Radians to Degrees Conversion Calculator (rad to °)

Radians to Degrees Conversion is a mathematical process used to convert angles measured in radians to degrees. Radians and degrees are two common units for measuring angles, and this conversion facilitates ease of understanding and communication between these units.

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What Are Radians and Degrees?

Radians and degrees are units of angular measurement. Radians are based on the radius of a circle, and there are \( 2\pi \) radians in a full circle, while degrees divide a circle into 360 equal parts.

Radians

Radians are a unit of angular measurement commonly used in mathematics and physics. One radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. In mathematical terms, this can be expressed as:

1 radian = \(\frac{180}{\pi}\) degrees

Degrees

Degrees, on the other hand, are a more familiar unit of angular measurement. A full circle is divided into 360 degrees, with each degree further divided into 60 minutes and each minute divided into 60 seconds.

The Radian to Degree Conversion Formula

Converting radians to degrees is a straightforward process and can be done using the following formula:

Degrees = Radians \(\times\) \(\frac{180}{\pi}\)

Now, let’s break down the steps to convert radians to degrees:

Identify the Value in Radians: Begin by determining the value you want to convert from radians to degrees.
Use the Conversion Formula: Apply the conversion formula mentioned above to calculate the equivalent value in degrees.
Perform the Calculation: Input the radian value into the formula, multiply it by \(\frac{180}{\pi}\), and calculate the result.
Interpret the Result: The result of this calculation represents the equivalent value in degrees.

Let’s illustrate this process with an example:

Example: Converting Radians to Degrees

Suppose we have an angle of 2.5 radians, and we want to convert it into degrees. Using the conversion formula:

Degrees = \(2.5 \times \frac{180}{\pi}\)

Let’s calculate the result:

Degrees = \(2.5 \times \frac{180}{\pi}\) ≈ 143.24 degrees

So, 2.5 radians is approximately equivalent to 143.24 degrees.

Understanding the Conversion Calculator

The Radians to Degrees Conversion Calculator transforms angles from radians to degrees. The conversion formula is straightforward:

\( \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \)

The calculator multiplies the angle in radians by the constant \( \frac{180}{\pi} \) to provide the equivalent angle in degrees.

Examples of Conversions

Example 1: Converting Radians

Let’s convert \( 2.5 \) radians to degrees using the Radians to Degrees Conversion Calculator:

\( 2.5 \) radians \( = 143.24^\circ \)

The conversion result is \( 143.24^\circ \).

Example 2: Converting Multiple Radians

You can also convert multiple radians at once. Let’s convert \( 1.2 \) radians, \( 3.0 \) radians, and \( 0.5 \) radians:

\( 1.2 \) radians \( = 68.75^\circ \)
\( 3.0 \) radians \( = 171.85^\circ \)
\( 0.5 \) radians \( = 28.65^\circ \)

The conversion results are \( 68.75^\circ \), \( 171.85^\circ \), and \( 28.65^\circ \) respectively.

Example 3: Converting π Radians

Converting angles in terms of \( \pi \) radians is common. Let’s convert \( \frac{\pi}{4} \) radians and \( \frac{3\pi}{2} \) radians:

\( \frac{\pi}{4} \) radians \( = 45^\circ \)
\( \frac{3\pi}{2} \) radians \( = 270^\circ \)

The conversion results are \( 45^\circ \) and \( 270^\circ \) respectively.

Solution Explanation

The Radians to Degrees Conversion Calculator uses the conversion formula \( \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \) to accurately convert radians to degrees. It simplifies angular measurements for practical applications.

How to Use an Online Conversion Calculator

Using an online Radians to Degrees Conversion Calculator is straightforward:

Input the Radians: Enter the angle in radians that you want to convert.
Click Convert: Press the “Convert” or “Calculate” button to initiate the conversion process.
View the Result: The calculator will display the angle in degrees.

These online calculators provide a convenient way to perform Radians to Degrees conversions.

