2 radians is approximately 114.5916 degrees.
Table of Contents
To convert radians to degrees, multiply the radian value by 180 divided by π (pi). This converts the angle measure from the radian system, which is based on the radius of a circle, to degrees, which divide a circle into 360 parts.
Conversion Tool
Result in degrees:
Conversion Formula
The formula for converting radians to degrees is:
Degrees = Radians × (180 / π)
This formula works because a full circle is 360 degrees or 2π radians. So one radian equals 180 divided by π degrees. Multiplying a radian value by this factor changes the measure into degrees.
Example calculation for 2 radians:
- Start with 2 radians.
- Multiply by 180: 2 × 180 = 360.
- Divide by π (approximately 3.1416): 360 ÷ 3.1416 ≈ 114.5916 degrees.
Conversion Example
- Convert 1.5 radians to degrees:
- Multiply 1.5 by 180 = 270.
- Divide 270 by π ≈ 3.1416.
- Result: 270 ÷ 3.1416 ≈ 85.9437 degrees.
- Convert 0.75 radians to degrees:
- 0.75 × 180 = 135.
- 135 ÷ 3.1416 ≈ 42.9737 degrees.
- Convert -1 radians to degrees:
- -1 × 180 = -180.
- -180 ÷ 3.1416 ≈ -57.2958 degrees.
- Convert 3.14 radians to degrees:
- 3.14 × 180 ≈ 565.2.
- 565.2 ÷ 3.1416 ≈ 179.9087 degrees.
- Convert 4 radians to degrees:
- 4 × 180 = 720.
- 720 ÷ 3.1416 ≈ 229.1831 degrees.
Conversion Chart
| Radians | Degrees | Radians | Degrees |
|---|---|---|---|
| -23.0 | -1318.1169 | 2.0 | 114.5916 |
| -22.0 | -1260.1663 | 3.0 | 171.8873 |
| -21.0 | -1202.2157 | 4.0 | 229.1831 |
| -20.0 | -1144.2652 | 5.0 | 286.4789 |
| -19.0 | -1086.3146 | 6.0 | 343.7746 |
| -18.0 | -1028.3640 | 7.0 | 401.0704 |
| -17.0 | -970.4134 | 8.0 | 458.3661 |
| -16.0 | -912.4629 | 9.0 | 515.6619 |
| -15.0 | -854.5123 | 10.0 | 572.9577 |
| -14.0 | -796.5617 | 11.0 | 630.2534 |
| -13.0 | -738.6111 | 12.0 | 687.5492 |
| -12.0 | -680.6605 | 13.0 | 744.8449 |
| -11.0 | -622.7099 | 14.0 | 802.1407 |
| -10.0 | -564.7594 | 15.0 | 859.4365 |
| -9.0 | -506.8088 | 16.0 | 916.7322 |
| -8.0 | -448.8582 | 17.0 | 974.0280 |
| -7.0 | -390.9076 | 18.0 | 1031.3237 |
| -6.0 | -332.9570 | 19.0 | 1088.6195 |
| -5.0 | -275.0065 | 20.0 | 1145.9153 |
| -4.0 | -217.0559 | 21.0 | 1203.2110 |
| -3.0 | -159.1053 | 22.0 | 1260.5068 |
| -2.0 | -101.1547 | 23.0 | 1317.8025 |
| -1.0 | -43.2041 | 24.0 | 1375.0983 |
| 0.0 | 0.0000 | 25.0 | 1432.3941 |
| 1.0 | 57.2958 | 26.0 | 1489.6898 |
| 1.5 | 85.9437 | 27.0 | 1546.9856 |
This chart shows the equivalent degrees for radians from -23.0 to 27.0. Locate the radian value in the left or right column, then read its corresponding degrees value next to it to quickly find the angle in degrees.
Related Conversion Questions
- How many degrees equals 2 radians exactly?
- What is the degree measure for an angle of 2 radians?
- Convert 2 radians into degrees, can you show the steps?
- Is 2 radians more or less than 100 degrees?
- How do I change 2 radians into degrees without a calculator?
- What angle in degrees corresponds to 2 radians in trigonometry?
- Why does 2 radians equal approximately 114.59 degrees?
Conversion Definitions
Radians: Radians are units measuring angles based on the radius of a circle. One radian is the angle formed when the arc length equals the radius. This unit is widely used in mathematics and physics because it relates angles directly to circle geometry and trigonometric functions.
Degrees: Degrees measure angles by dividing a full circle into 360 equal parts. Each degree represents 1/360 of a circle’s rotation. Degrees are common in navigation, engineering, and everyday use, making angles easier to understand compared to radian units.
Conversion FAQs
Can radians be negative, and how does that affect conversion to degrees?
Yes, radians can be negative, representing angles measured clockwise from the positive x-axis. When converting negative radians to degrees, multiply by 180/π as usual, resulting in a negative degree value, indicating direction.
Why multiply by 180 instead of some other number when converting radians?
Because a circle has 360 degrees, and 2π radians equals 360 degrees, multiplying by 180 converts the radian fraction of π into degrees. The factor 180/π converts the radian measure to the degree scale accurately.
Is the conversion formula exact or approximate?
The formula Degrees = Radians × (180/π) is exact mathematically. However, since π is irrational, decimal approximations are used in practice, causing small rounding errors depending on how many decimals are kept.
When converting radians to degrees, should I always use π = 3.1416?
Using π as 3.1416 is a common approximation sufficient for most calculations. For higher precision, more digits of π should be used, but for everyday conversions, 3.1416 works fine.
Can this conversion be reversed easily?
Yes, converting degrees back to radians involves multiplying degrees by π/180. This reverses the earlier multiplication by 180/π, so both conversions are straightforward and inverse operations.