0.5 radians is approximately 28.6479 degrees.
To convert radians to degrees, multiply the radian value by 180 and divide by π (pi). Since 0.5 radians is half of one radian, multiplying by 180/π gives the degree equivalent, which is about 28.6479 degrees.
Conversion Tool
Result in degrees:
Conversion Formula
The formula to convert radians to degrees is:
degrees = radians × (180 / π)
This formula works because a full circle has 2π radians or 360 degrees. So, one radian equals 180/π degrees. By multiplying the radian measure by 180 and dividing it by π, the equivalent angle measured in degrees is found.
Example calculation for 0.5 radians:
- Multiply 0.5 by 180: 0.5 × 180 = 90
- Divide the result by π (approximately 3.1416): 90 ÷ 3.1416 ≈ 28.6479
- So, 0.5 radians ≈ 28.6479 degrees
Conversion Example
- Convert 1.2 radians to degrees:
- Multiply 1.2 by 180: 1.2 × 180 = 216
- Divide 216 by π ≈ 216 ÷ 3.1416 ≈ 68.7549
- Result: 1.2 radians ≈ 68.7549 degrees
- Convert 2 radians to degrees:
- Multiply 2 × 180 = 360
- Divide 360 by π ≈ 360 ÷ 3.1416 ≈ 114.5916
- Result: 2 radians ≈ 114.5916 degrees
- Convert 0.75 radians to degrees:
- 0.75 × 180 = 135
- 135 ÷ 3.1416 ≈ 42.9738
- 0.75 radians ≈ 42.9738 degrees
- Convert -1 radians to degrees:
- -1 × 180 = -180
- -180 ÷ 3.1416 ≈ -57.2958
- -1 radian ≈ -57.2958 degrees
Conversion Chart
The table below shows radian values from -24.5 to 25.5, with their degree equivalents. To use, find the radian value on the left, then read across to see the corresponding degrees on the right.
| Radians | Degrees | Radians | Degrees |
|---|---|---|---|
| -24.5 | -1403.84 | 1.5 | 85.9437 |
| -23.5 | -1346.63 | 2.5 | 143.2394 |
| -22.5 | -1289.42 | 3.5 | 200.5351 |
| -21.5 | -1232.21 | 4.5 | 257.8308 |
| -20.5 | -1175.00 | 5.5 | 315.1265 |
| -19.5 | -1117.79 | 6.5 | 372.4222 |
| -18.5 | -1060.58 | 7.5 | 429.7179 |
| -17.5 | -1003.37 | 8.5 | 487.0136 |
| -16.5 | -946.16 | 9.5 | 544.3093 |
| -15.5 | -888.95 | 10.5 | 601.6050 |
| -14.5 | -831.74 | 11.5 | 658.9007 |
| -13.5 | -774.53 | 12.5 | 716.1964 |
| -12.5 | -717.32 | 13.5 | 773.4921 |
| -11.5 | -660.11 | 14.5 | 830.7878 |
| -10.5 | -602.90 | 15.5 | 888.0835 |
| -9.5 | -545.69 | 16.5 | 945.3792 |
| -8.5 | -488.48 | 17.5 | 1002.6749 |
| -7.5 | -431.27 | 18.5 | 1059.9706 |
| -6.5 | -374.06 | 19.5 | 1117.2663 |
| -5.5 | -316.85 | 20.5 | 1174.5620 |
| -4.5 | -259.64 | 21.5 | 1231.8577 |
| -3.5 | -202.43 | 22.5 | 1289.1534 |
| -2.5 | -145.22 | 23.5 | 1346.4491 |
| -1.5 | -88.01 | 24.5 | 1403.7448 |
| -0.5 | -28.6479 | 25.5 | 1461.0405 |
| 0 | 0 | ||
| 0.5 | 28.6479 |
Related Conversion Questions
- How many degrees are in 0.5 radians exactly?
- What is the fastest way to convert 0.5 radians into degrees?
- Is 0.5 radians larger or smaller than 30 degrees?
- Why does multiplying 0.5 radians by 180/π give degrees?
- Can 0.5 radians be converted to degrees without a calculator?
- How to convert 0.5 radians to degrees in Excel?
- What angle in degrees corresponds to 0.5 radians in a circle?
Conversion Definitions
Radians: A radian is a unit to measure 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 way to measure angles related directly to a circle’s geometry without depending on degrees or minutes.
Degrees: Degrees measure angles by dividing a full circle into 360 equal parts. Each degree is 1/360 of a circle. This system is widely used in navigation, geometry, and everyday applications, making angles easier to communicate and understand compared to radians in many situations.
Conversion FAQs
Why is π used in converting radians to degrees?
Pi (π) represents the ratio of a circle’s circumference to its diameter, approximately 3.1416. Since radians relate angles to arc length and radius, π naturally appears in conversion formulas to translate between the radian system and the degree system, which divides the circle into 360 parts.
Can I convert radians to degrees without a calculator?
Yes, you can approximate by knowing π is about 3.14 and using the formula degrees = radians × (180 / π). For simple values like 0.5 radians, multiply 0.5 by 180 (90), then divide by 3.14 to get roughly 28.65 degrees. Though not exact, it gives a close estimation.
What happens if the radian value is negative?
Negative radians indicate rotation in the opposite direction, usually clockwise. When converting to degrees, the formula still works the same way, producing a negative degree value that indicates the angle’s direction relative to a positive rotation.
Why does the conversion factor use 180 degrees?
Because a full circle contains 360 degrees, half a circle is 180 degrees. This half-circle corresponds to π radians. Using 180 degrees in the conversion formula allows translating the radian measure into a scale familiar for practical use, the degree system.
Is the radian-to-degree conversion exact or approximate?
The formula is exact mathematically. However, since π is irrational (non-terminating decimal), any decimal representation of the conversion is an approximation. The exact conversion involves π itself, but decimal results round to a usable number of decimal places.