Pentagon Area CalculatorFree online math calculator — instant results, no sign-up
Calculate the area of a regular pentagon.
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About the Pentagon Area Calculator
The Pentagon Area Calculator finds the area of a regular pentagon from its side length. It assumes all five sides and all five interior angles are equal. With the default side length of 5, the calculated area is 43.0119350147 square units.
- Side length
- The length of one of the regular pentagon’s five equal sides, measured in a consistent linear unit such as centimeters, meters, or inches; the default is 5.
Formula and method
A = (1/4) × √(5(5 + 2√5)) × s²; with s = 5, A = (1/4) × √(5(5 + 2√5)) × 5² ≈ 43.0119350147.
- AArea of the regular pentagon, expressed in square units.
- sLength of each of the pentagon’s five equal sides, expressed in linear units.
The calculator squares the side length and multiplies it by the regular-pentagon area factor, √(5(5 + 2√5))/4. This factor comes from dividing a regular pentagon into five congruent triangles meeting at its center. For the default input, squaring 5 gives 25, and multiplying by the factor gives approximately 43.0119350147.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Side length5
Results
- Result43.0119350147
How to use the Pentagon Area Calculator
- 1Confirm that the pentagon is regular: all five sides and all five interior angles must be equal.
- 2Enter the length of one side in the Side length field, or leave the default value of 5.
- 3Use a positive side length measured in your chosen linear unit.
- 4Run the calculation to obtain the pentagon’s area.
- 5Read the Result as square units: with Side length set to 5, Result = 43.0119350147.
Reading your result
The Result row reports the area enclosed by the regular pentagon, not its perimeter. For the default side length of 5, Result = 43.0119350147 square units. If the side length is measured in centimeters, the result is in square centimeters; if it is measured in meters, the result is in square meters.
Limitations
The formula applies only to regular pentagons. A pentagon with equal sides but unequal angles is not necessarily regular, and its area cannot be determined from one side length alone. Side length must be positive for a nondegenerate pentagon. The displayed decimal result is an approximation, and its precision does not imply that the input measurement is equally precise.
Common questions
Why does this calculator need only one side length?+
Regular pentagons all have the same shape, so one side length fixes the pentagon’s size and area. The regular-pentagon factor in the formula incorporates its five-sided geometry.
Can I use this calculator for a pentagon with five equal sides but unequal angles?+
No. The calculator requires both equal sides and equal angles. Each interior angle of a regular pentagon is 108°, and an equilateral pentagon with different angles may have a different area.
How is the default result of 43.0119350147 obtained?+
Substitute the default side length, 5, into A = √(5(5 + 2√5)) × s² / 4. This gives A = √(5(5 + 2√5)) × 25 / 4 ≈ 43.0119350147 square units.
Do I need to measure the pentagon’s apothem?+
No. For a regular pentagon, the apothem is determined by its side length. The calculator’s formula already incorporates that relationship, so no separate apothem input is needed.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.