What Is the Difference between a Hexagon and an Octagon? | Spot It At A Glance

A hexagon has 6 sides, while an octagon has 8; if they’re regular, their interior angles are 120° and 135°.

You’ve seen both shapes a thousand times. A honeycomb cell. A stop sign. A pencil barrel. A tiled floor pattern. The names can blur together, so let’s pin them down in a way that sticks.

The cleanest difference is the side count: six vs eight. From there, everything else follows—angle totals, diagonal counts, symmetry, and the way each shape behaves when you try to measure it or draw it.

This article gives you fast identification tricks, then builds into the math and the “why it matters” stuff you’ll meet in class, crafts, design, and test questions.

Difference Between A Hexagon And An Octagon For Quick Identification

If you only remember one trick, make it this: trace the edges with your finger and count out loud. Sounds simple, yet it beats guessing from a picture where sides are short, skewed, or partly hidden.

Side Count Is The Defining Test

• Hexagon: 6 sides and 6 corners (vertices).
• Octagon: 8 sides and 8 corners (vertices).

If a shape looks “roundish” because the corners are chopped off, it may still be a polygon. Polygons can have short sides that make the outline feel close to a circle. Counting keeps you honest.

Two Real-World Memory Hooks

• Hexagon → bees: honeycomb cells are hexagonal because the shape packs tightly with no gaps.
• Octagon → stop signs: the classic road stop sign is an octagon, which makes it easy to spot even when partly covered.

A Quick Corner Check When Counting Is Hard

If the picture hides sides, corners can be easier to spot. Each corner marks a vertex, and the vertex count matches the side count for polygons.

Still stuck? Draw tiny dots on each corner first. Then count the dots. It’s a small move that clears up messy worksheets fast.

How The Angle Math Changes From 6 Sides To 8

Once you know the side count, you can compute angle totals without memorizing separate rules for each shape.

Interior Angle Sum Formula

The sum of interior angles for any simple polygon is:

(n − 2) × 180°

Here, n means the number of sides.

Hexagon Interior Angle Sum

For a hexagon, n = 6:

(6 − 2) × 180° = 4 × 180° = 720°

Octagon Interior Angle Sum

For an octagon, n = 8:

(8 − 2) × 180° = 6 × 180° = 1080°

Regular Shapes Have Equal Angles

A shape is regular when all sides match and all angles match.

• Regular hexagon: each interior angle is 720° ÷ 6 = 120°.
• Regular octagon: each interior angle is 1080° ÷ 8 = 135°.

That’s a nice test-taking shortcut: if you see 120° at every corner, think “six.” If you see 135° at every corner, think “eight.”

Regular Vs Irregular: Same Name, Different Behavior

In worksheets and real objects, you’ll meet both regular and irregular polygons. The name “hexagon” or “octagon” only promises the side count. It does not promise equal sides or equal angles.

Regular Hexagon

A regular hexagon is a tidy shape: equal edges, equal corners, strong symmetry, and clean formulas. Many geometry problems quietly assume “regular” even when the diagram looks perfect but the word isn’t printed.

Irregular Hexagon

An irregular hexagon still has six sides. The sides can differ in length, and the interior angles can differ too. The total interior angle sum stays at 720°, but you can’t jump to “each angle is 120°.”

Regular Octagon

A regular octagon has eight equal sides and eight equal angles. Its 135° corners are a common checkpoint in middle school and high school geometry.

Irregular Octagon

An irregular octagon keeps the eight-side promise, yet it can stretch into many outlines. The angle sum stays 1080°, still you must use the given measurements to solve for missing angles or side lengths.

If you want a short, reliable definition from a reference work, Britannica describes a hexagon as a six-sided polygon and notes the regular form has 120° interior angles. Britannica’s hexagon definition lines up with the classroom meaning.

What Changes In Symmetry, Diagonals, And Rotations

Side count changes more than the outline. It changes how the shape behaves when you spin it, fold it, or draw lines inside it.

Lines Of Symmetry In Regular Forms

• Regular hexagon: 6 lines of symmetry.
• Regular octagon: 8 lines of symmetry.

Each line of symmetry slices the shape into mirror halves. In regular polygons, the symmetry count matches the side count.

Rotational Symmetry

Rotational symmetry means the shape matches itself after a turn smaller than a full 360° spin.

• Regular hexagon: matches every 60° turn.
• Regular octagon: matches every 45° turn.

Diagonal Count

A diagonal connects two non-adjacent vertices. The diagonal count for an n-sided polygon is:

n(n − 3) ÷ 2

Run it twice and you get two useful facts:

• Hexagon: 6(6 − 3) ÷ 2 = 6×3 ÷ 2 = 9 diagonals.
• Octagon: 8(8 − 3) ÷ 2 = 8×5 ÷ 2 = 20 diagonals.

That jump is big. More sides means more ways to draw diagonals, which is why octagon puzzles can feel busier even when the picture looks only slightly more complex than a hexagon.

Hexagon Vs Octagon Comparison Table

Here’s a compact comparison you can use for homework, quizzes, or design work. It covers side count, angle totals, common regular-case values, and a few “shape behavior” facts.

