Pentagon Area Calculator
The area of a regular pentagon from its side length, with its perimeter.
A regular pentagon divides into five identical triangles from the center, giving an area of 5a² ÷ (4·tan(36°)), about 1.
How the pentagon area calculator works
A regular pentagon divides into five identical triangles from the center, giving an area of 5a² ÷ (4·tan(36°)), about 1.720 a². Its interior angles are 108°, which is why pentagons cannot tile a flat plane — three leave a 36° gap and four overlap. The pentagon is also where the golden ratio appears: the diagonal divided by the side is exactly φ.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Side 10 | 172.0477 | 172.05 |
| Side 1 | 1.7205 | 1.7205 |
| Side 25 | 1,075.2984 | 1,075.3 |
FAQFrequently asked questions
What is the area of a regular pentagon?
About 1.720 times the side squared — exactly 5a² ÷ (4·tan 36°).
What are its interior angles?
108° each, and they add to 540°.
Why can pentagons not tile a floor?
Because 108° does not divide 360° — three meet with a 36° gap left over.
Where does the golden ratio come in?
A regular pentagon's diagonal divided by its side is exactly φ, about 1.618.
Is this for regular pentagons only?
Yes. An irregular five-sided shape must be split into triangles and added up.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.