0.707 radians is approximately 40.5156 degrees.
To convert radians to degrees, you multiply the radian value by 180 and then divide by π (pi). This converts the angular measurement from the radian scale into degrees, which is often easier to understand in everyday settings.
Conversion Tool
Result in degrees:
Conversion Formula
The formula to convert radians (rad) to degrees (°) is:
degrees = radians × (180 ÷ π)
This works because a full circle in radians is 2π, which equals 360 degrees. So, one radian equals 180/π degrees. By multiplying the radian value by 180 and dividing by π, you translate the radian measure into degrees.
For example, converting 0.707 radians:
- Multiply 0.707 by 180: 0.707 × 180 = 127.26
- Divide by π (~3.1416): 127.26 ÷ 3.1416 ≈ 40.5156 degrees
Conversion Example
Let’s convert 2.5 radians to degrees step-by-step:
- Start with the radian value: 2.5
- Multiply by 180: 2.5 × 180 = 450
- Divide by π: 450 ÷ 3.1416 ≈ 143.2394 degrees
- So, 2.5 radians is about 143.2394 degrees
Another example using 1.2 radians:
- Multiply 1.2 by 180: 1.2 × 180 = 216
- Divide by π: 216 ÷ 3.1416 ≈ 68.7549 degrees
And for 0 radians:
- 0 × 180 = 0
- 0 ÷ π = 0 degrees
Conversion Chart
The table below shows radian values from -24.3 to 25.7 and their corresponding degrees. You can find the degree equivalent for a radian by locating the radian value in the left column and reading its degree value on the right.
| Radians | Degrees |
|---|---|
| -24.3 | -1392.9640 |
| -20.0 | -1145.9156 |
| -15.5 | -887.5520 |
| -10.7 | -613.0272 |
| -5.2 | -297.8981 |
| -1.0 | -57.2958 |
| 0 | 0.0000 |
| 0.707 | 40.5156 |
| 3.14 | 179.9087 |
| 7.5 | 429.9722 |
| 12.3 | 704.8933 |
| 18.0 | 1031.0062 |
| 22.2 | 1272.4689 |
| 25.7 | 1473.8334 |
Related Conversion Questions
- How many degrees are in 0.707 radians?
- What is the degree equivalent of 0.707 radians in decimal form?
- Can 0.707 radians be converted to degrees without a calculator?
- Why does 0.707 radians equal about 40.5 degrees?
- Is 0.707 radians closer to 40 or 41 degrees?
- How to convert 0.707 radians to degrees step-by-step?
- What’s the formula to turn 0.707 radians into degrees?
Conversion Definitions
Radians: A radian is a measure of angle based on the radius of a circle. One radian is the angle made when the arc length equals the radius length. There are 2π radians in a full circle, about 6.283 radians total.
Degrees: Degrees divide a circle into 360 equal parts. Each degree represents 1/360 of a full rotation. Degrees are used widely in navigation, geometry, and everyday angle measurements because they are easy to visualize.
Conversion FAQs
Why is π used in converting radians to degrees?
Pi (π) represents the ratio of a circle’s circumference to its diameter, which connects radians to the full circle measure. Since a circle has 2π radians and 360 degrees, π appears in formulas converting radians to degrees to maintain this proportional relationship.
Can I convert radians to degrees without a calculator?
You can estimate by knowing π is about 3.1416. Multiply the radians by 180 and divide by π. For rough mental math, use 3.14 for π and round results, but precise values need a calculator or conversion table.
What happens if I input a negative radian value in the converter?
Negative radians represent angles measured clockwise from the positive x-axis. The converter will output a negative degree value, indicating the angle’s direction but still using the same conversion formula.
Is 0.707 radians a large or small angle?
0.707 radians is about 40.5 degrees, which is less than half a right angle (90 degrees). It’s a moderate, acute angle often seen in trigonometry and physics problems.
Why use degrees instead of radians sometimes?
Degrees are often easier to visualize and communicate in everyday contexts, like navigation or construction. Radians are better for calculus and advanced math due to their natural relation to circle properties, but degrees remain popular for practical use.