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Math & Statisticsgeometry

Angle Converter

Angles across degrees, radians, gradians and arcseconds. Radians are the natural unit because they make the trigonometric derivatives come out clean, which is why every programming language expects them.

Also called: degrees to radians, radians converter.

Result
0.017453

1 Degree is 0.017453 Radian. The factor is 0.0174532925, and the inverse is 57.2957795131. The table below gives the same value in every angle unit at once.

Conversion factor
0.0174532925
Inverse factor
57.2957795131
Value in radian
0.0174532925
Converting from
Degree
Converting to
Radian
Dimension
angle
How this is calculated

The same value in every angle unit

UnitValue
Degree1
Radian0.02
Gradian1.11
Turn0
Arcminute60
Arcsecond3,600
Milliradian17.45
Method and background

How this is calculated

A radian is the angle subtending an arc equal to the radius, so a full turn is two pi radians rather than a round number. That looks inconvenient until calculus, where the derivative of sine is cosine only if the angle is in radians. Degrees survive because 360 divides evenly by almost everything, which mattered enormously before decimals.

result = value * factor_from / factor_to
k
Each unit's size in radian

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a right angle in radians

Value
90
From
Degree
To
Radian

Result1.570796

pi / 2, computed independently

Open this example

a full turn in degrees

Value
1
From
Turn
To
Degree

Result360

arithmetic identity

Open this example

an arcsecond is very small

Value
3,600
From
Arcsecond
To
Degree

Result1

boundary: 3600 arcseconds make a degree

Open this example