several equivalent ways, including A = n a^2 / (4 tan(pi/n)), A = P × r / 2, A = n r^2 tan(pi/n), A = n R^2 sin(2pi/n) / 2, and the classic formula A = n × a × r / 2.

Initial Data

Area of a regular polygon formulas

$$A= \frac{n a^2}{4\tan(\pi/n)}$$

№ of sides, side length, and apothem № of sides, perimeter, and apothem № of sides and side length № of sides and apothem № of sides and circumradius

№ of sides (n)

Side length (a)

Area (A)

2-dimensional shapes

3-dimensional shapes

Area of a Regular Polygon Calculator FAQs

How do you find the area of a regular polygon?
You need the number of sides and one matching measure. This calculator supports side length, perimeter and apothem, apothem, circumradius, and the classic side-and-apothem formula for regular polygons.

What is the formula for the area of a regular polygon with side length?
A common formula is A = n a^2 / (4 tan(pi/n)), where n is the number of sides and a is the side length.

How do you find the area of a regular polygon from the apothem?
If you know the number of sides and the apothem r, you can use A = n r^2 tan(pi/n). Another equivalent form is A = P r / 2 if the perimeter is known.

How do you find the area of a regular polygon from the perimeter and apothem?
Use A = P r / 2, where P is the perimeter and r is the apothem.

What is the classic regular polygon area formula?
The classic formula is A = n × a × r / 2, where n is the number of sides, a is the side length, and r is the apothem.

How do you find the area of a regular polygon from the circumradius?
Use A = n R^2 sin(2pi/n) / 2, where R is the circumradius and n is the number of sides.

Can this calculator be used for a regular pentagon or hexagon?
Yes. Enter 5 sides for a regular pentagon, 6 sides for a regular hexagon, 8 sides for a regular octagon, and so on.

Does the number of sides have to be an integer?
Yes. A regular polygon must have a whole number of sides, and it must be at least 3.