Heptagon
Calculate regular heptagon: side length, perimeter, area, interior/exterior angles, circumradius, inradius. Free online 7-sided polygon geometry calculator.
About This Calculator
This heptagon calculator is a free online geometry tool that computes all key properties of a regular heptagon (also known as a septagon or 7-sided polygon). Simply enter the side length to instantly calculate the area, perimeter, interior and exterior angles, circumcircle radius, and incircle radius (apothem). It is ideal for students learning geometry, teachers preparing lesson materials, engineers working with heptagonal shapes, and anyone needing quick accurate 2D polygon calculations.
How It Works
A regular heptagon has seven equal sides and seven equal angles. The calculator uses standard geometric formulas: area = (7/4) x side^2 x cot(pi/7), perimeter = 7 x side, interior angle = (n-2) x 180 deg/n = 128.57 deg, exterior angle = 360 deg/n = 51.43 deg, circumradius = side / (2 x sin(pi/7)), and inradius = side / (2 x tan(pi/7)). Results are displayed instantly with two to three decimal place precision.
Applications of Heptagons
Heptagons appear in architecture, design, coinage (such as UK 20p and 50p coins which are curved heptagons), and nature. Understanding heptagon geometry is useful for tessellation studies, structural design, and mathematical exploration of polygon properties.
Frequently Asked Questions
What is a heptagon?
A heptagon is a polygon with seven sides and seven angles. It is also known as a septagon. In a regular heptagon, all sides have equal length and all interior angles are equal at approximately 128.57 degrees. The word heptagon comes from the Greek hept meaning seven and gonia meaning angle.
How do you calculate the area of a regular heptagon?
The area of a regular heptagon with side length a is calculated using the formula: Area = (7/4) x a^2 x cot(pi/7), which simplifies to approximately 3.634 x a^2. For example, a heptagon with side length 8 cm has an area of about 232.57 square centimeters.
What are the interior and exterior angles of a regular heptagon?
Each interior angle of a regular heptagon measures approximately 128.57 degrees, calculated as (n-2) x 180 deg / n where n = 7. Each exterior angle measures approximately 51.43 degrees, calculated as 360 deg / n. The sum of interior angles is 900 degrees.
What is the difference between circumradius and inradius of a heptagon?
The circumradius (R) is the radius of the circle that passes through all seven vertices of the heptagon, calculated as R = a / (2 x sin(pi/7)). The inradius or apothem (r) is the radius of the largest circle that fits inside the heptagon, touching the midpoint of each side, calculated as r = a / (2 x tan(pi/7)). The inradius is always smaller than the circumradius.
How many diagonals does a heptagon have?
A heptagon has 14 diagonals. The formula for the number of diagonals in any n-sided polygon is n x (n-3) / 2. For a heptagon (n = 7), this gives 7 x 4 / 2 = 14 diagonals.
Is a heptagon the same as a septagon?
Yes, heptagon and septagon are two names for the same seven-sided polygon. Heptagon comes from the Greek hept meaning seven, while septagon comes from the Latin septem meaning seven. Both terms are used interchangeably in geometry.
Is this heptagon calculator free to use?
Yes, this heptagon calculator on Calculy is completely free to use with no registration or download required. It works on any device including desktop, tablet, and mobile browsers.