Enter the original angle into the calculator to evaluate the reference angle. The reference angle is also known as the acute angle, or smallest angle made between the angle and the x-axis.

## Reference Angle Formula

The reference angle for any angle for any angle can be calculated through the following formula:

RA = ABS (180-x)

- Where RA is the reference angle in degrees
- X = the original angle in degrees

Reference angles are typically used in trigonometric theorem problems. They help solve proofs for the trig functions. In general, when someone is looking for a reference angle, they have a given angle theta to start with. The key to solving a reference angle is to understand which quadrant the angle lies in.

## How to calculate a reference angle

The following is a step by step guide on how to calculate the reference angle of any angle.

- First, the standard or original angle must be measured or calculated. For this example we will assume the use of a protractor to measure an angle of 120 degrees.
- Next, the quadrant that this angle lays in must be determined. The quadrant that an angle is in changes every 90 degrees. Therefore, this angle would be in the second quadrant.
- Finally, the angle must be put into the formula above to calculate the reference angle. So RA = ABS (180-120) = ABS (60) = 60. We find that the reference angle is 60 degrees.
- Analyze these results and check using the graphic above to make sure it lies in the correct quadrant.

For more math related calculators, click here.

## Related Terms

reference angle calculator |

reference angle formula |

how to calculate reference angle |

reference angle |

how to find reference angle |

reference angle definition |

find the reference angle |

how to find reference angle in radians |

reference angle radians |

coterminal angles and reference angles |

reference angle of 210 |

reference angle of 120 |

find the reference angle for the given angle |

reference angle calculator radians |

define reference angle |

coterminal and reference angles |

find reference angle calculator |

how do you find the reference angle |

reference angle finder |

find the reference angle calculator |

reference angle radians calculator |

trig reference angles |

how to find the reference angle in radians |

unit circle reference angle |

negative reference angle |

finding reference angles in radians |

trigonometry reference angle |

reference angle of 30 |

reference and coterminal angles |

reference angle example |

reference angle calc |

reference angle of 60 |

reference angle meaning |

reference angle of a negative angle |

reference angle for negative angles |

reference angle rules |

reference angle of 150 degrees |

ref angle |

find the reference angle for |

use reference angles to find the exact value |

reference angle for 120 degrees |

how to determine reference angles |

reference angle of 30 degrees |

reference number unit circle calculator |

use reference angles to find the exact value of the expression |

reference number calculator unit circle |

reference angle of 90 |

reference angle lies in which quadrant |

the reference angle |

how to find reference angle in degrees |

coterminal and reference angles calculator |

reference angle for 120 |

reference angle circle |

reference angle for 240 |

reference angle of 240 degrees |

reference angle table |

sin 210 degrees reference angle |

how to find the reference angle of a negative angle |

formula for reference angle |

determine the reference angle |

reference angle for 330 degrees |

reference angle equation |

radian reference angle calculator |

reference angle of degrees |

use the reference angle to find the exact value |

reference angle for 100 degrees |

using reference angles to evaluate trigonometric functions |

evaluate without using a calculator by using ratios in a reference triangle |

find the reference angle for the given angle calculator |

reference angle solver |

reference angle problems |

corresponding reference angle |

reference angle of 205 |

determine reference angle |

reference angle for 90 degrees |

all reference angles must be |

reference angle ppt |

reference angle of 45 degrees |

tan reference angles |

precalculus reference angles |

reference angle for |

how to calculate the reference angle |

trigonometry reference |

unit circle and reference angles |

reference angle of 270 degrees |

find reference angle in radians calculator |

coterminal and related angles |

pre calc reference angles |

using reference angles |