A regular N-gon is a type of polygon that has exactly N sides, and all of those sides are of equal length. Additionally, all the interior angles of a regular N-gon are equal, which gives it perfect rotational symmetry. The "N" simply refers to the number of sides (or vertices) the polygon has. So, for example:
These shapes are commonly found in art, architecture, design, and mathematics. The symmetry and balance of regular polygons make them both visually appealing and mathematically significant. Depending on the number of sides, a regular N-gon can appear almost circular (if it has many sides) or more angular (if it has fewer sides). Each regular N-gon can also be inscribed in a circle (called the circumcircle) or contain a circle inside it that touches all sides (called the incircle).
The Regular N-gon Calculator is a helpful online tool designed to calculate various geometric properties of any regular polygon. It is ideal for anyone who works with geometry, including students, teachers, engineers, architects, and hobbyists. Instead of doing complex formulas by hand, you can simply enter two basic values: the length of a side (edge) and the total number of sides (vertices).
Once you enter these values and click "Calculate," the tool will automatically display useful results such as:
You can also choose how many decimal places you'd like the results to be rounded to. The calculator helps you save time, reduce errors, and better understand the geometry of regular polygons without needing to memorize complex formulas.
The Regular N-gon Calculator features a clean and simple interface designed for ease of use. It includes clearly labeled input fields, automatic output fields, and action buttons that make calculations fast and intuitive. The layout is organized vertically, guiding the user step-by-step from input to result.
The calculator form includes:
This field is where you enter the length of one side of the regular N-gon. It must be a positive number. This value is essential for determining the size of the polygon and calculating other properties like perimeter, area, and radii.
Here, you enter how many sides (or corners) the polygon has. The minimum number is 3, since a polygon must have at least three sides. The higher the number, the more the shape resembles a circle. This value affects nearly every other calculation, including angles, diagonals, and radii.
After entering the edge length and the number of vertices, the Regular N-gon Calculator instantly computes several important geometric values. These results help you understand the shape and structure of the polygon without needing to do complex math manually. Below is a breakdown of each result field and what it represents:
The perimeter is the total distance around the polygon. It is calculated by multiplying the edge length by the number of sides. For example, if each side is 5 units long and the polygon has 6 sides, the perimeter will be 30 units.
This is the vertical distance from the center of the polygon to the midpoint of one of its sides. It’s especially useful when working with layouts or designs where height clearance is important. The calculator determines this value based on the number of sides and the edge length.
The area represents the total surface enclosed within the polygon. It is calculated using a special formula for regular polygons that considers both the edge length and the number of sides. This value is useful for space planning, geometry lessons, and design projects.
This is the radius of the circle that passes through all the polygon's vertices. It's called the circumcircle and helps visualize how the polygon fits inside a circle. It’s useful in geometry, modeling, and design applications.
The incircle is the largest circle that can fit entirely inside the polygon and touch all of its sides. The radius of this circle is called the incircle radius. This value is commonly used in tiling, layout design, and architectural calculations.
This is the measure of the interior angle between two adjacent sides of the polygon. All interior angles are equal in a regular polygon. Knowing the angle helps in design symmetry and when connecting multiple polygons together.
This field shows how many unique diagonals can be drawn inside the polygon. A diagonal is a line that connects two non-adjacent vertices. The number increases significantly with each additional side.
This value calculates the length of a diagonal that skips a specific number of edges. For example, if you choose 2, the calculator finds the length of a diagonal that jumps across two sides of the polygon. This is useful in construction, tiling, and advanced geometric studies.
The Regular N-gon Calculator includes a few additional features to enhance usability and ensure precision. These options allow you to control the accuracy of the results and easily perform new calculations when needed.
Below the main input and output fields, there is a dropdown menu labeled "Round to". This menu lets you select how many decimal places you want the results to be rounded to. You can choose from 0 to 15 decimal places, depending on how precise you want your answers to be.
For example, if you select:
This feature is especially helpful when working on projects that require a specific level of accuracy.
After entering the edge length and the number of vertices, click the "Calculate" button to run the computation. The calculator will process your inputs and automatically fill in all the result fields, including the perimeter, area, angle, radii, height, and diagonals.
If any required input is missing or invalid (such as a number of vertices less than 3), the calculator will display an alert message prompting you to correct the values.
To start over or clear all values, simply click the "Delete" button. This will reset all input and output fields, allowing you to enter new data and perform a fresh calculation. It’s a quick way to clear the form without having to manually erase each field.
After performing a calculation, the Regular N-gon Calculator displays a visual diagram of the polygon. This illustration updates automatically based on the number of vertices you entered. It helps you better understand the shape and see how the properties relate to the geometry of the N-gon.
The diagram is shown as an image element, and it visually reflects the number of sides and symmetry of the polygon. This can be especially useful for educational purposes or design visualization, giving you a quick and intuitive grasp of the structure you're working with.
To ensure accurate results, the calculator includes built-in validation checks. If incorrect or incomplete information is entered, it will display an alert message to guide you:
These features help avoid confusion and prevent inaccurate or meaningless results.
In addition to the core functionality, the calculator includes a few helpful tools:
These features combine to make the Regular N-gon Calculator a comprehensive and user-friendly tool for exploring regular polygons with ease.