Angle Converter
Convert degrees, radians, gradians, and turns instantly.
What it does
Angle conversion rescales one full turn across unit systems. Degrees split the circle into 360, radians measure arc per radius for 2π per turn, gradians use 400, and turns count whole revolutions directly.
The tool above moves between all four units. Pick both ends, enter the value, and the answer updates with every equivalent below it.
The default of 180° converts to 3.1416 rad (π), 200 gon, and half a turn. A right angle reads 90°, 1.5708 rad, 100 gon, or a quarter turn by the same ratios.
The radian follows NIST SI definitions with BIPM maintaining the degree to radian relation through π. Gradians survive mainly in surveying instruments alongside the turn in rotations work.
How to use
- Enter the angle value in the source unit.
- Pick the source unit on the left and the target on the right.
- Read the converted line first.
- Scan the all units note for the rest.
- Feed radians to trig functions unless set to degrees.
Formula
- 57.29577951
- Degrees in one radian (180/π).
- 0.9
- Degrees in one gradian.
- hub
- Degrees as the single middle step.
Going through degrees keeps one path for all twelve pairs. The radian factor carries π, so results round at four places by display only.
Worked example
Example: 180° to radians
Value 180, from degrees, to radians.
- Degrees first: 180 stays 180.
- Divide by radian factor: 180 / 57.29577951 = 3.14159265.
- Round to four places: 3.1416 rad.
- Result: 180° = 3.1416 rad (exactly π).
- Reverse: 3.1416 x 57.29577951 = 180.0001° back.
Reference table
| Turn | Degrees | Radians |
|---|---|---|
| 1/4 | 90° | 1.5708 |
| 1/2 | 180° | 3.1416 |
| 3/4 | 270° | 4.7124 |
| Full | 360° | 6.2832 |
Limits
- Plane angles only; solid angles use steradians.
- Display rounds at four places.
- Bearings and slopes need their own conventions.
- Beyond turns, normalize first for clarity.
Common mistakes
- Feeding degrees to radian mode trig functions.
- Reading 180 as π without checking units.
- Mixing gradians with grades (percent slope).
- Rounding π to 3.14 mid chain on precision work.
- Confusing turns with radians past one circle.
Try it yourself
Quick checks. Answers sit tucked under each question.
90° in radians?
90 / 57.29577951 = 1.5708 rad.
1 rad in degrees?
1 x 57.29577951 = 57.2958°.
Half turn in gon?
180 / 0.9 = 200 gon.
Questions
How many radians in 180°?
π, shown as 3.1416 rad.
Degrees or radians for math?
Radians. Calculus trig formulas assume radian measure.
What is a gradian?
1/400 of a circle (0.9°), used in some surveying tools.
What is a turn?
One full circle: 360°, 2π rad, 400 gon.
Why 360 degrees?
Babylonian base sixty heritage, kept by convention, not physics.
How do bearings fit?
Bearings clock from north; convert to standard math angles first.