Angle Converter
Enter an angle in any unit to see it in the others, or enter degrees, minutes and seconds to get decimal degrees.
Or enter degrees, minutes and seconds:
Worked examples
Right angle into gradians
90 degrees
100 gradians.
Gradians split a right angle into 100 parts, which is why 90 degrees equals 100 gradians.
One radian into degrees
1 radian
About 57.2958 degrees.
A full turn is 6.2832 radians, which is 360 degrees, so one radian is 360 divided by 6.2832.
About Angle Converter
Angles are measured in several units, and each one is common in a different field. Degrees are used in everyday geometry and on most maps, radians appear in higher maths and science, gradians are used in some surveying work, and turns are a handy way to count full rotations. This angle converter takes an angle in any of these units and shows it in all of the others at once, so you can check a figure from a textbook, a sensor or a mapping tool without doing the arithmetic by hand.
The page also converts between decimal degrees and degrees, minutes and seconds. Map coordinates and older navigation tables often use the second style, where each degree is split into 60 minutes and each minute into 60 seconds. Enter the three parts in the boxes below the main converter to get a single decimal figure, which is easier to type into most maps and calculators. Results are shown to about six significant figures, which is more than enough for everyday work.
How to use Angle Converter
- Type an angle into the amount box and choose its unit, such as degrees or radians.
- Read the table to see the same angle in degrees, radians, gradians and turns.
- Check the degrees, minutes and seconds row if you need the traditional format.
- To convert degrees, minutes and seconds, type each part into its own box below the table.
- Read the decimal degrees in the box underneath, and copy it if you need it elsewhere.
Common uses
- Checking a radian value from a maths formula against degrees
- Turning a map coordinate written in minutes and seconds into decimal degrees
- Converting a gradian reading from a surveying instrument
- Counting how many turns a wheel makes in a set angle
Frequently asked questions
How many radians are in a degree?
There are pi divided by 180 radians in one degree, which is about 0.0174533 radians. In the other direction, one radian is about 57.2958 degrees. A full circle is 2 pi radians, or about 6.2832 radians, which matches 360 degrees. Radians are the natural unit in many formulas, so calculators often need to be set to radians before a trigonometry function is used.
What is a gradian?
A gradian divides a right angle into 100 equal parts, so a full turn is 400 gradians. It is sometimes called a gon. Gradians are used in some surveying instruments and older engineering work, because they make a right angle easy to split into decimal parts. Most everyday angles are still given in degrees, which is why the converter shows both.
What does a turn mean for an angle?
One turn is a complete rotation, equal to 360 degrees. It is a convenient way to talk about things that spin, such as a wheel, a motor or a dial, since two turns means two full rotations. A quarter turn is 90 degrees, and half a turn is 180 degrees. Converting to turns is simple, because the number of degrees is divided by 360.
How do I convert degrees, minutes and seconds to decimal degrees?
Divide the minutes by 60 and the seconds by 3,600, then add them to the degrees. For example, 12 degrees, 30 minutes and 15 seconds is 12 plus 0.5 plus 0.0041667, which gives 12.5042 degrees. For a negative angle, put the minus sign on the degrees box, and the converter applies it to the whole value.
Why do map coordinates use minutes and seconds?
Minutes and seconds allow very precise positions to be written without long decimals. Older maps, charts and navigation tables were printed this way, and many systems still show latitude and longitude in this form. Decimal degrees describe exactly the same position as one number, so both styles point to the same place on the map.