Symmetry Calculator
Find the lines of symmetry, the order of rotational symmetry and the angle of rotation of polygons, quadrilaterals, triangles, circles and capital letters.
About the Symmetry Calculator
A line of symmetry folds a shape onto itself. A shape has rotational symmetry of order k if it looks the same k times in a full turn, so the smallest angle of rotation is 360° ÷ k. A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
Letter shapes depend on the font; the answers assume plain block capitals.
The formula
angle of rotation = 360° ÷ order
Worked example
A regular hexagon
- 6 lines of symmetry
- Order 6: it repeats every 60°
Questions people ask
Does a parallelogram have a line of symmetry?
No (unless it's a rectangle or rhombus), but it has rotational symmetry of order 2.
What is point symmetry?
The shape looks the same after a half turn about its centre, like the letters S, N and Z.