Angle Converter

1. Enter the value you want to convert.
2. Choose the from unit.
3. Choose the to unit.
4. Read the result, plus radians and degrees.

Here is what each result means:

An angle measures the amount of turn between two directions or lines. It is written in several units because different fields prefer different ones. Everyday life and navigation use degrees, where a full circle is 360. Mathematics and physics use radians, the natural unit for calculus and circular motion, where a full circle is 2 pi. Surveying sometimes uses gradians, where a right angle is a neat 100.

For very small angles, degrees are split further: each degree is 60 arcminutes, and each arcminute is 60 arcseconds. Astronomers and surveyors use these tiny units to describe the apparent size of distant objects or precise bearings. A full revolution, or turn, is simply one complete circle, a handy unit for rotations.

This converter bridges every unit through the radian, the SI unit. It multiplies your value by the radians in its unit, then divides by the radians in the target unit. Because a full circle has fixed sizes in every unit, 360 degrees, 2 pi radians, 400 gradians or one revolution, the conversions are exact ratios.

The link that ties them together is the circle itself. Once you fix how big a full turn is in each unit, every fraction of a turn follows. That is why converting an angle never changes the turn it describes, only the number and unit used to write it down.

It converts through the radian, the SI unit of angle.

1. Your value is multiplied by its unit's size in radians.
2. That gives the angle in radians, the common base.
3. Dividing by the target unit's size in radians gives the result.

For trigonometry and geometry, see the slope calculator and the triangle area calculator.

Convert 180 degrees to radians.

Result: 180 degrees is pi radians, about 3.14159, which is also half a revolution or 200 gradians. A right angle of 90 degrees is pi over 2 radians, about 1.5708.

A full turn has a fixed size in every unit.

These fixed sizes are the key to every conversion. The gradian is designed so a right angle is exactly 100, which some surveyors find convenient, while the radian is designed so the arc length equals the radius times the angle.

The two most common units suit different tasks.

Degrees are easy to picture and divide neatly, which is why they dominate everyday use. Radians make the formulas of calculus and circular motion simpler, so they are standard in science. Converting between them is one of the most common angle tasks.

The Two Units

The ratio between the from-unit and to-unit sets the result; each has a fixed size in radians.

Small-angle Units

Arcminutes and arcseconds split a degree into sixtieths, so their radian values are tiny.

Whole Turns

Angles beyond a full circle keep counting; the converter does not wrap them to under 360 degrees.

Maths and Physics

Switch between degrees and radians for trigonometry or rotation.

Surveying and Astronomy

Work with gradians, arcminutes and arcseconds.

Engineering and Design

Convert an angle to the unit a tool or formula expects.

1. Degrees Where Radians Are Needed

Many calculators and functions expect radians. Feeding degrees gives a wrong trig result.

2. Forgetting Pi

A full circle is 2 pi radians, not 6.28 as a round figure. Keep pi in the working for accuracy.

3. Mixing Arcminutes and Minutes of Time

An arcminute is an angle, a sixtieth of a degree, not a minute of time.

4. Confusing Gradians and Degrees

A right angle is 100 gradians but 90 degrees. They look similar but differ.

5. Expecting Wrap-around

The converter keeps whole turns; it does not reduce 450 degrees to 90.

Conversions use fixed, exact factors relative to the radian.

Pi radians, about 3.14159. A full circle is 360 degrees or 2 pi radians, so 180 degrees is half of that, which is pi.

Multiply degrees by pi and divide by 180. So 90 degrees is 90 times pi over 180, which is pi over 2, about 1.5708 radians.

A radian is the angle where the arc length equals the radius. A full circle is 2 pi radians, and it is the natural unit for maths and physics.

A gradian, or gon, divides a right angle into 100 parts, so a full circle is 400 gradians. It is used in some surveying work.

They split a degree into small parts: one degree is 60 arcminutes, and one arcminute is 60 arcseconds. They are used in astronomy and surveying.

About 57.2958 degrees. It is 180 divided by pi, since pi radians equal 180 degrees.

Radians make the formulas of calculus and circular motion simpler, with no extra constants. Many trig functions expect radians, so convert first if your angle is in degrees.

A revolution, or turn, is one complete circle: 360 degrees or 2 pi radians. It is a convenient unit for counting full rotations.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Radian (Wikipedia).
• Angle (Wikipedia).
• Gradian (Wikipedia).