Choose language

PL, EN, ES, DE, FR, RU

# Pentagon calculator - diagonals, area, perimeter, sides

Pentagon calculator will help you calculate the long diagonal of the pentagon, the medium diagonal of the pentagon, the shorter diagonal of the pentagon, the side length, height, area of the pentagon, circumference and radius of the circumscribed circle and the radius of the circle inscribed in the regular pentagon.

## Diagonal of a regular pentagon

$$p=\frac{\sqrt{5}+1}{2}\cdot a$$ ## Height of a regular pentagon

$$h=\frac{\sqrt{5+2\sqrt{5}}}{2}\cdot a$$ ## Perimeter of a regular pentagon

$$L = 5\cdot a$$ ## Area of a regular pentagon

$$P_{pow} = \frac{a^2}{4}\cdot\sqrt{25+10\cdot\sqrt{5}}$$ ## Radius of the circle circumscribed on a regular pentagon

$$R=\frac{a\cdot\sqrt{50+10\cdot\sqrt{5}}}{10}$$ ## Radius of the circle inscribed in a regular pentagon

$$r=\frac{a\cdot\sqrt{25+10\cdot\sqrt{5}}}{10}$$ Pentagon - information

Regular pentagon - a convex figure, a pentagon with all sides of equal length and all angles. Regular pentagons are the walls of polyhedrons such as regular dodecahedron and truncated icosahedron. A regular pentagon with side length a has the following properties:
1. every inside angle has a measure $${\frac {3}{5}}\pi =108^{\circ }}$$
2. the center angle of the circumscribed circle based on the side of the pentagon has a measure $${\frac {2}{5}}\pi =72^{\circ }}$$
3. the area of this figure is expressed by the formula $$P={\frac {5a^{2}}{4}}\operatorname {ctg} {\frac {\pi }{5}}={\frac {a^{2}}{4}}{\sqrt {25+10{\sqrt {5}}}}\approx 1{,}72048\cdot a^{2}}$$
4. the radius of the circle circumscribed on a regular pentagon has length $$R=a{\frac {\sqrt {50+10{\sqrt {5}}}}{10}}=a{\frac {1}{\sqrt {3-\varphi }}}}$$
5. the radius of the circle inscribed in a regular pentagon has the length $$r={\frac {a{\sqrt {25+10{\sqrt {5}}}}}{10}}={\frac {R}{\varphi }}}$$
6. the diagonal has the length $$d={\frac {{\sqrt {5}}+1}{2}}a=\varphi a}$$ where $$\varphi$$ is a golden number

## Users of this calculator also used

### Rail Fence, Zig-Zag - encoder / decoder

Rail Fence, Zig-Zag cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Rail Fence, Zig-Zag cipher.

### Fraction calculator - multiplying fractions step by step with explanation

With the Fractions Calculator, you can multiplying any two mixed numbers or proper and improper fractions.
Fractions Calculator will show you the result of operations on fractions step by step and will give you explanations of the operations performed to multiplying fraction. You will learn how to simplify fractions, how to find a common denominator, how to find the least common multiple and the greatest common divisor.

### HUBBERT curve calculator

With the Hubbert Curve Calculator you will calculate the curve values. In addition to the response results, the calculator will also plot the selected function. You can choose a ready-made function, e.g. hubb(x) or enter your own function, e.g. hubb(x^2), hubb(x+3), etc.

### Daltons law of partial volume

Thanks to the calculator, you can calculate the partial volume according to Daltons law.

### Fibonacci sequence calculator

Using the calculator, you can easily and quickly calculate the sum of the Fibonacci sequence, find a value or find the nth term.

### ROT47 cipher - encoder / decoder

ROT47 cipher online encoder and decoder. Encrypt and decrypt any cipher created in a ROT47 cipher. You can use any shift and additionally a key for more precise text encoding.

### Mean square, arithmetic mean of the squares, power mean of second order

With this calculator you will calculate the mean square or arithmetic mean of the squares also known as the power mean of the second order.