Angle Converter

An angle converter transforms an angular measurement from one unit to an equivalent value in another unit. Angles measure the amount of rotation between two rays sharing a common endpoint. The most common units are degrees (everyday use), radians (mathematics and physics), and gradians (surveying). Our angle converter covers 14 units across common, navigation, and scientific systems, using exact conversion factors based on the mathematical relationship between degrees and radians (π radians = 180°). Every conversion also shows the DMS (degrees-minutes-seconds) representation for geographic and astronomical use.

1. 1. Select Your Source and Target Units: Choose the angle unit you are converting from and the unit you want to convert to from the 14 available options. Use the swap button (⇄) to instantly reverse the conversion direction.
2. 2. Enter Your Value: Type the angle value you want to convert. The angle converter accepts any number including decimals and negative values. The input label updates automatically to show the selected unit.
3. 3. View the Result, DMS, and Full Table: Click Convert Angle to see the direct result, the DMS (degrees-minutes-seconds) representation of the input angle, and a complete table showing your input converted to all 14 angle units grouped by system.

• Degree (°): The most common angle unit. A full circle = 360°. Defined as 1/360 of a full rotation. Used in everyday geometry, navigation, and most engineering applications.
• Radian (rad): The SI unit of angle. A full circle = 2π rad ≈ 6.2832 rad. Defined as the angle subtended by an arc equal in length to the radius. Used in mathematics, physics, and programming.
• Gradian / Gon (grad): A full circle = 400 grad. Defined so that a right angle = 100 grad, making decimal arithmetic convenient. Used in surveying, geodesy, and some European engineering traditions.
• Turn (revolution): A full circle = 1 turn. The most intuitive unit for rotational quantities. Used in mechanical engineering, motor control, and some programming APIs.
• Arcminute (′): 1° = 60 arcminutes. Used in astronomy for celestial coordinates, in navigation for latitude/longitude precision, and in optics for angular resolution.
• Arcsecond (″): 1° = 3,600 arcseconds. Used in astronomy for star positions, in geodesy for precise coordinates, and in GPS accuracy specifications (1 arcsecond ≈ 30 m on Earth's surface).
• Milliradian (mrad): 1 mrad ≈ 0.0573°. Used in optics, ballistics, and precision engineering. At 1,000 m range, 1 mrad subtends exactly 1 m — making it ideal for range estimation.
• Angular Mil (NATO): 6,400 mils per circle. Used by NATO military forces for artillery targeting and range estimation. 1 NATO mil ≈ 0.0563°.

• Degrees ↔ Radians: rad = deg × π / 180 | deg = rad × 180 / π
• Degrees ↔ Gradians: grad = deg × 400 / 360 = deg × 10/9 | deg = grad × 0.9
• Degrees ↔ Turns: turn = deg / 360 | deg = turn × 360
• Degrees ↔ Arcminutes: arcmin = deg × 60 | deg = arcmin / 60
• Degrees ↔ Arcseconds: arcsec = deg × 3600 | deg = arcsec / 3600
• DMS conversion: deg = D + M/60 + S/3600 | D = floor(deg), M = floor((deg-D)×60), S = ((deg-D)×60-M)×60