Heptagon Calculator
Calculate area, perimeter, angles, and other properties of a regular heptagon (7-sided polygon)
Calculate Heptagon Properties
Length of one side of the regular heptagon
Heptagon Properties
Formulas Used
Perimeter: P = 7 × a
Area: A = (7/4) × a² × cot(π/7) ≈ 3.634 × a²
Interior Angle: α = (7-2) × 180° / 7 = 128.57°
Exterior Angle: β = 360° / 7 = 51.43°
Circumradius: R = a / (2 × sin(π/7))
Inradius: r = a / (2 × tan(π/7))
Example Calculation
Regular Heptagon with Side Length 8 cm
Given: Side length (a) = 8 cm
Perimeter: P = 7 × 8 = 56 cm
Area: A = 3.634 × 8² = 3.634 × 64 = 232.58 cm²
Interior Angle: α = (7-2) × 180° / 7 = 128.57°
Circumradius: R = 8 / (2 × sin(π/7)) = 9.22 cm
Inradius: r = 8 / (2 × tan(π/7)) = 8.31 cm
Heptagon Properties
Sides & Vertices
7 equal sides and 7 vertices
Interior Angles
Each angle = 128.57°
Sum = 900°
Exterior Angles
Each angle = 51.43°
Sum = 360°
Heptagon Facts
Also called a septagon (from Latin)
Cannot be constructed with compass and straightedge
Interior angle ≈ 128.57° (5π/7 radians)
Area coefficient ≈ 3.634 for unit side
Understanding Heptagons
What is a Heptagon?
A heptagon (also called a septagon) is a seven-sided polygon. The name comes from Greek "hept" meaning seven. In a regular heptagon, all sides are equal in length and all interior angles are equal.
Key Properties
- •7 equal sides and 7 equal angles
- •Sum of interior angles = 900°
- •Each interior angle ≈ 128.57°
- •Each exterior angle ≈ 51.43°
Mathematical Formulas
Perimeter
P = 7 × a
Area
A = (7/4) × a² × cot(π/7)
A ≈ 3.634 × a²
Circumradius
R = a / (2 × sin(π/7))
Inradius
r = a / (2 × tan(π/7))
Applications and Uses
Architecture
Used in architectural designs and decorative patterns
Engineering
Applied in mechanical engineering and structural design
Art & Design
Featured in geometric art and logo designs