Pentagon Calculator

How to Use the Pentagon Calculator

Welcome to the Pentagon Calculator, an easy-to-use tool designed to help you calculate key geometric properties of a regular pentagon. This guide will walk you through the steps to enter your data and interpret the results.

Step 1: Enter the Side Length

• Locate the input field labeled Side Length (meters).
• Enter the length of one side of the pentagon in meters. Note that the input must be a number between 0.0001 and 1,000,000, as these are the valid minimum and maximum values for the calculation.
• If you enter a number with decimals, you can be as precise as up to four decimal places (e.g., 10.1234).

Step 2: Review the Calculated Results

Once you have entered the side length, the calculator will automatically compute several properties of the pentagon:

• Perimeter: The perimeter is calculated using the formula: sideLength * 5. It is displayed with up to four decimal places and is followed by the unit ‘m’.
• Area: The area of the pentagon is computed using the formula: (5 * pow(sideLength, 2) * (1 / 4) * sqrt(5 + 2 * sqrt(5))). The value is shown with four decimal places and in square meters (‘m²’).
• Inradius (radius of inscribed circle): This is determined using the formula: sideLength * (sqrt(5 + 2 * sqrt(5))) / 4. The result is presented with four decimal places followed by the unit ‘m’.
• Circumradius (radius of circumscribed circle): Calculated by the formula: sideLength * sqrt(10 + 2 * sqrt(5)) / 4. It displays the radius with four decimal places in meters.
• Interior Angle: For a regular pentagon, each interior angle is a constant 108°.

Conclusion

This calculator is a user-friendly tool to help you quickly determine essential properties of a regular pentagon based on the length of one side. The calculations provided are accurate and formatted for clarity, ensuring you have all the necessary information at your fingertips.