How to Create a Regular Heptagon

Accurately construct a heptagon with our simple guide

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Last Updated: February 13, 2026 References

A regular heptagon (also called septagon) is a polygon with seven equal sides and seven equal angles.^{[1]
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Expert Source

Zina Savva
Mathematics Educator

Expert Interview} Accurately constructing polygons is an important part of geometry, and for regular heptagons there are multiple ways to draw one. Here is the easiest method if you are using a straight edge and compass.

Steps

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1
Draw an arbitrary circle, centred at a point $X$ . Keep in mind that you will need some extra space around the circle for construction lines.^{[2]
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2
Draw the radius $AX$ .^{[3]
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3
Draw a circle with radius $AX$ , centred at $A$ . This circle intersects the first circle at points $B$ and $C$ .^{[4]
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4
Connect $B$ and $C$ . $BC$ bisects $AX$ in $E$ .^{[5]
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5
Draw a third circle with radius $BE$ , centred at $B$ . This circle intersects circle a in $D$ .^{[6]
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6
Use your compass to trace the distance BD around the circle. You should end up exactly where you started. There is an error of about .2% for this method, which is negligible for any heptagon that fits on a regular A4 piece of paper. If you don't end up exactly where you started, there were probably some inaccuracies with the construction tools (e.g. the thickness of the pencil).^{[7]
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7
Connect adjacent vertices.
8
Erase the construction lines if needed.

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How do I build a pentagon?

Donagan

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See Construct a Regular Pentagon.

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Tips

Put a piece of cardboard or a book under your paper so your compass doesn't slip.

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Sharpen your pencils before beginning, for increased precision.

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Trace over with a pen so it is easier to see.

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Warnings

Since 7 cannot be written as the product of a power of two and a Fermat prime, it is impossible to do an exact compass and straightedge construction of a heptagon.^{[8]
X
Expert Source

Zina Savva
Mathematics Educator

Expert Interview} However, the above method has an error of less than 0.2%. When the circumscribed circle of the heptagon has a radius of 1 meter, there will be an error of approx. 1.7 mm.

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