Table of Radians and Degrees

Radians (rad)	Radians (rad)	Degrees (°)
0 rad	0 rad	0°
π/6 rad	0.5235987756 rad	30°
π/4 rad	0.7853981634 rad	45°
π/3 rad	1.0471975512 rad	60°
π/2 rad	1.5707963268 rad	90°
2π/3 rad	2.0943951024 rad	120°
3π/4 rad	2.3561944902 rad	135°
5π/6 rad	2.6179938780 rad	150°
π rad	3.1415926536 rad	180°
3π/2 rad	4.7123889804 rad	270°
2π rad	6.2831853072 rad	360°

Radian Values with Fractions

Radians	Degrees
2 π rad	360°
π rad	180°
^π⁄₂ rad	90°
^π⁄₃ rad	60°
^π⁄₄ rad	45°
^π⁄₅ rad	36°
^π⁄₆ rad	30°
^π⁄₉ rad	20°
^π⁄₁₀ rad	18°
^π⁄₁₂ rad	15°
^π⁄₁₅ rad	12°
^π⁄₁₈ rad	10°
^π⁄₃₀ rad	6°
^π⁄₃₆ rad	5°
^π⁄₆₀ rad	3°
^π⁄₉₀ rad	2°

Radian Values with Decimals

Radians	Degrees
0.1 π rad	18°
0.2 π rad	36°
0.3 π rad	54°
0.4 π rad	72°
0.5 π rad	90°
0.6 π rad	108°
0.7 π rad	126°
0.8 π rad	144°
0.9 π rad	162°
1 π rad	180°
1.1 π rad	198°
1.2 π rad	216°
1.3 π rad	234°
1.4 π rad	252°
1.5 π rad	270°
1.6 π rad	288°
1.7 π rad	306°
1.8 π rad	324°
1.9 π rad	342°
2 π rad	360°

Radian Values without Pi (π)

Radians	Degrees
0.1 rad	5.72958°
0.2 rad	11.45916°
0.3 rad	17.18874°
0.4 rad	22.91832°
0.5 rad	28.6479°
0.6 rad	34.37748°
0.7 rad	40.10706°
0.8 rad	45.83664°
0.9 rad	51.56622°
1 rad	57.2958°
1.1 rad	63.02538°
1.2 rad	68.75496°
1.3 rad	74.48454°
1.4 rad	80.21412°
1.5 rad	85.9437°
1.6 rad	91.67328°
1.7 rad	97.40286°
1.8 rad	103.13244°
1.9 rad	108.86202°
2 rad	114.5916°

