Degree to Radian Converter (° to rad)
1 degree = 0.0174533 radian. A full circle is 360 degrees or 2π radians, so 180 degrees is π radians.
Result
90 ° = 1.5707963 rad
How to convert degree to radian
A full circle is 360 degrees or 2π radians, so 180 degrees is π radians. Degrees are used in everyday geometry and navigation, while radians are the natural unit in calculus, physics and programming.
Formula
rad = ° × 0.0174533
Worked example
90 ° × 0.0174533 = 1.5708 rad
Degree to Radian quick-reference table
| Degree (°) | Radian (rad) |
|---|---|
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.0472 rad |
| 90 ° | 1.5708 rad |
| 180 ° | 3.14159 rad |
| 360 ° | 6.28319 rad |
Real-life examples
A 90 degree right angle is π/2 radians (1.5708). A programmer calling sin() or cos() usually has to convert degrees to radians first.
Frequently asked questions
What is the formula to convert degrees to radians?
Multiply by π/180. For example 45 degrees x π/180 = 0.7854 rad.
How many degrees is 1 radian?
1 radian is 180/π, which is about 57.2958 degrees.
What is 1 degree in radian?
1 degree = 0.0174533 radian (° to rad).
What is the formula to convert ° to rad?
rad = ° × 0.0174533. For example, 90 ° × 0.0174533 = 1.5708 rad.
How do I convert rad back to °?
Use the reverse converter: 1 radian = 57.2958 degree. Check: 1.5708 rad converts back to 90 °.
Reverse conversion
Need the other direction? Radian to Degree converter (rad to °): 1 radian = 57.2958 degree.
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