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Regular polygon exterior-angle relation: Angle Calculator

Regular polygon exterior-angle relation: Calculate angle from Side count. Check the formula, input units and worked result on this page.

Enter your values

Formula symbol: n. Enter a numeric value. Use a whole number. Must be greater than zero. Allowed range: 3–10,000.

Use a decimal point, without thousands separators.

Lengths use cm, areas cm² and volumes cm³ on one consistent scale. The positive real branch is selected; the supplied quantities must describe the stated shape.
Example result
Angle
60 °

The initial result uses the example values. Enter your own values and calculate again.

Edit inputs

How it works

Exterior angle is the turn from one side to the next, not the interior angle. A convex regular polygon requires an integer side count of at least three. This form solves for angle; enter the known quantities in Side count.

Inputs and units
Regular polygon exterior-angle relation: Angle Calculator · Inputs and units
InputExample valueWhat to enter
Side count6Formula symbol: n. Enter a numeric value. Use a whole number. Must be greater than zero. Allowed range: 3–10,000.
θ = 360°/n

Worked example

Show example inputs and results

This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.

Side count
6

Complete example results

Angle
60 °

Reading the result

The result solves for angle from the entered quantities. Check the result unit and the formula conditions before using it.

Questions and answers

Can I use the example values for my own calculation?

The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.

When can I use the angle result?

Lengths use cm, areas cm² and volumes cm³ on one consistent scale. The positive real branch is selected; the supplied quantities must describe the stated shape.

Why are some results rounded?

Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.

Are my inputs sent to a server?

The calculator processes inputs in your browser. Its code does not send your values to a server.

Method sources: openstax.org

Methods & accuracy

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