Angle

Angle Converter

Details

How to use Angle Converter

What the tool does, how to run it, and what to expect from the result.

How to convert angle units

Enter an angle, choose the unit it is in, and choose the unit you want. Degrees, radians, gradians, arcminutes, arcseconds and turns all update at once from a single value.

The degree is the internal base, and every other unit is defined against it exactly, so the radian value that comes back for 180 degrees is pi to 12 significant figures rather than a truncated 3.14.

  • Reduce any degrees-minutes-seconds figure to a single decimal number first.
  • Type the angle in the Value box, for example 90.
  • Pick the From unit, for example Degree.
  • Pick the To unit, for example Radian.
  • Copy the result straight into code, where trigonometric functions expect radians.
Tips

Getting a better result out of Angle Converter

Specific settings and thresholds, not general advice.

  • The internal base on this page is the degree, not the radian. 1 radian is 57.2957795131 degrees, and 180 degrees is 3.14159265359 radians, which is pi.
  • A full turn is 360 degrees, 2 pi radians, or 400 gradians. The gradian exists so that a right angle is a round 100.
  • Trigonometric functions in JavaScript, Python and C take radians, so Math.sin(90) is not 1. Convert 90 degrees to 1.5707963268 radians first.
  • 1 degree is 60 arcminutes and 3,600 arcseconds. A coordinate written as 40 degrees 26 minutes 46 seconds is 40.446111 degrees in decimal.
  • One arcsecond of latitude is about 31 meters on the ground, which is why GPS precision and telescope resolution are both quoted in arcseconds.
Limits

What Angle Converter does not do

The honest boundary, so you do not lose time finding it yourself.

  • No NATO mils (6,400 per turn) and no artillery mils.
  • It will not parse a degrees-minutes-seconds string. Convert 40 deg 26 min 46 s to a single decimal number yourself.
  • No angle arithmetic. It will not add two bearings or normalise an angle into a 0 to 360 range.
  • One value at a time, and no trigonometric functions.
At a glance

Who Angle Converter is for

A quick way to understand who this helps, what it solves, and where it connects next.

Best fit

Students, engineers, developers, makers, and anyone who needs a quick, accurate angle conversion.

Ideal for

Fast, reliable angle conversions without installing an app or trusting a server with your numbers.

FAQ

Common questions

Short answers for the questions people usually have before trying a utility like this.

Does my data get uploaded anywhere?

No. Everything runs locally in your browser and nothing is sent to a server.

Is this free to use?

Yes. It is completely free, with no account, no signup, and no usage limits.

Does it work on a phone?

Yes. The page runs in any modern mobile browser, on iPhone and Android alike, with no app to install.

How many radians is 90 degrees?

1.5707963268 radians, which is pi/2. The full set is worth memorising: 90 degrees is pi/2, 180 degrees is pi (3.14159265359), and 360 degrees is 2 pi (6.28318530718).

What is a gradian?

A gradian, or gon, divides a full turn into 400 parts instead of 360, so a right angle is exactly 100 gradians. It survives in European surveying and on some scientific calculators, and 1 gradian is 0.9 degrees exactly.

Can I paste coordinates like 40 26 46?

Not as a single string. Convert them first: divide the minutes by 60, the seconds by 3,600, and add them to the degrees, so 40 degrees 26 minutes 46 seconds becomes 40.446111 degrees. Then enter that number with Degree selected.

Why does Math.sin(90) not return 1 in my code?

Because the standard library expects radians, and 90 radians is over 14 full turns. Convert 90 degrees to 1.5707963268 radians and Math.sin returns 1. This is the single most common bug that sends people to an angle converter.

How many degrees is one radian?

57.2957795131 degrees, which is 180/pi. A radian is the angle subtended when the arc length equals the radius, so it is the natural unit for any calculation involving arc length or angular velocity.

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