Angle Conversion Calculator

Angle Conversion Calculator

Convert angles accurately between decimal degrees, degrees-minutes-seconds (DMS), radians, gradians/gon, milliradians, turns, NATO mils and arc units.

Surveying note: confirm which angular convention your instrument or project uses. NATO mils use 6,400 mils per full circle; other military systems may differ.

How to use this tool

1. Select the input unitChoose the unit used by your source angle. DMS provides separate degree, minute and second fields.
2. Enter the angleUse positive or negative values. Optionally normalise the result to one full positive revolution.
3. Convert and exportReview all equivalent units, then copy the results, download CSV or print/save a PDF.

Quick example: select Load 45° example to verify that 45° equals π/4 radians, 50 gon and 800 NATO mils.

1. Enter an angle

Scientific notation is accepted, for example 1.2e-3.

2. Conversion results

Enter an angle and select Convert angle.

Angle units used in surveying

  • Degrees: one full revolution is 360°.
  • DMS: one degree contains 60 minutes and one minute contains 60 seconds.
  • Radians: one full revolution is 2π radians.
  • Gradians/gon: one full revolution is 400 gon; a right angle is 100 gon.
  • Milliradians: 1 radian equals 1,000 mrad.
  • NATO mils: one full revolution is 6,400 mils.

Frequently asked questions

How do I convert decimal degrees to DMS?

Select decimal degrees, enter the value and convert. The calculator separates the whole degrees, minutes and seconds while preserving the sign.

How many radians are in 180 degrees?

180 degrees equals π radians, approximately 3.1415926536 radians.

Are gradians and gon the same unit?

Yes. Gradian, grad and gon refer to the same angular division: 400 gon in one full circle.

How many NATO mils are in a circle?

The NATO convention uses 6,400 mils per full circle. Confirm the convention because some systems use a different number.

Can negative DMS angles be entered?

Yes. Put the negative sign on the degrees value and enter minutes and seconds as positive values from zero to less than 60.

Does normalising change the direction?

No. Normalising expresses the same direction as a value from zero inclusive to one positive revolution exclusive.

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