Angle Converter
This angle converter turns any angle measurement into another unit instantly, moving between degrees (°), radians (rad), gradians (grad), arcminutes (arcmin) and arcseconds (arcsec). Type the angle, mark which unit you are coming from and which one you are heading to: the conversion is instant and works just as well for turning a trigonometry exercise into radians as for reading a nautical chart in gradians.
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How it works
Every conversion passes through the degree, which acts as a bridge unit. Each unit has its equivalence: a radian is 57.29578° (which is 180/π), a gradian is 0.9°, an arcminute is 1/60 of a degree and an arcsecond 1/3600. The converter multiplies your value by the factor of the source unit to bring it to degrees, then divides by the target factor. The most requested case is turning degrees into radians with the formula degrees × π/180. For example, 180° × π/180 = π ≈ 3.1416 radians, which is a half turn; and 90° × π/180 = π/2 ≈ 1.5708 radians, a right angle. For the reverse, radians to degrees, you use radians × 180/π. Always working against the degree lets even the smallest units, such as astronomy's arcsecond, fit in without losing precision.
Notable angles in degrees and radians
The same angles come up again and again in trigonometry and geometry, and it helps to have their radian value on hand as a fraction of π. The table gathers them: to go from degrees to radians you multiply by π/180, and the result is usually written as a multiple of π (that is why 180° is π and a full turn, 360°, is 2π). The half turn (180°) and the full turn (360°) are the most common references; any angle larger than 360° can be reduced by subtracting full turns until it sits between 0° and 360°, which is common when working with rotations.
| Degrees | Radians |
|---|---|
| 0° | 0 |
| 30° | π/6 ≈ 0.5236 |
| 45° | π/4 ≈ 0.7854 |
| 60° | π/3 ≈ 1.0472 |
| 90° | π/2 ≈ 1.5708 |
| 120° | 2π/3 ≈ 2.0944 |
| 135° | 3π/4 ≈ 2.3562 |
| 180° | π ≈ 3.1416 |
| 270° | 3π/2 ≈ 4.7124 |
| 360° | 2π ≈ 6.2832 |
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Preguntas frecuentes
- How many degrees are in one radian?
- One radian equals about 57.29578 degrees, which is 180/π. A full circle is 2π radians, or 360 degrees, so π radians equals exactly 180°.
- How do I convert degrees to radians?
- Multiply the degrees by π/180 (about 0.0174533). For example, 90° × π/180 = 1.5708 rad, which is π/2. To go back, multiply radians by 180/π.
- What is a gradian?
- A gradian (grad or gon) divides a right angle into 100 parts, so a full circle is 400 gradians. That makes 1 gradian equal to 0.9 degrees. It is used in surveying and some engineering fields.
- What are arcminutes and arcseconds?
- An arcminute is 1/60 of a degree and an arcsecond is 1/60 of an arcminute, so 1/3600 of a degree. They measure very small angles in astronomy, navigation and optics.
- How many radians is a full circle?
- A full circle is 2π radians, about 6.2832 rad, which equals 360 degrees or 400 gradians. Half a circle is π radians or 180°.
- What are π/2, π/3 and π/4 in degrees?
- They are the most used notable angles. π/2 is 90° (a right angle), π/3 is 60°, π/4 is 45° and π/6 is 30°. To go from radians to degrees you multiply by 180/π; for example, π/4 × 180/π = 45°.
- Why do calculators have a DEG and a RAD mode?
- Because trigonometric functions (sine, cosine, tangent) give different results depending on the angle unit. In DEG mode they read the number as degrees, in RAD mode as radians. If sin(90) gives you almost 0 instead of 1, your calculator is in radians: 90 radians is not a right angle. Convert first or switch the mode.