Unit converter

Angle converter

Convert degrees, radians, gradians, turns, arcminutes, and arcseconds.

Enter a value and choose units. Results update instantly.

1 ° = 0.0174532925 rad

All Angle units

From 1 °
UnitValue
Radian rad 0.0174532925
Degree ° 1
Gradian gon 1.1111111111
Turn turn 0.0027777778
Arcminute ′ 60
Arcsecond ″ 3,600
NATO mil mil 17.7777777778
Recent conversions
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Common tasks

Degree to Radian° to rad Radian to Degreerad to ° Degree to Gradian° to gon Turn to Degreeturn to ° Degree to Arcminute° to ′ NATO mil to Degreemil to °

Reference

How angle conversion works

Plane angle can be expressed as a fraction of a full turn or as an arc-to-radius ratio in radians. Conversions use the mathematical constant pi.

Values are converted to radian first, then from that reference into the requested unit. Keeping a single documented reference reduces inconsistent pair-by-pair constants.

Accuracy note: Displayed decimal results approximate irrational conversions that involve pi.

Unit reference

UnitSymbol1 unit in rad
Radianrad1
Degree°0.01745329252
Gradiangon0.015707963268
Turnturn6.28318530718
Arcminute′0.000290888209
Arcsecond″0.000004848137
NATO milmil0.000981747704

Long-tail directory

Every indexed conversion

Choose a source unit to see all available destinations.

From Radian (rad)
Radian to DegreeRadian to GradianRadian to TurnRadian to ArcminuteRadian to ArcsecondRadian to NATO mil
From Degree (°)
Degree to RadianDegree to GradianDegree to TurnDegree to ArcminuteDegree to ArcsecondDegree to NATO mil
From Gradian (gon)
Gradian to RadianGradian to DegreeGradian to TurnGradian to ArcminuteGradian to ArcsecondGradian to NATO mil
From Turn (turn)
Turn to RadianTurn to DegreeTurn to GradianTurn to ArcminuteTurn to ArcsecondTurn to NATO mil
From Arcminute (′)
Arcminute to RadianArcminute to DegreeArcminute to GradianArcminute to TurnArcminute to ArcsecondArcminute to NATO mil
From Arcsecond (″)
Arcsecond to RadianArcsecond to DegreeArcsecond to GradianArcsecond to TurnArcsecond to ArcminuteArcsecond to NATO mil
From NATO mil (mil)
NATO mil to RadianNATO mil to DegreeNATO mil to GradianNATO mil to TurnNATO mil to ArcminuteNATO mil to Arcsecond

Primary source

Definitions and standards

Conversion constants and definitions for this category are checked against BIPM SI Brochure: Plane angle.

See Methods & sources for rounding rules, exact-value handling, and review policy.

Questions

Angle FAQ

What is the reference unit for angle conversions?

ConvertWin uses radian (rad) as the internal reference for this category, then converts to the selected output unit.

How accurate is this angle converter?

Displayed decimal results approximate irrational conversions that involve pi.