Radian to Degree Two Decimals in Terms of Pi

Radians	Degrees	Radians	Degrees
0.01 p rad	1.8°	1 p rad	180°
0.02 p rad	3.6°	1.01 p rad	181.8°
0.03 p rad	5.4°	1.02 p rad	183.6°
0.04 p rad	7.2°	1.03 p rad	185.4°
0.05 p rad	9°	1.04 p rad	187.2°
0.06 p rad	10.8°	1.05 p rad	189°
0.07 p rad	12.6°	1.06 p rad	190.8°
0.08 p rad	14.4°	1.07 p rad	192.6°
0.09 p rad	16.2°	1.08 p rad	194.4°
0.1 p rad	18°	1.09 p rad	196.2°
0.11 p rad	19.8°	1.1 p rad	198°
0.12 p rad	21.6°	1.11 p rad	199.8°
0.13 p rad	23.4°	1.12 p rad	201.6°
0.14 p rad	25.2°	1.13 p rad	203.4°
0.15 p rad	27°	1.14 p rad	205.2°
0.16 p rad	28.8°	1.15 p rad	207°
0.17 p rad	30.6°	1.16 p rad	208.8°
0.18 p rad	32.4°	1.17 p rad	210.6°
0.19 p rad	34.2°	1.18 p rad	212.4°
0.2 p rad	36°	1.19 p rad	214.2°
0.21 p rad	37.8°	1.2 p rad	216°
0.22 p rad	39.6°	1.21 p rad	217.8°
0.23 p rad	41.4°	1.22 p rad	219.6°
0.24 p rad	43.2°	1.23 p rad	221.4°
0.25 p rad	45°	1.24 p rad	223.2°
0.26 p rad	46.8°	1.25 p rad	225°
0.27 p rad	48.6°	1.26 p rad	226.8°
0.28 p rad	50.4°	1.27 p rad	228.6°
0.29 p rad	52.2°	1.28 p rad	230.4°
0.3 p rad	54°	1.29 p rad	232.2°
0.31 p rad	55.8°	1.3 p rad	234°
0.32 p rad	57.6°	1.31 p rad	235.8°
0.33 p rad	59.4°	1.32 p rad	237.6°
0.34 p rad	61.2°	1.33 p rad	239.4°
0.35 p rad	63°	1.34 p rad	241.2°
0.36 p rad	64.8°	1.35 p rad	243°
0.37 p rad	66.6°	1.36 p rad	244.8°
0.38 p rad	68.4°	1.37 p rad	246.6°
0.39 p rad	70.2°	1.38 p rad	248.4°
0.4 p rad	72°	1.39 p rad	250.2°
0.41 p rad	73.8°	1.4 p rad	252°
0.42 p rad	75.6°	1.41 p rad	253.8°
0.43 p rad	77.4°	1.42 p rad	255.6°
0.44 p rad	79.2°	1.43 p rad	257.4°
0.45 p rad	81°	1.44 p rad	259.2°
0.46 p rad	82.8°	1.45 p rad	261°
0.47 p rad	84.6°	1.46 p rad	262.8°
0.48 p rad	86.4°	1.47 p rad	264.6°
0.49 p rad	88.2°	1.48 p rad	266.4°
0.5 p rad	90°	1.49 p rad	268.2°
0.51 p rad	91.8°	1.5 p rad	270°
0.52 p rad	93.6°	1.51 p rad	271.8°
0.53 p rad	95.4°	1.52 p rad	273.6°
0.54 p rad	97.2°	1.53 p rad	275.4°
0.55 p rad	99°	1.54 p rad	277.2°
0.56 p rad	100.8°	1.55 p rad	279°
0.57 p rad	102.6°	1.56 p rad	280.8°
0.58 p rad	104.4°	1.57 p rad	282.6°
0.59 p rad	106.2°	1.58 p rad	284.4°
0.6 p rad	108°	1.59 p rad	286.2°
0.61 p rad	109.8°	1.6 p rad	288°
0.62 p rad	111.6°	1.61 p rad	289.8°
0.63 p rad	113.4°	1.62 p rad	291.6°
0.64 p rad	115.2°	1.63 p rad	293.4°
0.65 p rad	117°	1.64 p rad	295.2°
0.66 p rad	118.8°	1.65 p rad	297°
0.67 p rad	120.6°	1.66 p rad	298.8°
0.68 p rad	122.4°	1.67 p rad	300.6°
0.69 p rad	124.2°	1.68 p rad	302.4°
0.7 p rad	126°	1.69 p rad	304.2°
0.71 p rad	127.8°	1.7 p rad	306°
0.72 p rad	129.6°	1.71 p rad	307.8°
0.73 p rad	131.4°	1.72 p rad	309.6°
0.74 p rad	133.2°	1.73 p rad	311.4°
0.75 p rad	135°	1.74 p rad	313.2°
0.76 p rad	136.8°	1.75 p rad	315°
0.77 p rad	138.6°	1.76 p rad	316.8°
0.78 p rad	140.4°	1.77 p rad	318.6°
0.79 p rad	142.2°	1.78 p rad	320.4°
0.8 p rad	144°	1.79 p rad	322.2°
0.81 p rad	145.8°	1.8 p rad	324°
0.82 p rad	147.6°	1.81 p rad	325.8°
0.83 p rad	149.4°	1.82 p rad	327.6°
0.84 p rad	151.2°	1.83 p rad	329.4°
0.85 p rad	153°	1.84 p rad	331.2°
0.86 p rad	154.8°	1.85 p rad	333°
0.87 p rad	156.6°	1.86 p rad	334.8°
0.88 p rad	158.4°	1.87 p rad	336.6°
0.89 p rad	160.2°	1.88 p rad	338.4°
0.9 p rad	162°	1.89 p rad	340.2°
0.91 p rad	163.8°	1.9 p rad	342°
0.92 p rad	165.6°	1.91 p rad	343.8°
0.93 p rad	167.4°	1.92 p rad	345.6°
0.94 p rad	169.2°	1.93 p rad	347.4°
0.95 p rad	171°	1.94 p rad	349.2°
0.96 p rad	172.8°	1.95 p rad	351°
0.97 p rad	174.6°	1.96 p rad	352.8°
0.98 p rad	176.4°	1.97 p rad	354.6°
0.99 p rad	178.2°	1.98 p rad	356.4°
1 p rad	180°	1.99 p rad	358.2°
		2 p rad	360°

