Regular n-gon Area Calculator
Formulas Used:
A = (n × s²) / [4 × tan(π/n)]
A = (n × s × a) / 2
A = (n × R² × sin(2π/n)) / 2
In geometry, not all shapes are simple triangles or squares. Many objects have five, six, seven, or even more sides. These shapes are called polygons. When a polygon has all sides and angles equal, it is known as a regular n‑gon, where “n” means the number of sides.
Knowing the area of an n‑gon is important in school math, architecture, engineering, design, and even land measurement. But calculating it by hand can be confusing, especially when the number of sides increases.
The N‑Gon Area Calculator makes this task easy. You only need to enter the number of sides and the side length (or apothem), and the calculator gives you the area instantly.
What the N‑Gon Area Calculator Is
A Regular Polygon Area Tool
The N‑Gon Area Calculator is an online geometry tool that finds the area of a regular polygon. A regular polygon has:
- Equal side lengths
- Equal interior angles
- A symmetrical shape
Examples of regular polygons include:
- Triangle (3 sides)
- Square (4 sides)
- Pentagon (5 sides)
- Hexagon (6 sides)
- Octagon (8 sides)
The calculator works for any value of n greater than 2.
Why N‑Gon Area Matters
Knowing the area of an n‑gon helps with:
- Solving geometry problems
- Designing floor patterns
- Planning construction layouts
- Creating digital graphics
- Measuring land or surfaces
Accurate area calculations help avoid design mistakes and material waste.
How the Calculator Works
Step 1: Enter the Number of Sides (n)
This tells the calculator what type of polygon you are working with.
Step 2: Enter the Side Length (s)
This is the length of one side of the polygon.
Step 3: (Optional) Enter the Apothem
Some calculators allow you to use the apothem, which is the distance from the center to the middle of a side.
Step 4: Get the Area
The calculator applies the correct polygon area formula and shows the result instantly.
Key Formulas Used
Regular N‑Gon Area Using Side Length
Area = (n × s²) ÷ (4 × tan(π ÷ n))
Where:
- n = number of sides
- s = side length
- π ≈ 3.1416
This formula works for all regular polygons.
Area Using Apothem
Area = (Perimeter × Apothem) ÷ 2
Perimeter = n × s
This formula is useful when the apothem is known instead of side length.
Step‑by‑Step Example
Example: Regular Hexagon
Given:
- n = 6
- s = 4 cm
Step 1: Apply the formula
Area = (6 × 4²) ÷ (4 × tan(π ÷ 6))
Step 2: Simplify
Area = (6 × 16) ÷ (4 × 0.577)
Area ≈ 96 ÷ 2.308
Area ≈ 41.57 cm²
Result:
The area of the hexagon is 41.57 cm².
Features of the N‑Gon Area Calculator
Simple Inputs
Only the number of sides and side length are needed.
Fast Results
The calculator gives answers instantly.
Accurate Geometry
Uses standard mathematical formulas.
Supports Many Shapes
Works for triangles, pentagons, hexagons, and more.
Student Friendly
Easy to understand and use.
Uses and Applications
Education
Students use the N‑Gon Area Calculator to solve geometry problems and understand polygon properties better.
Architecture & Design
Designers use polygon areas for floor patterns, layouts, and decorative shapes.
Engineering
Engineers calculate polygon areas for structural parts and components.
Land & Space Planning
Regular polygon shapes are used in planning and surveying.
Helpful Tips for Accurate Results
Use Regular Polygons Only
The formulas work only for shapes with equal sides.
Measure Side Length Carefully
Small errors can change the result.
Keep Units Consistent
Do not mix cm with m or inches with feet.
Double‑Check the Number of Sides
Wrong n value gives wrong area.
Common Mistakes to Avoid
Using Irregular Polygons
The calculator is for regular shapes only.
Mixing Units
Always stay in one unit system.
Entering Wrong Side Length
Accurate measurement is important.
Forgetting the Shape Type
Different polygons need correct n values.
FAQs
What is an n‑gon?
A polygon with n sides.
What is a regular polygon?
A shape with equal sides and angles.
Can I use this for any n value?
Yes, for all n greater than 2.
What is an apothem?
It is the distance from the center to a side.
Is the calculator accurate?
Yes, when correct values are entered.
Final Words
The N‑Gon Area Calculator is a powerful and simple tool for finding the area of regular polygons. By entering just the number of sides and the side length, you can get fast and accurate results.
Whether you are a student, designer, engineer, or planner, this calculator helps you work with polygon shapes confidently and correctly.