Angular measure units converter
Angle units converter. Converts radians, degrees, turns and many more.

Inputs data - value and unit, which we're going to convert


45 (degree) is equal to:

(plain text)
radianShow sourceradradrad0.785398163
pi × radianShow sourceπ×rad\pi \times radπ × rad0.25

(plain text)
degreeShow source^\circ°45
minute of arcShow source''2700
second of arcShow source"""162000

(plain text)
turnShow source--0.125
quadrantShow source--0.5
right angleShow source--0.5
sextantShow source--0.75
octantShow source--1
signShow source--1.5
hour angle (1/24 of turn)Show source--3
pointShow source--4
minute angle (1/60 of turn)Show source--7.5

(plain text)
grad; gradian; gonShow source--50
milShow source--785.398163397
mil NATOShow source--800
mil SovietShow source--750
mil Sweden (streck)Show source--787.5

Some facts

  • The angle is part of the plane bounded by two half-lines having a common origin.
  • The half-lines forming an angle are called the arms, and the point in which the arms are in contact is called the vertex.
  • In everyday language, we often say "angle", when we think the angular measure.
  • Angles are used to give location of object on the map. Point on the map is localized by two angles (coordinates): latitude and longitude. The reason of this, is fact, that the Earth is roughly spherical shape.
  • In everyday life, most common angle units are degrees. In cartography, minutes (1/60 of degree) and - in case of more detailed measurements - seconds (1/60 of minute) are useful. Mathematicians and physicists use mainly radians.
  • The concept of angle is stricly related to trigonometric functions, which have angle argument. Example trigonometric functions are sinus (sin), cosinus (cos) or tangens (tg).
  • There are more general concepts of angle expanding definition to 3D space or even to spaces with more than three dimensions. The equivalent of plane angle in three-dimensional space is solid angle.
  • If we sort arms of the angle, in such a way that one arm will be considered first and the second one final, then we will call such angle - directed angle. The directed angle can be defined by pair of two vectors with common origin {u, v}.
  • There are many interesting angle related properties:
    • The sum of all angles in triangle is 180 degrees (π).
    • The sum of all angles in any quadrilateral (so in rectangle or square too) is 360 degrees (2π).
    • In trapezium (br-eng: trapezium, us-eng: trapezoid) the sum of the neighbouring angles next to both short and long basis is 180 degrees (π).
  • Circle can contains two kinds of angles:
    • Inscribed angle – when its vertex is localized on boundaries of circle.
    • Central angle – when its vertex is localized in the center of circle.

Angles classification

angle nameangular measure
in degrees
angular measure
in radians
zero angle0
half-whole angle180°π
whole angle360°
right angle90°π/2
acute anglefrom 0° to 90°from 0 to π/2
obtuse anglefrom 90° to 180°from π/2 to π

How to convert

  • Enter the number to field "value" - enter the NUMBER only, no other words, symbols or unit names. You can use dot (.) or comma (,) to enter fractions.
    • 1000000
    • 123,23
    • 999.99999
  • Find and select your starting unit in field "unit". Some unit calculators have huge number of different units to select from - it's just how complicated our world is...
  • And... you got the result in the table below. You'll find several results for many different units - we show you all results we know at once. Just find the one you're looking for.

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