Angle Converter

Angle Convert is the Best Online Angle Converter Tool, free without app. Angle Convert Tool helps to management, analysis, editing, generate and convert data. Use our angle conversion calculator to quickly convert angle measurements, including degrees, radians, and grads.

Best Angle Converter Tool

See a complete list of conversion calculators for each unit of angle by selecting one below.

1. radian converters
2. milliradian converters
3. degree converters
4. minute of arc converters
5. second of arc converters
6. gradian converters
7. revolution converters
8. circle converters
9. mil converters

What is Angle?

a measure of an angle or of the amount of turning necessary to bring one line or plane into coincidence with or parallel to another.[1] Put another way, angle is the amount that one line or plane is turned from another.

Angles are used in geometry and trigonometry, geography and mapping, and construction, so understanding how to work with angles can be very important. A protractor is a common tool to help calculate angle between two lines.

Two common measures of angle are degrees and radians. A full circle consists of 360 degrees, meaning a line is 360 degrees from itself, which is 2π in radians. Angles are measured using a protractor, learn how to use a protractor or download a printable protractor to use to measure an angle for your project.

How to Convert Units of Angles?

Conversions are performed by using a conversion factor. By knowing the conversion factor, converting between units can become a simple multiplication problem:

S * C = E

Where S is our starting value, C is our conversion factor, and E is our end converted result.

To simply convert from any unit into degrees, for example, from 5 radians, just multiply by the value in the right column in the table below.

5 radians * 57.29578 [degrees / radian] = 286.4789 degrees

To convert from degrees back into units in the left column divide by the value in the right column or, multiply by the reciprocal, 1/x.

286.4789 degrees / 57.29578  [degrees / radian] = 5 radians

To convert among any units in the left column, say from A to B, you can multiply by the factor for A to convert A into degrees then divide by the factor for B to convert out of degrees.  Or, you can find the single factor you need by dividing the A factor by the B factor.

For example, to convert from radians to revolutions you would multiply by 57.29578 then divide by 360.  Or, multiply by 57.29578/360 = 0.1591549. So, to convert directly from radians to revolutions you multiply by 0.1591549.

To understand how to also convert the units follow this example. Say you want to convert from radians to degrees. Since you can multiply anything by 1 and still retain the original value, but in different units, set it up so that radian will cancel out leaving you with degree.

Since:
1 degree = 0.01745329 radians, 1 degree / 0.01745329 radians = 1

We can write the conversion as:
1 radian = 1 radian * (1 degree / 0.01745329 radians) = 57.29578 degrees

And we now have our factor for conversion from radians to degrees since 1 * 57.29578 = 57.29578.  Note that there are rounding errors in these values.

Knowing that 1 radian = 57.29578 degrees we can now find the conversion factor for converting back.  Dividing both sides of the equation by 57.29578 we get about 0.01745329 radians = 1 degrees.  So, the conversion factor to multiply by to convert from degrees to radians is about 0.01745329.