Inradius of Heptagon given Height Calculator

Inradius Formula:

\[ r_i = \frac{h \times \tan\left(\frac{\pi/2}{7}\right)}{\tan\left(\frac{\pi}{7}\right)} \]

Inradius of Heptagon (m):

1. What is Inradius of Heptagon?

Definition: The inradius of a heptagon is the radius of the circle that fits perfectly inside the heptagon, touching all its sides.

Purpose: Knowing the inradius helps in geometric calculations, construction planning, and design of heptagonal shapes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{h \times \tan\left(\frac{\pi/2}{7}\right)}{\tan\left(\frac{\pi}{7}\right)} \]

Where:

\( r_i \) — Inradius of the heptagon (meters)
\( h \) — Height of the heptagon (meters)
\( \pi \) — Mathematical constant (~3.14159)
\( \tan \) — Trigonometric tangent function

Explanation: The formula relates the height of a regular heptagon to its inradius through trigonometric functions of angles based on its seven sides.

3. Importance of Inradius Calculation

Details: The inradius is crucial for determining the largest circle that fits inside the heptagon, which is important in engineering and design applications.

4. Using the Calculator

Tips: Enter the height of the heptagon in meters and the desired tolerance percentage (default ±5%). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical height for a heptagon?
A: Heights vary by application. For a regular heptagon, height depends on side length and is approximately 2.075 times the side length.

Q2: Why include a tolerance percentage?
A: Tolerance accounts for measurement errors and manufacturing variations in real-world applications.

Q3: Can this calculator be used for irregular heptagons?
A: No, this formula only works for regular heptagons where all sides and angles are equal.

Q4: How precise are the calculations?
A: Calculations use PHP's floating-point precision (about 14 decimal digits) but display 6 decimal places for readability.

Q5: What if my height measurement is in different units?
A: Convert your measurement to meters before entering, or convert the result from meters to your desired unit.