20 radians is approximately 1145.9156 degrees.
Table of Contents
To convert radians to degrees, multiply the radian value by 180 and divide it by π (pi). Since π radians equals 180 degrees, this formula changes the unit from radians to degrees.
Conversion Tool
Result in degrees:
Conversion Formula
The formula to convert radians to degrees is:
Degrees = Radians × (180 ÷ π)
This works because one full circle equals 2π radians or 360 degrees. Dividing both sides by 2, π radians equals 180 degrees, so multiplying radians by (180/π) converts the radian measure to degrees.
Example calculation for 20 radians:
- Start with 20 radians.
- Multiply by 180: 20 × 180 = 3600.
- Divide by π (≈ 3.1416): 3600 ÷ 3.1416 ≈ 1145.9156 degrees.
Conversion Example
- Convert 5 radians to degrees:
– Multiply 5 by 180 → 5 × 180 = 900.
– Divide by π → 900 ÷ 3.1416 ≈ 286.4789 degrees. - Convert 1.57 radians to degrees:
– Multiply 1.57 × 180 = 282.6.
– Divide by π → 282.6 ÷ 3.1416 ≈ 90.05 degrees. - Convert 3 radians to degrees:
– 3 × 180 = 540.
– 540 ÷ 3.1416 ≈ 171.8873 degrees. - Convert 0.5 radians to degrees:
– 0.5 × 180 = 90.
– 90 ÷ 3.1416 ≈ 28.6479 degrees. - Convert 10 radians to degrees:
– 10 × 180 = 1800.
– 1800 ÷ 3.1416 ≈ 572.9578 degrees.
Conversion Chart
| Radians | Degrees |
|---|---|
| -5.0 | -286.4789 |
| 0.0 | 0.0000 |
| 5.0 | 286.4789 |
| 10.0 | 572.9578 |
| 15.0 | 859.4366 |
| 20.0 | 1145.9156 |
| 25.0 | 1432.3945 |
| 30.0 | 1718.8733 |
| 35.0 | 2005.3522 |
| 40.0 | 2291.8310 |
| 45.0 | 2578.3099 |
This chart shows radians values in the left column and their corresponding degrees on the right. You can find the degrees for a radian by looking across the row. Negative radians produce negative degree values, indicating rotation direction.
Related Conversion Questions
- How many degrees equal 20 radians exactly?
- What is the degree equivalent of 20 radians in terms of full rotations?
- Can 20 radians be converted to degrees without a calculator?
- Is 20 radians more than 360 degrees or less?
- What formula should I use to change 20 radians into degrees?
- How does 20 radians compare to degrees in trigonometry problems?
- Why does 20 radians convert to such a large degree value?
Conversion Definitions
Radians: A radian is a unit measuring angles based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It relates directly to the circle’s geometry, making it convenient in calculus and physics for angular measurements.
Degrees: Degrees measure angles by dividing a full circle into 360 equal parts. Each degree is 1/360th of the circle. This unit is common in everyday use, navigation, and geometry, offering an intuitive way to express angles.
Conversion FAQs
Why does converting 20 radians result in a degree value greater than 360?
Since 2π radians equal 360 degrees, any radian value above about 6.283 results in degrees more than 360. Twenty radians is much larger than 2π, so its degree equivalent surpasses a full circle multiple times, showing multiple rotations.
Is it possible for radians to be negative, and how does that affect degrees?
Yes, radians can be negative, indicating rotation in the opposite direction. When converting, negative radians become negative degrees representing the same angle but reversed rotation compared to positive angles.
Can I convert degrees back to radians using a similar formula?
Yes, to convert degrees to radians, multiply degrees by π and divide by 180. This reverses the process, turning degrees into the radian measure used in many math and science fields.
Does converting radians to degrees affect precision?
Conversion involves π, an irrational number, so the degree result is always an approximation when using decimal numbers. Precision depends on how many decimal places are kept in calculations and displayed results.
Why use radians instead of degrees in scientific calculations?
Radians simplify mathematical expressions, especially in calculus and physics, because they relate directly to circle geometry and trigonometric functions. Degrees are more intuitive but less natural in advanced formulas.