Table of Contents
Welcome to degrees to radians, our website dedicated to the conversion of angular measures.
If you have been looking for deg to rad in the search engine of your preference, then you have come to the right site, too.
Both, radians as well as degrees are measurements of plane angles.
The former is a SI derived and the standard unit for measuring angles by distance traveled, the latter is a SI (International System of Units) accepted unit for angle which indicates how far we tilt our heads.
Our converter is next.
Read on to learn how to convert from degree to radian, and note that whilst the unit degree intuitively seems the correct choice for measuring rotations and angles, it is in fact the unit radian that makes math easier.
In degrees, a full counterclockwise rotation is defined as 360°, whereas the equivalence in radians is 2π. Positive degrees & radians move anticlockwise!
A full clockwise revolution means -360° and -2π, respectively.
Definition: The unit of measure radian is defined as distance traveled / radius; the angle θ in the unit radian is equal to an arc’s length s divided by its radius r: θ = s / r.
In other words, the ratio of the two lengths s and r can be seen as the alternate definition of radian.
Degrees are represented by the degree symbol °, but the short form deg can also be seen frequently.
In turn, radians (radius units) are usually denoted by the unit symbol rad.
Additional InformationHere are some more facts and figures related to the measurement of angles:
The history for choosing 360 degrees for a full rotation is unknown, but the number 360 is close to the number of days in a year and approximately the time in which earth completes a revolution around the sun.
And 360, besides 1 and 360, is divisible by 22 more numbers: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120 and 180.
Pi radians equal 180 degrees, so one degree equals 0.01745329252 radians.
How to Convert Degrees to RadiansNow that we know the answer to what is a radian, here’s how to convert degree to radian: We divide the angle in degrees by 180° and multiply the term by π.
For example, for 60° we get the angle in radians like this: rad = 60° × π / 180° = π/3 ≈ 1.0471975512.
You can find the degree to radian formula right below, yet in any case it is recommended using our app!
FormulaFrom the explanations above we can come up with the formula, also known as degrees to radians equation:
To use the equation substitute deg with your angle in degrees and do the math.
Spelled out, the angle in radian is equal to the angle in degrees divided by pi.
Observe that the conversion formula is also valid for negative degrees, that is clockwise revolution.
- Example 1: 45° → π/4
- Example 2: 30° → π/6
- Example 3: -90° → -π/2
Easier than applying the formula is using our calculator.
Our tool is straightforward and you certainly don’t want to miss it.
There, in our app, enter your angle in °; our tool does the rest automatically for you, rounding the result to 10 decimal places.
ConverterTo improve user experience we have placed our converter at the top of this article.
If you hit reset, then our app reinitializes the conversion, yet if you fill in the lower field our app inverts the calculation.
More conversion sites can be found in the sidebar, under useful sites.
And the most frequent degree to radian conversions on our site are:
In the next section of our article we are going to explain how the search form of our site can be used for converting degrees to radians, for we have already conducted many angle conversions.
Degrees to Radians TableThe following table contains frequent angles:
|15°||π/12 ≈ 0.261799388 rad|
|30°||π/6 ≈ 0.523598776 rad|
|45°||π/4 ≈ 0.785398163 rad|
|60°||π/3 ≈ 1.047197551 rad|
|75°||5π/12 ≈ 1.308996939 rad|
|90°||π/2 ≈ 1.570796327 rad|
|105°||7π/12 ≈ 1.832595715 rad|
|120°||2π/3 ≈ 2.094395102 rad|
|135°||3π/4 ≈ 2.35619449 rad|
|150°||5π/6 ≈ 2.617993878 rad|
|165°||11π/12 ≈ 2.879793266 rad|
|180°||π ≈ 3.141592654 rad|
|195°||13π/12 ≈ 3.403392041 rad|
|210°||7π/6 ≈ 3.665191429 rad|
|225°||5π/4 ≈ 3.926990817 rad|
|240°||4π/3 ≈ 4.188790205 rad|
|255°||17π/12 ≈ 4.450589593 rad|
|270°||3π/2 ≈ 4.71238898 rad|
|285°||19π/12 ≈ 4.974188368 rad|
|300°||5π/3 ≈ 5.235987756 rad|
|315°||7π/4 ≈ 5.497787144 rad|
|330°||11π/6 ≈ 5.759586532 rad|
|345°||23π/12 ≈ 6.021385919 rad|
|360°||2π ≈ 6.283185307 rad|
Converting Deg to RadIf you are mainly interested in the result of an angle conversion, and if using our calculator is not practical, for instance when using a smart phone, you can enter a query in the search form.
The form is labelled search conversions and located in the sidebar for desktop and tablet computer users.
Visitors having a mobile device can find it at the bottom of this page.
There, in the aforementioned form, with x being your angle in °, you may enter x deg in rad, to be taken to a result page including the post containing your conversion.
Here you can change radians to degrees.
Next, we will have a look at the frequently asked questions about the subject matter, e.g. how to turn degrees into radians, followed by the summary of our information.
Frequently Asked QuestionsThe FAQs in the context of this page include, but are not limited, to the ones in the accordion. Click on the question which is of interest to you to see the collapsible content answer.
How do you convert degrees to radians?
To change degrees to radians multiply the degrees by π/180°.
What is the radian of 1 degree?
1° = π/180 radians.
Why do we convert degrees to radians?
We convert degrees to radians for the sake of differentiating and integrating trigonometric functions.
What is radian?
Radian is a unit, defined as the angle at the center of a circle whose arc is the length of the radius.
How do you convert degrees to radians without a calculator?
Because 180° corresponds to π radians you can convert degrees to radians by building the proportion 180°:π = °:rad, and solving rad = °/180° × π.
Are radians a unit?
Radian, denoted by the symbol rad, is both, the standard unit of angular measure in many areas of math, as well as the SI unit for measuring angles.
What is difference between Radian and degree?
Radians measure angles by distance traveled, whereas degrees measure angles by how far we have tilted our heads.
Using our information and tool, you can answer these questions with ease.
Yet, if something else remains unclear get in touch with us.
Last but not least we would like to emphasize that many trigonometric functions have their arguments more naturally are expressed in radians than degrees.
And remember that whilst the unit degree is arbitrary and accounts for an observer’s perspective, the unit of angle radians reflect the viewpoint of the mover such as in y = arcsin(x) with −π/2 ≤ y ≤ π/2.
Finally, as radians are the distance along the unit circle, it is much easier to change rotational speed in rad to linear speed than in °: use linear speed = angular speed × radius of the rotation.
Ahead you can find the conversion of common angles, as well as the summary of our content.
SummaryYou have made it to concluding section of our information about the degrees conversion.
The following image sums our content about the unit conversions of plane angles up:
° is the degree sign; rad is short for radian.
If you have been looking for how many radians in a circle, degrees to radians in terms of pi, then you have, in all likelihood, found the answers, too.
The same applies if you googled for degree to radian converter, angle to radians or something similar like, for instance, relation between radian and degree.
Last, but not least, here are the equivalences of common angles:
- 15° ⇔ π/12
- 30° ⇔ π/6
- 36° ⇔ π/5
- 45° ⇔ π/4
- 60° ⇔ π/3
- 72° ⇔ 2π/5
- 90° ⇔ π/2
- 120° ⇔ 2π/3
- 144° ⇔ 4π/5
- 180° ⇔ π
- 270° ⇔ 3π/2
- 360° ⇔ 2π
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