Feature	Hexagon	Octagon
Sides (n)	6	8
Vertices	6	8
Interior Angle Sum	720°	1080°
Each Interior Angle (Regular)	120°	135°
Exterior Angle (Regular)	60°	45°
Lines Of Symmetry (Regular)	6	8
Rotational Match (Regular)	Every 60°	Every 45°
Diagonals	9	20
Common Everyday Cue	Honeycomb cell	Stop sign

Area And Perimeter: What You Can Compute Fast

Perimeter is the easier one: add up the side lengths. If the polygon is regular, it’s just side length times the number of sides.

Perimeter

• Regular hexagon perimeter: P = 6s
• Regular octagon perimeter: P = 8s

Here, s is one side length.

Area Of A Regular Hexagon

A regular hexagon can be split into 6 equal equilateral triangles. That makes its area formula clean:

A = (3√3 ÷ 2) s²

If you prefer a method you can picture, draw lines from the center to each vertex. You get 6 triangles. Find the area of one triangle, then multiply by 6.

Area Of A Regular Octagon

A regular octagon has a common closed-form area formula too:

A = 2(1 + √2) s²

One classroom-friendly way to see it: sketch the octagon as a square with its corners cut off evenly. That picture often helps you remember why √2 shows up.

Irregular Shapes Need Different Moves

If the shape is irregular, there’s no single short formula that works every time. You usually:

• split it into triangles and rectangles you can measure,
• use coordinates and the shoelace formula,
• or use given lengths with a diagram that tells you which parts match.

When you want a plain-language definition to anchor your work, Britannica’s dictionary entry describes an octagon as a flat shape with eight sides and eight angles. Britannica Dictionary definition of octagon matches what you’re doing in geometry problems.

Common Mix-Ups And How To Avoid Them

Most mistakes happen for one of three reasons: counting errors, regular-vs-irregular confusion, or mixing up angle rules.

Mix-Up 1: Counting Sides On A Shape With Short Edges

Some diagrams use tiny edges that hide in the outline. Use a pencil and place a dot at each corner. Then count the dots. That’s often faster than trying to follow the edges with your eyes.

Mix-Up 2: Assuming Regular Without Being Told

If a problem gives one side length and asks for perimeter, it may be hinting at a regular polygon. Still, don’t assume. Scan for words like “regular,” tick marks that show equal sides, or equal angle marks.

Mix-Up 3: Using The Wrong “Each Angle” Value

Students sometimes memorize 120° and then paste it everywhere. Stop and ask: “How many sides?”

• Six sides → regular interior angles are 120°.
• Eight sides → regular interior angles are 135°.

Mix-Up 4: Confusing Interior And Exterior Angles

Exterior angles are the turns you make when you walk around the outside of the shape. In a regular polygon, each exterior angle is:

360° ÷ n

So you get 60° for a regular hexagon and 45° for a regular octagon. If you’re drawing a shape from scratch, exterior angles are often the easiest way to keep your turns consistent.

Where You’ll See Hexagons And Octagons In Real Life

These shapes pop up for practical reasons: packing, visibility, grip, and clean symmetry.

Hexagons In Everyday Objects

• Honeycomb patterns: hexagons tile without gaps, so they’re common in nature-inspired designs.
• Bolts and nuts: a hex head gives six flat sides for a wrench to grip.
• Game boards: many strategy games use hex grids because movement feels even in many directions.

Octagons In Everyday Objects

• Stop signs: the eight-sided outline stands out, even from the back.
• Tiles and decor: octagons pair well with small square “dot” tiles to fill gaps.
• Tables and frames: octagonal outlines can offer more “faces” than a square while still feeling structured.

When you’re asked why a designer picked one over the other, side count is often the hidden reason: more sides can feel closer to a circle, while fewer sides can feel sharper and easier to align in grids.

Fast Practice: Identify, Then Verify With One Calculation

Want a way to check your answer without a teacher’s key? Use this mini routine:

1. Count sides or vertices.
2. Compute the interior angle sum using (n − 2) × 180°.
3. If the picture looks regular, divide by n to get each interior angle.
4. See if that angle matches what you’d expect: 120° for six, 135° for eight.

This works even when the diagram is slightly off-scale, since the sum formula is always true for simple polygons.

Quick Reference Table For Tests And Homework

This second table is built for speed. It’s the stuff teachers love to ask when time is tight.

Task	Hexagon Result	Octagon Result
Angle sum (use n)	720°	1080°
Each interior angle (regular)	120°	135°
Each exterior angle (regular)	60°	45°
Perimeter (regular, side s)	6s	8s
Diagonals	9	20
Area (regular, side s)	(3√3 ÷ 2)s²	2(1 + √2)s²

A Simple Way To Explain The Difference Out Loud

If someone asks you the difference and you want a clean one-sentence reply, say it like this:

A hexagon has six sides and a regular one has 120° corners; an octagon has eight sides and a regular one has 135° corners.

That line covers identification plus a bit of math, and it stays correct even if the shapes are irregular, since the side counts never change.