Common angles and their equivalents across all unit systems, plus exact trigonometric values.
Degrees
Radians (exact)
Radians (dec)
Gradians
Turns
sin
cos
tan
Conversion Formulas
From
To
Formula
Degrees
Radians
rad = deg × π/180
Radians
Degrees
deg = rad × 180/π
Degrees
Gradians
grad = deg × 10/9
Gradians
Degrees
deg = grad × 9/10
Degrees
Turns
turns = deg / 360
Turns
Degrees
deg = turns × 360
Degrees
Arcminutes
arcmin = deg × 60
Degrees
Arcseconds
arcsec = deg × 3600
Radians
Milliradians
mrad = rad × 1000
Trigonometric Identities
sin²θ + cos²θ = 1
tan θ = sin θ / cos θ
sin(90° − θ) = cos θ
cos(90° − θ) = sin θ
sin(−θ) = −sin θ
cos(−θ) = cos θ
sin(180° − θ) = sin θ
cos(180° − θ) = −cos θ
sec θ = 1 / cos θ
csc θ = 1 / sin θ
cot θ = cos θ / sin θ
Radian: The SI unit of angle. 1 radian = angle subtended at the center of a circle by an arc equal in length to the radius. A full circle = 2π radians ≈ 6.2832 rad.
Angle Units Explained
Degree (°): The most common unit. A full circle is 360°. Originated from the Babylonian base-60 number system. One degree = 1/360 of a full rotation.
Radian (rad): The SI standard unit. Defined as the angle subtended by an arc equal in length to the radius. A full circle = 2π rad ≈ 6.2832 rad. Used in mathematics, physics, and engineering.
Gradian (grad / gon): A metric unit where a full circle = 400 gradians. Designed so that a right angle = 100 grad. Used in surveying and civil engineering.
Turn (rev): The most natural unit — 1 turn = 1 full rotation = 360° = 2π rad = 400 grad. Used in some engineering contexts.
Arcminute ('): 1/60 of a degree. Used in navigation, astronomy, and geographic coordinates. 1° = 60 arcminutes.
Arcsecond (''): 1/60 of an arcminute = 1/3600 of a degree. Used in astronomy for very precise angular measurements.
Milliradian (mrad): 1/1000 of a radian. Used in military applications, ballistics, and optics for precise small-angle measurements.