 # Reference Angle Calculator

## Enter an angle below:

°

### How does the Reference Angle Calculator work?

Free Reference Angle Calculator - Calculates the reference angle for a given angle. Also known as the positive acute angle.
This calculator has 1 input.

### What 4 formulas are used for the Reference Angle Calculator?

Quadrant 3 = θ - 180
Quadrant 4 = 360 - θ

For more math formulas, check out our Formula Dossier

### What 10 concepts are covered in the Reference Angle Calculator?

angle
the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
cos
cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
cot
The length of the adjacent side divided by the length of the side opposite the angle. Also equals 1/tan(θ)
csc
the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/sin(θ)
defined as one hundredth of the right angle. This is equal to π/200 or 9/10°
a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 180°/π ~ 57.3 degrees.
reference angle
the smallest possible angle made by the terminal side of the given angle with the x-axis.
sec
the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos(θ)
sin
sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
tan
the ratio of the opposite side to the adjacent side of a particular angle of the right triangle.