Welcome to the Hexagon Radius Calculator! This handy tool is designed to quickly calculate different radii of a regular hexagon—whether you’re working with the side length, circumradius, or inradius (also called apothem). The calculator makes it easy to switch between these values without needing to remember complex geometric formulas. Simply enter the value you know, and the calculator will instantly provide the others. You can dive in and start using it right away, or keep reading to explore the formulas, examples, and parameter explanations in more detail.
Understanding the Formula
A regular hexagon has two main radii:
- Circumradius (R): Distance from the hexagon’s center to any of its vertices.
- Inradius / Apothem (r): Distance from the center to the midpoint of a side (perpendicular).
Both are directly related to the side length (s) of the hexagon.
1. When Side Length (s) is Known
- Circumradius: R = s
- Inradius: r = (s × √3) ÷ 2
2. When Circumradius (R) is Known
- Side Length: s = R
- Inradius: r = (R × √3) ÷ 2
3. When Inradius (r) is Known
- Side Length: s = (2 × r) ÷ √3
- Circumradius: R = (2 × r) ÷ √3
These formulas work because a regular hexagon can be divided into six equilateral triangles, which makes its geometry easier to handle.
Parameters Explained
- s (Side Length): The length of one edge of the hexagon. This is often the easiest measurement to find in real-life shapes.
- R (Circumradius): The radius that connects the center to a vertex. Useful for inscribed circles or circumscribed constructions.
- r (Inradius/Apothem): The radius from the center to the middle of a side. Commonly used when calculating the area of a hexagon.
Each of these parameters can be derived from the others, so knowing just one value is enough to calculate the rest.
How to Use the Hexagon Radius Calculator — Step-by-Step Example
Suppose you know the side length (s) is 8 cm and you want to find the circumradius and inradius.
- Enter 8 into the calculator as the side length.
- Circumradius: R = s = 8 cm.
- Inradius: r = (s × √3) ÷ 2 = (8 × 1.732) ÷ 2 ≈ 6.93 cm.
Final Answer:
- Circumradius = 8 cm
- Inradius = 6.93 cm
This means the circle touching all vertices of the hexagon has a radius of 8 cm, while the inscribed circle touching the sides has a radius of about 6.93 cm.
Additional Information
Here’s a quick reference table for different side lengths:
| Side Length (s) | Circumradius (R) | Inradius (r) |
|---|---|---|
| 4 | 4 | 3.46 |
| 6 | 6 | 5.20 |
| 10 | 10 | 8.66 |
| 12 | 12 | 10.39 |
This table helps you quickly estimate values without doing full calculations.
FAQs
The circumradius reaches from the center to a vertex, while the inradius reaches from the center to the midpoint of a side.
Yes, once you know the side length (s), you can use the area formula: Area = (3√3 ÷ 2) × s².
Absolutely! It’s commonly used in construction, design, tiling, and any situation where hexagonal patterns or shapes are involved.