Angle Converter

You can quickly determine the size of an angle in 10 different units using this angle converter:

Degrees, minutes of arc, and seconds of arc; radians, gradians, turns, minutes of arc, seconds of arc, milliradians, and microradians; and degrees (deg), radians (rad), milliradians (mrad), and microradians (rad).

Would you like to learn the formula for converting radians to degrees and how to convert degrees to radians? then continue reading! We'll also define acute and obtuse angles and respond to the burning question: What is an angle?

Describe an angle. oblique and acute angles:

An angle is a shape made up of two rays that originate from the same vertex. You might wonder why angles are important. If you know how far away a tower is from you and what angle the earth makes with the tower's top, you can make an educated guess as to how tall it is. The circumference of our own planet may be measured using the same method, as well as the size of the moon. You must also know the angle at which you toss anything if you want to know how far it will go. Angles are useful in a wide variety of other areas, but for now, let's concentrate on fundamental geometry. Angles can be divided bytheir sizes.

Angles can also be grouped in various ways, though. Among them are:

two angles that add up to a right angle (90°) are said to be complementary angles;
Additional angles: a pair of compounded angles equals 180 degrees (straight angle);
An acute angle used as a reference for all other angles. Don't be reluctant to use the reference angle calculator to learn more; and
A central angle has a vertex at the centre of a circle and arms that reach the perimeter of the circle.

How do you convert degrees to radians and what does a radian mean?

Angles can also be grouped in various ways, though. Among them are:

The most common unit used to measure angles is the radian. 1 radian, or 57.2958 degrees, is the angle that produces an arc with length R, where R is the radius:

The circumference is equal to 2R since a full turn is equal to 2radians. We made a table with the most typical angles to make things simpler for you:

DegreesRadians15° ^π/_{12 ,}30°^π/_{6 ,}45°^π/_4,60°^π/_{3 ,}90°^π/_{2 ,}180°π , 270°^3π/_2,360°2π

As you can see, 180 degrees is equivalent to radians, hence the formula for converting degrees to radians is:

Radians are equal to /180°*degrees.

The radians to degrees conversion formula is therefore predictable:

degree = 180 degree/* radian

Let's examine an illustration: In radians, what is a 300° angle?

Radians equal /180° * 300°, or 5 3 rad.

And you now understand how to change degrees into radians.

How do you convert decimal degrees to degrees in minutes and seconds?

Sometimes used in conjunction with degrees are minutes of arc and seconds of arc. They are frequently used, for instance, to specify coordinates. In that case, how do you translate DMS (degrees minutes seconds) to decimal degrees? The solution is simple: treat degrees like work hours. One degree is equivalent to one degree, and one hour is equal to one hour. In both situations, a minute is divided into sixty seconds. So, 3600 seconds are equal to one degree:

1 degree = 60 minutes of arc = 3600 seconds of arc

When you realize that, figuring out the formula is easy:

Decimal degrees = degrees + minutes/60 + seconds/3600

Let's say you want to figure out what 48°37'45" is in decimal degrees:

48°37'52" = 48 + 37/60 + 52/3600 = 48.6311°

So 48°37'45" is the same as 48.6311°.

various units:

You often use degrees or radians to express the size of an angle. There are other units, though, that you might encounter. Turn is one of them. Two radians, or 360 degrees, make up one spin. Use one of the following formulas to convert between these units.

Degrees to turns formula: turn = degrees / 360°; and
Radians to turns equation: turn = radians / 2π.

A gradian, or gon, is a less frequent unit. One gradian in this context is equal to one tenth of a right angle. Degrees to Graduates is calculated as follows: