How Many Degrees in a Hexagon? Geometry Explained
The Short Answer: 720 Degrees Total
A hexagon has 720 degrees when you add up all its interior angles. That's the bottom line.
Here's why: any polygon with n sides has interior angles that sum to (n-2) × 180°. Plug in 6 for n, and you get (6-2) × 180 = 4 × 180 = 720.
Simple math. No fluff needed.
What About Each Angle in a Regular Hexagon?
If you're dealing with a regular hexagon — where all sides and angles are equal — each interior angle is 120 degrees. You get that by dividing 720 by 6.
Interior vs. Exterior Angles
Don't confuse the two:
- Interior angles face inward, toward the center. Each one is 120° in a regular hexagon.
- Exterior angles sit outside the shape, formed by extending one side. They always sum to 360° for any polygon, and each one is 60° in a regular hexagon.
Quick check: 120° + 60° = 180°. That's always true for interior and exterior angles at the same vertex.
Comparing Hexagons to Other Polygons
| Polygon | Number of Sides | Sum of Interior Angles | Each Angle (Regular) |
|---|---|---|---|
| Triangle | 3 | 180° | 60° |
| Square | 4 | 360° | 90° |
| Pentagon | 5 | 540° | 108° |
| Hexagon | 6 | 720° | 120° |
| Octagon | 8 | 1080° | 135° |
Notice the pattern: each time you add a side, the total increases by 180°. That's the (n-2) × 180 formula in action.
Why Hexagons Show Up Everywhere
Bees aren't just cute — they're geometry geniuses. Honeycombs use hexagons because hexagons tile perfectly with no gaps, using less wax than squares or triangles would.
You'll also see hexagonal bolts, floor tiles, architectural elements, and game pieces. The 120° interior angles create a shape that packs tightly and distributes stress evenly.
How to Calculate Hexagon Angles: Getting Started
Need to find an angle for a project? Here's what to do:
- Identify your hexagon type. Regular (all sides equal) or irregular?
- For regular hexagons: Divide 720 by 6. That's 120° per interior angle.
- For exterior angles: Divide 360 by 6. That's 60° per exterior angle.
- For irregular hexagons: Measure each angle individually, or use the (n-2) × 180 formula to find the total if you know five of the six angles.
Quick Example
Say you know five interior angles of an irregular hexagon: 130°, 115°, 140°, 95°, and 120°. What's the sixth?
720 - (130 + 115 + 140 + 95 + 120) = 720 - 600 = 120°
That's it. Subtract what you know from the total.
The Formula Breakdown
If you want to understand the math behind it:
- Any polygon can be split into triangles by drawing diagonals from one vertex to all others.
- A hexagon splits into 4 triangles.
- Each triangle has 180°.
- 4 × 180° = 720°.
That's why the formula works. Triangles are the building blocks of all polygons.
Common Mistakes to Avoid
- Forgetting that exterior angles always sum to 360°, regardless of how many sides the polygon has.
- Confusing regular with irregular hexagons. The 120° rule only applies to regular hexagons.
- Using degrees when radians are needed for certain math or programming applications. 120° = 2π/3 radians.
That's the Geometry
A hexagon has 720 degrees in total interior angles, with each angle in a regular hexagon measuring 120 degrees. The exterior angles add up to 360 degrees, at 60 degrees each.
Use the (n-2) × 180 formula for any polygon. Subtract your known angles from the total for irregular shapes. Done.