Pentagon Calculator
Enter any one measurement of a regular pentagon (side, area, perimeter, diagonal, height, circumradius or inradius) to find the rest.
Change the values and press Calculate to work out your own figures.
Enter any one measurement of the regular pentagon.
Show the working
- From the side (a): side a = 3
- Area = n a² ÷ (4 tan(180° ÷ n)) = 5 × 3² ÷ (4 tan(36°))
- Area (A) = 15.48429661
How to use it
Enter any one measurement of the regular pentagon.
Enter the measurements (decimals, fractions such as 3/4, or mixed numbers such as 1 1/2) and, if you like, their unit; the answer is then also given in other units. Show the working gives the formula.
Key facts
A = ¼ √(5(5 + 2√5)) a²; d = φ a
The golden ratio
A regular pentagon's diagonal is φ ≈ 1.618 times its side.
Questions
What is the area of a regular pentagon with side 3?
≈ 15.48429661.
How many degrees is each angle?
108°.
Formulas
A = ¼ √(5(5 + 2√5)) a²; d = φ a
Sources
Limitations
- All measurements in one calculation use the same unit; the answer is also given in other units.
- Measurements up to 10¹⁵.