Key takeaways
- degrees = radians × 180 / π.
- 1 radian is about 57.2958°.
- π radians equals exactly 180°.
- This is the reverse of the degrees-to-radians conversion.
In this guide
What is this conversion for?
A full circle is 2π radians or 360 degrees. If a sensor, calculation, or formula gives you an angle in radians, this conversion tells you the same angle in the more familiar degree scale.
Why does this conversion matter?
Radians are precise and mathematically convenient, but they're hard to picture at a glance. A door swinging "2 radians" doesn't mean much intuitively — converting to degrees turns it into a number most people can immediately picture on a dial or protractor.
2 radians converts to about 114.6°, which is well past a right angle but short of a straight line — a detail that's much easier to grasp in degrees than in raw radians.
The formula
| Symbol | What it means | Example |
|---|---|---|
| radians | The angle you're starting with | 2 rad |
| π (pi) | A fixed number, about 3.14159 | 3.14159 |
| degrees | The same angle, measured in degrees | 114.59° |
How to convert radians to degrees step by step
- 1Start with your angle in radians.
- 2Multiply it by 180.
- 3Divide the result by π (3.14159).
- 4The answer is the angle in degrees.
Enter any angle in radians below to see the degree conversion worked out step by step.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Using π ≈ 3.14 for high-precision work. Rounding π too early can throw off results in engineering-grade calculations; use as many decimal places as your tool allows.
- Forgetting which unit a trig function expects. If you calculated with the sin, cos, tan calculator, double-check whether it wanted radians or degrees as input.
- Confusing radian *count* with a distance. "2 radians" is an angle, not a length, even though radians are defined using arc length.
Tips and tricks
- To go the other direction, use the degrees to radians calculator.
- If your converted answer is over 360°, you likely started with more than one full circle's worth of radians.
- Pair this with the sin, cos, tan calculator to read trig results in a more familiar unit.
Where you'll use it in real life
- Robotics and sensors: rotation sensors often report raw values in radians that need converting for a human-readable display.
- Navigation: compass bearings and headings are conventionally shown in degrees.
- Design and CAD: many tools calculate internally in radians but display angles in degrees.
- Education: converting back to degrees helps build intuition when first learning radians.
Quick summary
To convert radians to degrees, multiply by 180 and divide by π — the reverse of the degrees-to-radians formula. It turns an abstract radian value into an angle that's easy to picture. Try the calculator above with your own angle.
Worked example
A motion sensor reports that a door swung open by 2 radians. How many degrees is that, so it can be shown on a simple angle display?
- 01degrees = radians × 180 / π
- 02degrees = 2 × 180 / π
- 03degrees = 360 / 3.1415
- 04degrees = 114.5916°
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I convert radians to degrees?
Multiply the angle in radians by 180, then divide by π: degrees = radians × 180 / π.
What is 1 radian in degrees?
1 radian is about 57.2958°, since 180/π ≈ 57.2958.
What is π radians in degrees?
π radians equals exactly 180°, because half of a full circle (2π radians) is 180°.
Why does this conversion use 180 over π instead of the other way round?
Because 180° corresponds to π radians, so dividing degrees by π and multiplying by 180 (or the reverse for the other conversion) keeps the two scales matched.
