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Calculate the area of a regular pentagon based on its side length, perimeter, or diagonal. Ideal for math studies and engineering calculations.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
This calculator takes one positive side length and returns the area and perimeter of a regular pentagon. “Regular” means all five sides and all five interior angles are equal. A general five-sided shape may be irregular, so one side alone is not enough to determine its area.
The perimeter is five times the side length, a. For area, a regular polygon can be split into five congruent triangles from its center. Equivalently, area is one-half the apothem (the perpendicular distance from the center to a side) times the perimeter. For a regular pentagon, the apothem is a/(2 tan 36°), giving A = 5a²/(4 tan 36°), approximately 1.72048a². The page uses the rounded coefficient 1.72048 and displays area and perimeter to four decimal places.
If the input is in inches, perimeter is in inches and area is in square inches. If the input is in feet, area is square feet. The form accepts a number but has no unit selector, so keep the unit attached to your own measurement.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Confirm that the shape is intended to be a regular pentagon, rather than an irregular five-sided outline.
Choose a unit for your measurement, such as inches or centimeters, and enter the length of one side as a positive number.
Read the area and perimeter. For a side of 5 units, the page calculates an area of 43.0120 square units and a perimeter of 25.0000 units.
Write the units alongside the results. The page reports numbers without choosing between inches, feet, meters, or another unit.
Check that the area unit is squared. A result based on a 5-inch side is 43.0120 in², not 43.0120 in.
Use cases
See how the tool fits into real work and everyday tasks.
When a problem specifies a regular pentagon and gives one side, compare the calculator’s perimeter with 5a and use the area as a check on the formula substitution.
For a repeated pentagon in a drawing or craft plan, estimate the face area and outline length from the planned side size before laying out the final design.
Try two side lengths to see how the perimeter changes in direct proportion while area changes with the square of the side length. This is a geometric comparison, not a substitute for measuring a non-regular object.
Q&A
Find concise answers to common questions and confusing cases.
No. The formula assumes both equal sides and equal angles. An irregular pentagon needs more geometric information than a single side length.
The input is one side length. Divide a known perimeter by five only when the shape is regular; a diagonal is not interchangeable with a side.
The input has no unit selector. Perimeter keeps the input length unit, and area uses its square—for example, inches produce in².
Notes
Review scope, result limitations, and important precautions before use.
The calculator uses the approximate coefficient 1.72048 rather than retaining the full trigonometric value. Four displayed decimal places describe the calculation output, not the accuracy of a physical measurement. Measurement error in the side length also affects the area, since the side is squared.
Only a positive side length is needed by the arithmetic; the form cannot verify that a real object has five equal sides and equal angles. For construction, surveying, or another precision-sensitive use, verify the shape and measurements independently and use the precision appropriate to the work.
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