About this calculator
Type a number, choose the unit you have and the unit you want, and this converter gives you the answer at once, along with the same angles in every other unit it knows.
Every conversion factor is exact by definition wherever one exists, and each result shows the working so you can check it.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
180 ° to rad
- radians (rad)
- 3.14159265359 rad
- gradians (grad)
- 200 grad
- turns (turn)
- 0.5 turn
- arcminutes (′)
- 10,800′
- arcseconds (″)
- 648,000″
180° is 3.14159265359 rad.
Show the working
- Change to the base unit (rad): 180 ° × 0.0174532925199 = 3.14159265359 rad.
- Change to rad: 3.14159265359 ÷ 1 = 3.14159265359 rad.
1 rad to °
- degrees (°)
- 57.2957795131°
- gradians (grad)
- 63.6619772368 grad
- turns (turn)
- 0.159154943092 turn
- arcminutes (′)
- 3,437.74677078′
- arcseconds (″)
- 206,264.806247″
1 rad is 57.2957795131°.
Show the working
- Change to the base unit (rad): 1 rad × 1 = 1 rad.
- Change to °: 1 ÷ 0.0174532925199 = 57.2957795131 °.
45 ° to turn
- turns (turn)
- 0.125 turn
- radians (rad)
- 0.785398163397 rad
- gradians (grad)
- 50 grad
- arcminutes (′)
- 2,700′
- arcseconds (″)
- 162,000″
45° is 0.125 turn.
Show the working
- Change to the base unit (rad): 45 ° × 0.0174532925199 = 0.785398163397 rad.
- Change to turn: 0.785398163397 ÷ 6.28318530718 = 0.125 turn.
How to convert by hand
A full turn is 360 degrees, 2π radians (about 6.28319) or 400 gradians. To convert degrees to radians, multiply by π ÷ 180; to convert radians to degrees, multiply by 180 ÷ π.
For example, 90° × π ÷ 180 = π ÷ 2 ≈ 1.5708 rad, and 1 rad × 180 ÷ π ≈ 57.2958°.
Conversion factors used
Each unit is stored as its size in rad. The sizes below are the ones this converter uses.
| Unit | Size |
|---|---|
| degrees (°) | 0.0174532925199 rad |
| radians (rad) | 1 rad |
| gradians (grad) | 0.0157079632679 rad |
| turns (turn) | 6.28318530718 rad |
| arcminutes (′) | 0.00029088820867 rad |
| arcseconds (″) | 0.00000484813681 rad |
Common conversions
| From | To |
|---|---|
| 30 ° | 0.523598775598 rad |
| 45 ° | 0.785398163397 rad |
| 60 ° | 1.0471975512 rad |
| 90 ° | 1.57079632679 rad |
| 180 ° | 3.14159265359 rad |
| 360 ° | 6.28318530718 rad |
| 1 rad | 57.2957795131° |
| 1 ° | 60′ |
Why radians?
Radians measure an angle by the length of the arc it cuts from a circle of radius 1. That makes the formulas of calculus and physics much simpler, which is why scientific calculators and programming languages use radians for sin, cos and tan.
Frequently asked questions
How many degrees is one radian?
One radian is about 57.2958 degrees.
How do I convert degrees to radians?
Multiply the degrees by π ÷ 180.
How many gradians are in a right angle?
A right angle is 100 gradians.
How accurate is this converter?
It uses the exact defined factors wherever they exist and shows up to 12 significant digits, so the results are accurate to far more digits than you will normally need.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.