Regular Pentagon Calculator
Find the area of a regular pentagon using side length, perimeter, or apothem.
What this calculator does
This tool computes the area of a regular pentagon quickly and accurately. A regular pentagon has five equal sides and five equal angles. Once you provide one valid measurement (side length, perimeter, or apothem), the calculator determines the full set of geometric values, including:
- Area
- Perimeter
- Side length
- Apothem
- Circumradius (radius from center to a vertex)
Formulas for a regular pentagon
For a regular pentagon with side length s:
Perimeter: P = 5s
Apothem: a = s / (2 tan(π/5))
Area: A = (1/4) √(5(5 + 2√5)) · s²
Also: A = (1/2) · P · a
These formulas are mathematically equivalent for a regular pentagon. The calculator uses trigonometric relationships and displays rounded values according to your selected decimal places.
How to use the calculator
1) Choose what you know
Select side length, perimeter, or apothem from the dropdown.
2) Enter a positive number
Input must be greater than zero. Optional unit text helps label your results.
3) Click Calculate
You’ll get the area plus other useful geometric values instantly.
Example calculation
Suppose the side length is 10 cm. Then:
- Perimeter = 5 × 10 = 50 cm
- Apothem ≈ 6.8819 cm
- Area = 0.5 × 50 × 6.8819 ≈ 172.0477 cm2
This shows how quickly area scales with side length: if side length doubles, area grows by a factor of four.
Where this is useful
- Architecture and floor-plan layouts
- Tile, panel, and decorative design
- 3D modeling and CAD geometry
- Math homework, exam prep, and teaching
Tips for accurate results
- Use consistent units across measurements.
- Do not mix linear units (cm, m, in) in one input.
- Set higher decimal places for engineering or fabrication contexts.
- For reporting, round only at the final step.
FAQ
Can I use this for irregular pentagons?
No. This calculator is specifically for regular pentagons (all sides and angles equal).
What if I only know perimeter?
That works. The calculator converts perimeter to side length first, then computes area and the rest.
What unit does area use?
Area is always in square units. If your input unit is m, area is shown in m2. If no unit is entered, numeric results are still correct but unitless.