Angle Converter
Convert between degrees, radians, gradians and more.
Results update as you type.
How it works
An angle converter restates the size of an angle in a different unit, moving between degrees, radians, gradians, arcminutes, arcseconds and full turns. It reduces your value to degrees, used here as the common base, and then scales out to the unit you want, so one mechanism covers geometry homework, trigonometry, navigation bearings, astronomy and engineering drawings alike. This matters because different fields settle on different angle units, and mixing them silently breaks calculations. School geometry and everyday direction use degrees; calculus, physics and almost every programming language's trigonometric functions expect radians; surveying in parts of Europe uses gradians, where a right angle is a clean 100 units; astronomy and precise optics split a degree into sixty arcminutes and each of those into sixty arcseconds. Feeding degrees into a function that expects radians is one of the most common bugs in scientific code, and an angle converter makes the correct value obvious. The convert-through-degrees method works because every angle unit has a fixed ratio to the degree — a radian is 180/π degrees, a gradian is 0.9 degrees, a full turn is 360 degrees — so pivoting through that base keeps results exact and needs only one factor per unit. Students, programmers, surveyors, astronomers and engineers all reach for an angle converter whenever an angle appears in a unit their tool or formula does not expect.
Convert to degrees via known factors, then to the target unit
The input is multiplied by its unit's fixed number of degrees to express the angle in degrees, then divided by the target unit's degree value to complete the conversion. Because every angular unit is defined as a constant fraction or multiple of a full circle, each has a fixed ratio to the degree, so pivoting through that single base is exact and covers every pairing with just one stored factor per unit.
Source:International System of Units (SI) — NIST
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter value, from and to.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Converted angle updates instantly as you type — no button to press.
Frequently asked questions
How do I convert degrees to radians?
Multiply the degree figure by π and divide by 180, which is the same as dividing by about 57.2958. So 180 degrees is exactly π radians, 90 degrees is π/2, and 360 degrees is 2π. To reverse it, multiply radians by 180 and divide by π. Radians are the natural unit for calculus and programming, where trigonometric functions almost always expect radian inputs.
What is a gradian?
A gradian, also called a gon or grade, divides a right angle into exactly 100 units, so a full circle is 400 gradians and one gradian is 0.9 degrees. It was designed to fit the metric decimal system and is still used in some European surveying and civil engineering. Its appeal is that a quarter turn is a round 100, which simplifies slope and bearing arithmetic in the field.
What are arcminutes and arcseconds?
An arcminute is one-sixtieth of a degree, and an arcsecond is one-sixtieth of an arcminute, so there are 3,600 arcseconds in a single degree. Astronomers use them to describe tiny angular sizes and separations, such as the apparent width of a planet or the resolving power of a telescope. Latitude and longitude minutes and seconds use the same sixty-based subdivision of a degree.
Why do programming languages use radians?
Functions like sine and cosine in most languages, including JavaScript, Python and C, expect their input in radians because radians make the underlying calculus clean — the derivative of sine is cosine only when angles are in radians. Passing degrees directly produces wrong results silently, with no error raised. Converting degrees to radians first, by multiplying by π/180, is the standard fix this converter performs.
How many degrees are in a full turn?
A full turn, or one complete revolution, is exactly 360 degrees, 2π radians, 400 gradians or 21,600 arcminutes. The number 360 comes from ancient Babylonian astronomy and its convenient divisibility by many whole numbers. Expressing rotations as turns is handy in mechanical and animation contexts, where saying an object rotated 'two and a half turns' is clearer than quoting 900 degrees.