Enter Angle
90°
All Conversions
Key Formulas
Radians = Degrees × (π / 180)Gradians = Degrees × (10 / 9)1 Turn = 360° = 2π rad = 400 grad1° = 60 arcminutes = 3,600 arcsecondsConvert between degrees, radians, gradians, turns, arcminutes and arcseconds
Radians = Degrees × (π / 180)Gradians = Degrees × (10 / 9)1 Turn = 360° = 2π rad = 400 grad1° = 60 arcminutes = 3,600 arcsecondsAngles measure the rotation between two rays from a common point. Different systems divide a full rotation differently.
A full circle is 360°. The most common unit in everyday use, navigation, and geometry.
A full circle is 2π radians. The SI unit used in mathematics and physics. One radian is the angle where the arc length equals the radius.
A full circle is 400 gradians (gon). Used primarily in surveying where a right angle is exactly 100 gradians.
| Degrees | Radians (exact) | Radians (decimal) | Gradians | Turns |
|---|---|---|---|---|
| 0° | 0 | 0 | 0 | 0 |
| 30° | π/6 | 0.5236 | 33.333 | 0.0833 |
| 45° | π/4 | 0.7854 | 50 | 0.125 |
| 60° | π/3 | 1.0472 | 66.667 | 0.1667 |
| 90° | π/2 | 1.5708 | 100 | 0.25 |
| 120° | 2π/3 | 2.0944 | 133.333 | 0.3333 |
| 135° | 3π/4 | 2.3562 | 150 | 0.375 |
| 180° | π | 3.1416 | 200 | 0.5 |
| 270° | 3π/2 | 4.7124 | 300 | 0.75 |
| 360° | 2π | 6.2832 | 400 | 1 |
| From | To | Multiply by |
|---|---|---|
| Degrees | Radians | π / 180 ≈ 0.0174533 |
| Radians | Degrees | 180 / π ≈ 57.29578 |
| Degrees | Gradians | 10 / 9 ≈ 1.11111 |
| Gradians | Degrees | 0.9 |
| Degrees | Turns | 1 / 360 |
| Degrees | Arcminutes | 60 |
| Degrees | Arcseconds | 3600 |
| Degrees | NATO mils | 160 / 9 ≈ 17.7778 |
| Radians | Gradians | 200 / π ≈ 63.66198 |
Three conversions in full
75° to radians: 75 × π/180 = 75π/180 = 5π/12 = 1.3090 rad
2.5 rad to degrees: 2.5 × 180/π = 143.239°
37.5° to degrees-minutes-seconds: 0.5° × 60 = 30′, so 37° 30′ 00″
The last form, DMS, is what latitude and longitude are usually printed in.
Math.sin() in JavaScript, Python and C all expect radians.Spreadsheet and programming trigonometric functions almost always take radians. SIN(30) in Excel returns −0.988, not 0.5, because it reads 30 as 30 radians. Use SIN(RADIANS(30)) in Excel, or Math.sin(30 * Math.PI / 180) in JavaScript. The reverse functions have the same issue: ATAN returns radians, so wrap it in DEGREES().
180 degrees is exactly π radians, about 3.14159. That relationship is the origin of the π/180 conversion factor.
Multiply the number of degrees by π/180, or equivalently by 0.0174533. 90 degrees becomes 90π/180 = π/2 = 1.5708 radians.
A gradian, or gon, is one four-hundredth of a full turn, so a right angle is exactly 100 gradians. It was introduced during the French metric reforms and survives mainly in continental European surveying.
Because a radian is defined as the angle subtending an arc equal to the radius, the arc-length formula becomes simply s = rθ, and the derivative of sin x is exactly cos x. In degrees both pick up a stray factor of π/180.
A milliradian, one thousandth of a radian, which subtends 10 cm at 100 metres or 3.6 inches at 100 yards. NATO artillery uses a slightly rounded version where a full circle is 6,400 mils rather than the mathematically exact 6,283.
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