Rad to Deg
Convert radians into degrees for a more visual angle reading.
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Conversion Formula
Conversion Examples
Rad to Deg Table
| Radians | Degrees |
|---|---|
| 0.1 | 5.72957795 |
| 0.5 | 28.64788976 |
| 1 | 57.29577951 |
| 1.57079633 | 90.00000018 |
| 2 | 114.59155903 |
| 3.14159265 | 179.99999979 |
| 4 | 229.18311805 |
| 6.28318531 | 360.00000016 |
| 10 | 572.95779513 |
| 12.56637061 | 719.99999975 |
Popular Conversions
- 0.1 radians = 5.72957795 degrees
- 0.5 radians = 28.64788976 degrees
- 1 radians = 57.29577951 degrees
- 1.57079633 radians = 90.00000018 degrees
- 2 radians = 114.59155903 degrees
- 3.14159265 radians = 179.99999979 degrees
- 4 radians = 229.18311805 degrees
- 6.28318531 radians = 360.00000016 degrees
What is Radian and Degree?
Radian
Definition: A radian is an angle based on arc length and circle radius, with a full circle equal to 2 pi radians.
History/origin: Radians became the natural angle unit for higher mathematics because they simplify formulas.
Current use: Radians are used in trigonometry, calculus, physics, and engineering.
Degree
Definition: A degree divides a full circle into 360 equal parts.
History/origin: Degree measurement traces back to early astronomy and geometry traditions.
Current use: Degrees are used in geometry, navigation, drafting, machining, and slope interpretation.
Related Angle and Slope Conversions
These angle relationships help when a drawing, machine setting, or slope note uses a different format.
| Related Conversion | Factor or Rule | Formula |
|---|---|---|
| Rad to deg | 180 / pi | degrees = radians x 180 / pi |
| Rad to rev | 1 / (2 pi) | revolutions = radians / (2 pi) |
| Percent slope to degrees | atan(percent / 100) | degrees = arctan(percent / 100) x 180 / pi |
| Degrees to radians | pi / 180 | radians = degrees x pi / 180 |
| Revolutions to degrees | x 360 | degrees = revolutions x 360 |
| Revolutions to radians | x 2 pi | radians = revolutions x 2 pi |
| Slope ratio to percent | x 100 | percent slope = rise / run x 100 |
| Degrees to percent slope | tan(angle) x 100 | percent slope = tan(degrees) x 100 |
Typical Use Cases
Frequently Asked Questions
Q: Why do radians and degrees use different numbers for the same angle?
A: They are different angle scales. Degrees divide a full turn into 360 parts, while radians measure angle from arc length relative to radius.
Q: What is a quick checkpoint for Rad to Deg?
A: 0.5 radians equals 28.64788976 degrees, which is useful when checking whether pi-based angle work is moving in the correct direction.
Q: When are radians more useful than degrees?
A: Radians are often preferred in calculus, physics, and trigonometric formulas, while degrees are easier to read in everyday geometry and navigation-style contexts.
Q: Why does pi appear in angle conversions so often?
A: Because a full circle is 2pi radians. That fixed relationship is what links radians, degrees, and revolutions.
Q: How do I turn degrees back into radians?
A: radians = degrees x pi / 180. Use the reverse rule whenever the angle is already expressed in the target notation.
Q: Is this exact or approximate?
A: The calculation uses an exact factor.