Angle Converter Calculator

An angle converter can convert a single angle into all other units. Enter the value, select whether it is in degrees, radians, mils, revolutions or gradians and you will get the corresponding values for all units. You can also display the representation in "degrees-minutes-seconds" format, as well as labels for the type of angle and sine, cosine, tangent and reference angles if desired.

What is an Angle?

An angle is a geometric figure formed by two rays that have a common endpoint (vertex). It measures how much one ray rotates relative to the other. A full rotation brings the ray back to its original position.

The same rotation can be expressed in different units, similar to how a length can be given in meters or feet. A quarter of a full circle is 90 degrees, while an eighth of a full circle is 45 degrees. The size of the angle does not change; what changes is the unit used to measure it.

Degree, radiant and other units

A degree divides a full circle into 360 equal parts, a convention that comes from Babylonian astronomy. The radian relates the angle to the circle itself: one radian is the central angle that subtends an arc length equal to the radius of the circle. Thus a full circle is 2π radians. The radian is a natural unit in analysis and physics, as it simplifies many trigonometric formulae.

The grad (sometimes written as "gon") divides a right angle into 100 parts so that there are 400 grads in a full circle. A full turn or revolution is equivalent to one complete circle. Minutes and seconds are used to further subdivide the grad: one grad equals 60 minutes, and one minute equals 60 seconds, similar to how an hour is subdivided into minutes and seconds.

Conversion formulas

Any conversion will either use radians or degrees. The most common conversions are from degrees to radians and from radians to degrees:

Let's say we have an angle of 300 degrees. So you multiply 300 by pi over 180.

The other units follow a similar pattern, with each of the subsequent lines multiplying a radian value by a fixed factor.

Degrees, minutes and seconds.

In surveying and navigation work, angles are often expressed in degrees, minutes, and seconds, such as 45 degrees, 30 minutes, 36 seconds. This is a sexagesimal (base-60) representation of the angle in decimal form. To convert this to a normal decimal number, divide the minutes by 60, the seconds by 3600 and add these values to the whole degree:

So 45 degrees, 30 minutes and 36 seconds becomes 45 + 0.5 + 0.01 which is 45.51 degrees. When DMS input is enabled, angles can be entered in this way and the calculator will display the result in decimal as well as all other units.

Quick reference table

Some angles come up again and again. Here are four commonly used units of angle measure.

Naming Angles by Size

If you know the degree of an angle, then you can name it based on its size. Angles that are less than 90 degrees are acute angles. An angle that is exactly 90 degrees is a right angle. Angles between 90 and 180 degrees are obtuse angles. A straight angle measures 180 degrees, and angles that are greater than a straight angle up to a full rotation are reflex angles. When you input an angle, the calculator will label the type of angle for you.

This tool is for general education and everyday calculations. For measurements, navigation or technical work the results should be compared to a standard according to project requirements.