How do I convert degrees to radians?

Multiply the degree value by pi divided by 180. So 180 degrees equals pi radians (about 3.14159), 90 degrees equals pi/2 (about 1.5708) and 360 degrees equals 2*pi (about 6.28319). The converter does this for you the moment you type.

How do I convert radians to degrees?

Multiply the radian value by 180 divided by pi (about 57.29578). One radian is roughly 57.2958 degrees. The tool shows the exact figure with sensible precision as you type.

What is a gradian and how does it relate to degrees?

A gradian (also called a gon or grade) divides a right angle into 100 parts, so a full circle is 400 gradians. That makes one gradian exactly 0.9 degrees, and 100 gradians a quarter turn. Gradians are used in some surveying and civil-engineering contexts.

What is a turn or revolution?

A turn (revolution) is one complete rotation around a circle. One turn equals 360 degrees, 2*pi radians or 400 gradians. Half a turn is a straight angle (180 degrees) and a quarter turn is a right angle (90 degrees).

What are arcminutes and arcseconds?

They subdivide the degree the way minutes and seconds subdivide an hour. One degree contains 60 arcminutes, and one arcminute contains 60 arcseconds, so a degree is 3600 arcseconds. Astronomers and navigators use them to express very small angles precisely.

Is my data sent anywhere?

No. Every calculation happens locally in your browser using plain arithmetic. No values are uploaded, logged or stored on any server.

Angle Converter — Gera Tools

An angle converter that moves a single angle between the six units people actually use: degrees, radians, gradians (gons), turns (revolutions), arcminutes and arcseconds. It is built for students checking trigonometry homework, engineers and surveyors switching between degrees and gradians, astronomers working in arcminutes and arcseconds, and anyone who just needs degrees in radians without reaching for a calculator.

How it works

Every unit is defined by exactly how many degrees one of it contains, and the degree is used as the common base. When you type a value into any field the tool converts it to degrees, then re-expresses that same angle in every other unit. Because all six boxes are editable and kept in sync, you can start from whichever unit your problem is written in — there is no fixed input or output side. The headline line shows the chosen from-to pair, and the swap button flips them so you can read the conversion in the other direction without retyping.

The conversion factors are exact. One full turn is 360 degrees. One radian is 180/π degrees, approximately 57.29578, which is why π radians is a half turn and 2π radians is a whole circle. One gradian is 0.9 degrees because a right angle is split into 100 gradians and a full circle into 400. One arcminute is one sixtieth of a degree, and one arcsecond is one sixtieth of an arcminute, so a single degree contains 60 arcminutes or 3600 arcseconds. Results are shown to a sensible precision and switch to scientific notation for very large or very small angles.

Worked example

Suppose you have a right angle, 90 degrees, and you want it in the other units. Ninety degrees is a quarter turn (0.25 turn), it is π/2 radians (about 1.570796), it is exactly 100 gradians, it is 5,400 arcminutes and it is 324,000 arcseconds. Type 90 into the degree box and every one of those figures appears at once. Type 1 into the radian box instead and you will see roughly 57.29578 degrees, confirming the standard radian-to-degree factor.

Conversion reference table

Angle	Degrees	Radians	Gradians	Turns	Arcminutes
Full circle	360	2π ≈ 6.28319	400	1	21,600
Straight angle	180	π ≈ 3.14159	200	0.5	10,800
Right angle	90	π/2 ≈ 1.5708	100	0.25	5,400
60°	60	π/3 ≈ 1.0472	66.667	0.16667	3,600
45°	45	π/4 ≈ 0.7854	50	0.125	2,700
1 radian	57.29578	1	63.66198	0.159155	3,437.75
1°	1	0.0174533	1.11111	0.0027778	60

Every figure is calculated in your browser — no numbers are uploaded or stored.