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Welcome to radians to degrees, our article about the conversion of angular measures.
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How to Convert Radians to Degrees
Radians are SI derived and the standard unit, whereas degrees are non-SI, yet accepted by the organization International System of Units (SI).Keep reading to learn everything about rad to degrees, and make sure to check out our converter above.
Definition: Radians are defined as circular arc / radius of the arc, so if s stands for the arc’s length, and if r denotes the radius, the angle theta (θ) is the subtended angle in the unit radian: s / r = θ, or s = rθ.
As you can see, this ratio of the two lengths s and r does not naturally have a unit symbol as it is a pure number and as such as dimensionless quantity.
Therefore, in radian measure the unit symbol rad is usually omitted. For a circular arc taking on the form of a complete circle rθ = 2πr (the circumference of a circle).
It follows that θ = 2π, which answers the question how many rad in a circle.
In turn, as detailed on our home page, the answer to how many degrees in a circle is 360.
In other words, a complete revolution is 2π, equivalent to the magnitude of 360 degrees.Now that we know the relation between degree and radian, here’s how to obtain rad in deg: Divide the angle in radian by pi, and multiply the term by 180°.For example, to change π/4 to degrees calculate 0.25 π / π × 180° = 0.25 × 180° = 45°. The formula can be found in the section ahead.BTW: Positive angles show a counterclockwise revolution.It is recommended that you make use of our calculator for any radians to degrees conversion.
Formula
Taking into account the equivalence of 2π and 360°, we can produce the radians to degrees formula, also known as radians to degrees equation:- Example 1: π/2 → 90°
- Example 2: π/3 → 60°
- Example 3: π/4 → 45°
About our Converter
To improve user experience we have moved our converter to the top of this page.If you press “reset”, then our app reinitializes the conversion, but if you fill in the lower field our tool inverts the calculation to degrees to radians.More calculators like the one under consideration can be found following the links useful sites, located in the sidebar of the home page.Our frequent conversions include: BTW: If you come across the terms degree of arc, arc degree, or arcdegree, this is the full spelling for the unit of measurement of an angle, to differentiate it from temperature (degrees).Ahead is the explanation of the form search conversions which can be used to convert angles, because many values have already been converted by us.Rad to Deg Table
The table below contains frequent angles:| Radians | Degrees |
|---|---|
| 0 rad | 0° |
| π/12 ≈ 0.261799388 rad | 15° |
| π/6 ≈ 0.523598776 rad | 30° |
| π/4 ≈ 0.785398163 rad | 45° |
| π/3 ≈ 1.047197551 rad | 60° |
| 5π/12 ≈ 1.308996939 rad | 75° |
| π/2 ≈ 1.570796327 rad | 90° |
| 7π/12 ≈ 1.832595715 rad | 105° |
| 2π/3 ≈ 2.094395102 rad | 120° |
| 3π/4 ≈ 2.35619449 rad | 135° |
| 5π/6 ≈ 2.617993878 rad | 150° |
| 11π/12 ≈ 2.879793266 rad | 165° |
| π ≈ 3.141592654 rad | 180° |
| 13π/12 ≈ 3.403392041 rad | 195° |
| 7π/6 ≈ 3.665191429 rad | 210° |
| 5π/4 ≈ 3.926990817 rad | 225° |
| 4π/3 ≈ 4.188790205 rad | 240° |
| 17π/12 ≈ 4.450589593 rad | 255° |
| 3π/2 ≈ 4.71238898 rad | 270° |
| 19π/12 ≈ 4.974188368 rad | 285° |
| 5π/3 ≈ 5.235987756 rad | 300° |
| 7π/4 ≈ 5.497787144 rad | 315° |
| 11π/6 ≈ 5.759586532 rad | 330° |
| 23π/12 ≈ 6.021385919 rad | 345° |
| 2π ≈ 6.283185307 rad | 360° |
Converting Rad to Deg
In case you are primarily interested in the result, and making use of our angle conversion tool is inconvenient, such as, for example, whist using a mobile phone, you can utilize our search form.Simply insert your query in the aforementioned form, and you will be redirect to a result page, which displays the closest match for your particular query.The results most likely include the conversion you have been looking for.The form is displayed to you in the sidebar for desktop and tablet computer visitors, as well as in our menu.Users having a mobile device need to scroll down towards the end of this page or click on the search menu item. To use the form type x rad to °, provided that x is you angle.Here you can change degrees to radians.In the following paragraph we will review the FAQs in the context of this article.Frequently Asked Questions
Click on the question which is of interest to you to see the collapsible content answer.How do you convert from radians to degrees?
Multiply by the value in radians by 180/pi to get degrees.
What is meant by 1 radian?
1 radian is approximately 57.295779513 degrees.
Is pi equal to 180 degrees?
The perimeter of a circle is 360 degrees = 2 pi radian. So, for 180 degrees the 1/2 circle is equivalent to pi.
How many radians in a circle?
In every circle there are 2 pi radians.
Why is PI 180 degrees?
As the circumference of 360 degrees is equivalent to 2 PI, PI = 180 degrees.
How to turn radians into degrees?
To obtain degrees, divide the angle in radian by pi, then multiply the term by 180 degrees.
How many radians is degrees in pi?
One complete revolution (360°) = 2pi. Thus, pi equals 180°.
Conclusion
You have reached the end of our information regarding the unit conversion of plane angles, which we summarize using this image:- π/12 ⇔ 15°
- π/6 ⇔ 30°
- π/5 ⇔ 36°
- π/4 ⇔ 45°
- π/3 ⇔ 60°
- 2π/5 ⇔ 72°
- π/2 ⇔ 90°
- 2π/3 ⇔ 120°
- 4π/5 ⇔ 144°
- π ⇔ 180°
- 3π/2 ⇔ 270°
- 2π ⇔ 360°