Enter an angle in degrees, radians, gradians, minutes or seconds and the converter shows it in the others.
Most trouble with angles comes from calculators set to the wrong mode – if sin(30) doesn't give 0.5 you are in radians.
For example, if you have an angle measured in degrees and need to convert it to radians, simply enter the value in the degrees field and select radians as the desired unit. The angle converter will instantly provide you with the equivalent value in radians. This feature is especially handy when dealing with trigonometric functions that often require angles to be expressed in radians.
Units of Angle
Degrees divide a circle into 360 parts. The radian is the angle whose arc is as long as the radius, so a circle holds 2π of them and one radian is about 57.3°. Radians are the unit that maths and physics formulas expect.
Gradians (gon) divide a circle into 400 parts, so a right angle is 100 gon. Minutes and seconds of arc are 1/60 and 1/3,600 of a degree, and astronomers use them for the tiny angles between stars.
Variations of Milliradians
Milliradians (mrad, also called mils) are one thousandth of a radian, about 0.057°, and are used for small angles in military sights. Strictly a circle holds 6,283 of them, so armies round to a convenient whole number and the variants differ.
The NATO mil rounds the circle to 6,400 parts of 0.05625° each, which makes a quarter turn a clean 1,600 mils.
The Swedish mil, or streck, divides the circle into 6,300 parts of about 0.0571° each, and was used for artillery.
About Degrees
A degree (°) is 1/360 of a full turn, and an angle is measured by how far one line has rotated from another. The 360 is generally credited to the Babylonians, whose base-60 counting made it a convenient choice.
Each degree is split into 60 minutes (′) and each minute into 60 seconds (″), so 1° is 3,600″.
Multiply radians by 180/π to get degrees – 1 radian is about 57.3° – and multiply degrees by π/180 to go back, so 180° is π radians.
About Radians
The radian is the SI unit of angle. A full circle is 2π (about 6.28) radians, against 360 degrees.
The concept of radians is based on the relationship between the length of an arc and the radius of a circle. One radian is defined as the angle subtended by an arc that is equal in length to the radius of the circle. In other words, if we were to take a circle with a radius of 1 unit and measure an arc along its circumference that is also 1 unit long, the angle formed at the center of the circle would be 1 radian.
A radian is a ratio of two lengths, arc over radius, so it carries no units of its own and drops out of physics formulas – speed = radius × angular velocity works directly when the angle is in radians.
About Gradians
A gradian (also called a gon or grad) is 1/400 of a circle, so a right angle is exactly 100 gradians. It was introduced in France alongside the metric system as a decimal alternative to degrees.
Gradians are mostly found on surveying instruments in continental Europe, which are often marked in gons. One gradian is 0.9 degrees, or π/200 radians.
On a gradian scale a quarter turn is 100 and a half turn is 200, so right angles come out as round numbers. The catch is that 30° and 60° become 33.33 and 66.67 gradians.