Angle Conversion Calculators

Protractors are often used to measure angle
Convert one unit of angle to another. Start by selecting the angle unit to convert from.

Understanding Angle

understanding how to convert from one measure of angle to another

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.

Use our unit conversion tools above to convert between the different units of angle measures.

Units of Angle Measurement

Units of angle include radians, milliradians, degrees, minutes of arc, seconds of arc, gradians, revolutions, circles, and mils (NATO).

Common Angle Measurement Conversions

Degrees to radians angle conversion
1 degree is equal to 0.017453 radians
Degrees to gradians angle conversion
1 degree is equal to 1.111111 gradians
Radians to degrees angle conversion
1 radian is equal to 57.29578 degrees
Radians to gradians angle conversion
1 radian is equal to 63.661977 gradians
Gradians to degrees angle conversion
1 gradian is equal to 0.9 degrees
Degrees to mils (NATO) angle conversion
1 degree is equal to 17.777778 mils (NATO)

Angle Unit Conversion Table

Equivalent angle metric and imperial measurements
Convert From Radian Milliradian Degree Minute Of Arc Second Of Arc Gradian Revolution Circle Mil
1 radian = 1 rad 1,000 mrad 57.29578° 3,438 arcmin 206,265 arcsec 63.661977g 0.159155 r 0.159155 cir 1,019 mil
1 milliradian = 0.001 rad 1 mrad 0.057296° 3.437747 arcmin 206.264806 arcsec 0.063662g 0.000159 r 0.000159 cir 1.018592 mil
1 degree = 0.017453 rad 17.453293 mrad 60 arcmin 3,600 arcsec 1.111111g 0.002778 r 0.002778 cir 17.777778 mil
1 minute of arc = 0.000291 rad 0.290888 mrad 0.016667° 1 arcmin 60 arcsec 0.018519g 0.000046296 r 0.000046296 cir 0.296296 mil
1 second of arc = 0.0000048481 rad 0.004848 mrad 0.000278° 0.016667 arcmin 1 arcsec 0.000309g 0.0000007716 r 0.0000007716 cir 0.004938 mil
1 gradian = 0.015708 rad 15.707963 mrad 0.9° 54 arcmin 3,240 arcsec 1g 0.0025 r 0.0025 cir 16 mil
1 revolution = 6.283185 rad 6,283 mrad 360° 21,600 arcmin 1,296,000 arcsec 400g 1 r 1 cir 6,400 mil
1 circle = 6.283185 rad 6,283 mrad 360° 21,600 arcmin 1,296,000 arcsec 400g 1 r 1 cir 6,400 mil
1 mil = 0.000982 rad 0.981748 mrad 0.05625° 3.375 arcmin 202.5 arcsec 0.0625g 0.000156 r 0.000156 cir 1 mil

References

  1. Merriam-Webster, angle, https://www.merriam-webster.com/dictionary/angle