1 radian is equal to approximately 57.2958 degrees.
Table of Contents
Converting radians to degrees involves multiplying the radian value by 180 and then dividing by π (pi). This works because a full circle in radians is 2π, which corresponds to 360 degrees, so the ratio between radians and degrees is 180/π.
Conversion Tool
Result in degrees:
Conversion Formula
The formula to convert radians to degrees is:
degrees = radians × (180 ÷ π)
This formula works because the full circle is 2π radians, which equals 360 degrees. Dividing 360 degrees by 2π radians simplifies to 180/π, so multiplying any radian value by 180/π converts it to degrees.
Example calculation for 1 radian:
- Start with radians: 1
- Multiply by 180: 1 × 180 = 180
- Divide by π (approximately 3.1416): 180 ÷ 3.1416 ≈ 57.2958
- So, 1 radian ≈ 57.2958 degrees
Conversion Example
- Convert 2 radians to degrees:
- Multiply 2 × 180 = 360
- Divide 360 by π ≈ 3.1416
- 360 ÷ 3.1416 ≈ 114.5916 degrees
- Convert 0.5 radians to degrees:
- Multiply 0.5 × 180 = 90
- Divide 90 by π ≈ 28.6479 degrees
- Convert -1.2 radians to degrees:
- Multiply -1.2 × 180 = -216
- Divide -216 by π ≈ -68.7549 degrees
- Convert 3.14 radians to degrees:
- Multiply 3.14 × 180 = 565.2
- Divide 565.2 by π ≈ 179.999 degrees (almost 180 degrees)
Conversion Chart
| Radians | Degrees | Radians | Degrees |
|---|---|---|---|
| -24.0 | -1375.388 | 1.0 | 57.296 |
| -20.0 | -1145.916 | 2.0 | 114.592 |
| -16.0 | -916.444 | 3.0 | 171.887 |
| -12.0 | -686.973 | 4.0 | 229.183 |
| -8.0 | -457.501 | 5.0 | 286.479 |
| -4.0 | -228.0 | 6.0 | 343.775 |
| 0.0 | 0.000 | 10.0 | 572.958 |
| -2.0 | -114.592 | 14.0 | 802.430 |
| -1.0 | -57.296 | 18.0 | 1031.902 |
| -0.5 | -28.648 | 22.0 | 1261.374 |
| 0.5 | 28.648 | 26.0 | 1490.846 |
The chart shows radians values in the left column, with their equivalent degrees next to them. Use it to quickly find degree values for given radians without calculation. Note some radians are negative, representing angles clockwise from the positive x-axis.
Related Conversion Questions
- How many degrees are in 1 radian exactly?
- What is the degree equivalent of 1 radian in decimal form?
- Can I convert 1 radian to degrees using a simple formula?
- Is 1 radian more or less than 60 degrees?
- How do I convert radians to degrees on a calculator for the value 1?
- What does 1 radian equal in degrees for angle measurements?
- Why is 1 radian approximately 57.3 degrees and not 60?
Conversion Definitions
Radians: A radian is a unit for measuring angles based on the radius of a circle. One radian is the angle created when the arc length equals the radius length. It provides a natural measure for angles in mathematics and physics, especially when relating angles to circle properties.
Degrees: Degrees are a common unit for angles where a full circle is divided into 360 parts. Each degree represents 1/360th of a full rotation. Degrees are widely used in everyday applications like navigation, engineering, and geometry because of their simplicity and historical use.
Conversion FAQs
Why does multiplying radians by 180 and dividing by π convert it to degrees?
The full circle measures 360 degrees or 2π radians. Dividing 360 by 2π gives 180/π. This ratio converts radians into degrees because it scales the radian measure to the degree system. So multiplying radians by 180/π changes the unit properly.
Can degrees be converted back to radians easily?
Yes, to convert degrees to radians multiply the degree value by π and divide by 180. This reverses the previous conversion by scaling degrees back to radians using the same circular relationship.
Why is 1 radian approximately 57.2958 degrees, not a whole number?
The number 57.2958 comes from the ratio 180 divided by π. Since π is irrational and not a whole number, the degree equivalent of 1 radian is a non-integer decimal. It reflects the precise mathematical relationship between these units.
Are radians or degrees better for measuring angles?
Radians are more natural in math and calculus because they relate directly to circle properties and trigonometric functions. Degrees are easier for everyday use and rough measurements. Preference depends on context and calculation needs.
How to use the conversion tool correctly for negative radian values?
Simply enter negative radians as negative numbers in the tool. The same formula applies, so negative radians convert to negative degrees, representing angles measured clockwise from the positive axis.