Angle Converter
Convert degrees, radians, gradians, arcminutes and more. Free instant angle converter.
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All units
| Unit | Value | Copy |
|---|---|---|
| Degree° | 180 | |
| Radianrad | 3.1415927 | |
| Gradiangon | 200 | |
| Turnturn | 0.5 | |
| Arcminute' | 10800 | |
| Arcsecond" | 648000 | |
| Milliradianmrad | 3141.5927 |
Popular conversions
How angle conversion works
A full turn is 360 degrees, 2π radians or 400 gradians, so each unit is a fixed fraction of a turn. This page stores every unit in degrees. One radian is the angle at which the arc length equals the radius, 180/π ≈ 57.2958°. A degree splits into 60 arcminutes and each arcminute into 60 arcseconds, the system used for latitude, longitude and telescope work.
Calculators and programming languages (Math.sin, Excel's SIN) expect radians, so converting degrees to radians before calling a trig function is the most common use of this page.
Worked examples
Degrees to radians for code
45° × π/180 = 0.7854 rad (π/4). 30° is 0.5236 rad (π/6).
Radians back to degrees
2.5 rad × 180/π = 143.24°.
Decimal degrees to degrees, minutes and seconds
For a latitude of 40.7128°, keep the 40°, multiply 0.7128 by 60 = 42.768′, then multiply 0.768 by 60 = 46.08″. The result is 40° 42′ 46.08″.
Roof pitch to degrees
A 6/12 roof rises 6 inches per 12 inches of run. The angle is atan(6 ÷ 12) = atan(0.5) = 26.57°. A 12/12 roof is exactly 45°.
Milliradians at a distance
1 mrad is 1/1,000 of a radian, so it covers 10 cm at 100 m. 1° is 17.45 mrad.
Common angles in radians, gradians and turns
| ° | rad | gon | turn | |
|---|---|---|---|---|
| 1 | 0.0174533 | 1.11111 | 0.00277778 | |
| 30 | 0.523599 | 33.3333 | 0.0833333 | |
| 45 | 0.785398 | 50 | 0.125 | |
| 60 | 1.0472 | 66.6667 | 0.166667 | |
| Right angle | 90 | 1.5708 | 100 | 0.25 |
| Straight angle | 180 | 3.14159 | 200 | 0.5 |
| 270 | 4.71239 | 300 | 0.75 | |
| Full turn | 360 | 6.28319 | 400 | 1 |
Common mistakes
- Passing degrees to a function that expects radians. sin(90) in most software is sin of 90 radians (0.894), not 1. Convert first.
- Reading 40.30° as 40° 30′. Decimal degrees and minutes differ: 40.30° is 40° 18′.
- Confusing a slope percentage with degrees. A 10% grade rises 10 per 100 run, which is 5.71°, not 10°.
- Mixing compass bearings with math angles. A bearing is measured clockwise from north; a math angle is measured counterclockwise from the positive x-axis (east). A bearing of 30° is a math angle of 60°.
Sources
Frequently asked questions
How many radians is 180 degrees?
180° equals π (about 3.14159) radians.
What is a gradian?
A gradian (or gon) is 1/400 of a full turn, so 90° = 100 gon.
How do I convert degrees to radians?
Multiply degrees by π/180. 1° ≈ 0.0174533 rad, so 45° = π/4 ≈ 0.7854 rad.
How do I convert radians to degrees?
Multiply radians by 180/π. 1 rad ≈ 57.2958°, so 2 rad ≈ 114.59°.
How many arcminutes are in a degree?
A degree has 60 arcminutes, and each arcminute has 60 arcseconds, so 1° = 3,600 arcseconds.
How do I convert decimal degrees to degrees, minutes and seconds?
Keep the whole degrees, multiply the decimal part by 60 for minutes, then multiply the minutes' decimal part by 60 for seconds. 40.7128° = 40° 42′ 46.08″.
How do I convert a slope percentage to degrees?
Take the arctangent of the percentage ÷ 100. A 10% grade is atan(0.1) = 5.71°.