Shape Identifier Calculator

Work out shape identifier instantly with clear inputs, formula shown and shareable results.

About Shape Identifier Calculator

A polygon is named by its side count; its interior angles always sum to (sides - 2) x 180 degrees, and it has sides x (sides - 3) / 2 diagonals. Naming shapes by counting sides rather than recognising pictures is what lets a child identify an unfamiliar 11-sided figure with confidence.

Formulas

Interior angle sum

sum = (sides - 2) x 180 degrees

Diagonals

diagonals = sides x (sides - 3) / 2

Worked example

With the default values below, Shape Identifier Calculator returns Shape of Regular hexagon. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of sidesaccepts 3–20: 6
All sides and angles equal: Yes

Results

Shape: Regular hexagon
Interior angle sum: 720 deg
Each interior angle (regular only): 120.00 deg
Number of diagonals: 9

Step by step

1Values used
2Interior angle sum
3Diagonals
4Shape= Regular hexagon
5Interior angle sum= 720 deg
6Each interior angle (regular only)= 120.00 deg
7Number of diagonals= 9

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Shape Identifier figure worked out?

sum = (sides - 2) x 180 degrees. A polygon is named by its side count; its interior angles always sum to (sides - 2) x 180 degrees, and it has sides x (sides - 3) / 2 diagonals.

Why does this matter?

Naming shapes by counting sides rather than recognising pictures is what lets a child identify an unfamiliar 11-sided figure with confidence.

What do I need to enter?

Enter number of sides, all sides and angles equal. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.