Angle Converter
Convert between any two degree units in your browser — instant, accurate, and private.
Example
1 ° = 0.01745329 rad. Switch the unit menus to convert between any pair.
How it works
Every value is converted through a single degree base unit using internationally defined conversion factors, so any from/to pair stays consistent.
Good to know
Angle conversion shows up anywhere rotation or direction matters: a machinist programming a CNC rotary axis works in degrees, a physics or graphics engine expects radians, a surveyor in continental Europe reads a total station in gradians, and an astronomer or optician resolves features in arcminutes and arcseconds. A "turn" is the most intuitive of all — it is simply one full revolution — and it ties the whole family together: 1 turn = 360° = 2π rad = 400 gon.
The units come from different traditions. The degree is Babylonian, built on a base-60 system, which is also why a degree splits into 60 arcminutes and an arcminute into 60 arcseconds (so 1° = 3,600″). The radian is the "natural" mathematical unit, defined by the geometry of the circle itself rather than an arbitrary count, which is why calculus and trigonometry assume it. The gradian (also called the gon) is the metric-era attempt to decimalize angles so that a right angle is a clean 100, making it popular in surveying and some engineering fields.
A useful rule of thumb: one radian is just a hair over 57.3°, and one degree is about 0.01745 rad — close to 1/57.3. For the small angles common in optics and astronomy, remember that 1 arcsecond is roughly the width of a coin seen from about 4 km away, and there are 206,265 arcseconds in a radian (a handy small-angle constant).
The most common mistake is feeding degrees into a function that expects radians, or vice versa — most programming languages' sin/cos/tan operate in radians, so a value like 90 will silently give a wrong answer instead of 1. The second pitfall is precision: because radians involve π, no decimal value of a radian is ever truly exact, so converting degrees to radians and back can introduce tiny rounding drift. Keep extra significant figures during intermediate steps and round only the final result.
Frequently asked questions
What does the angle converter do?
It converts between common degree units instantly. Pick a unit to convert from and a unit to convert to, type a value, and the result updates live.
Which units does this converter support?
It includes 6 units: Degree, Radian, Gradian, Arcminute, Arcsecond, Turn.
Is this converter free and private?
Yes. It runs entirely in your browser, so your inputs never leave your device, there is no sign-up, and it works offline once loaded.
Are the conversions exact?
Conversions use internationally defined factors and are exact where the definitions are exact (for example, 1 inch = 2.54 cm). Displayed results are rounded for readability.
People also ask
How many degrees are in one radian?
One radian equals 180/π degrees, which is approximately 57.2958°. Conversely, one degree is about 0.0174533 radians.
What is the difference between a gradian and a degree?
A gradian (or gon) divides a right angle into 100 parts, while a degree divides it into 90. So 1 gradian = 0.9° and a full circle is 400 gradians versus 360 degrees.
How many arcseconds are in a degree?
There are 3,600 arcseconds in a degree, because one degree contains 60 arcminutes and each arcminute contains 60 arcseconds.
What is a turn in angle measurement?
A turn is one complete revolution around a circle. One turn equals 360°, 2π radians (about 6.2832 rad), or 400 gradians.
How do you convert degrees to radians?
Multiply the degree value by π/180 (about 0.0174533). For example, 90° × π/180 = π/2 ≈ 1.5708 radians.
How many arcminutes are in a radian?
There are about 3,437.75 arcminutes in a radian, since one radian is roughly 57.2958° and each degree holds 60 arcminutes.
Why do calculators sometimes give wrong trig answers in degrees?
Most calculators and programming languages compute sine, cosine, and tangent in radians by default. If you enter 90 expecting degrees, you get the radian result instead, so switch the mode to degrees or convert the value first.
How small is one arcsecond?
One arcsecond is 1/3,600 of a degree, an extremely tiny angle used in astronomy and optics. It is the apparent size of an object about 206,265 times farther away than its width.
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