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

# 45 (degree) is equal to:

 Unit Symbol Symbol(plain text) Value radian Show source$rad$ rad 0.785398163 pi × radian Show source$\pi \times rad$ π × rad 0.25
 Unit Symbol Symbol(plain text) Value degree Show source$^\circ$ ° 45 minute of arc Show source$'$ ' 2700 second of arc Show source$"$ " 162000
 Unit Symbol Symbol(plain text) Value turn Show source$-$ - 0.125 quadrant Show source$-$ - 0.5 right angle Show source$-$ - 0.5 sextant Show source$-$ - 0.75 octant Show source$-$ - 1 sign Show source$-$ - 1.5 hour angle (1/24 of turn) Show source$-$ - 3 point Show source$-$ - 4 minute angle (1/60 of turn) Show source$-$ - 7.5
 Unit Symbol Symbol(plain text) Value grad; gradian; gon Show source$-$ - 50 mil Show source$-$ - 785.398163397 mil NATO Show source$-$ - 800 mil Soviet Show 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 name angular measurein degrees angular measurein radians zero angle 0° 0 half-whole angle 180° π whole angle 360° 2π right angle 90° π/2 acute angle from 0° to 90° from 0 to π/2 obtuse angle from 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.
Examples:
• 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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