Radian to Degree Two Decimals Approximate

Radians	Degrees	Radians	Degrees
0.01 rad	0.572958°	1 rad	57.2958°
0.02 rad	1.145916°	1.01 rad	57.868758°
0.03 rad	1.718874°	1.02 rad	58.441716°
0.04 rad	2.291832°	1.03 rad	59.014674°
0.05 rad	2.86479°	1.04 rad	59.587632°
0.06 rad	3.437748°	1.05 rad	60.16059°
0.07 rad	4.010706°	1.06 rad	60.733548°
0.08 rad	4.583664°	1.07 rad	61.306506°
0.09 rad	5.156622°	1.08 rad	61.879464°
0.1 rad	5.72958°	1.09 rad	62.452422°
0.11 rad	6.302538°	1.1 rad	63.02538°
0.12 rad	6.875496°	1.11 rad	63.598338°
0.13 rad	7.448454°	1.12 rad	64.171296°
0.14 rad	8.021412°	1.13 rad	64.744254°
0.15 rad	8.59437°	1.14 rad	65.317212°
0.16 rad	9.167328°	1.15 rad	65.89017°
0.17 rad	9.740286°	1.16 rad	66.463128°
0.18 rad	10.313244°	1.17 rad	67.036086°
0.19 rad	10.886202°	1.18 rad	67.609044°
0.2 rad	11.45916°	1.19 rad	68.182002°
0.21 rad	12.032118°	1.2 rad	68.75496°
0.22 rad	12.605076°	1.21 rad	69.327918°
0.23 rad	13.178034°	1.22 rad	69.900876°
0.24 rad	13.750992°	1.23 rad	70.473834°
0.25 rad	14.32395°	1.24 rad	71.046792°
0.26 rad	14.896908°	1.25 rad	71.61975°
0.27 rad	15.469866°	1.26 rad	72.192708°
0.28 rad	16.042824°	1.27 rad	72.765666°
0.29 rad	16.615782°	1.28 rad	73.338624°
0.3 rad	17.18874°	1.29 rad	73.911582°
0.31 rad	17.761698°	1.3 rad	74.48454°
0.32 rad	18.334656°	1.31 rad	75.057498°
0.33 rad	18.907614°	1.32 rad	75.630456°
0.34 rad	19.480572°	1.33 rad	76.203414°
0.35 rad	20.05353°	1.34 rad	76.776372°
0.36 rad	20.626488°	1.35 rad	77.34933°
0.37 rad	21.199446°	1.36 rad	77.922288°
0.38 rad	21.772404°	1.37 rad	78.495246°
0.39 rad	22.345362°	1.38 rad	79.068204°
0.4 rad	22.91832°	1.39 rad	79.641162°
0.41 rad	23.491278°	1.4 rad	80.21412°
0.42 rad	24.064236°	1.41 rad	80.787078°
0.43 rad	24.637194°	1.42 rad	81.360036°
0.44 rad	25.210152°	1.43 rad	81.932994°
0.45 rad	25.78311°	1.44 rad	82.505952°
0.46 rad	26.356068°	1.45 rad	83.07891°
0.47 rad	26.929026°	1.46 rad	83.651868°
0.48 rad	27.501984°	1.47 rad	84.224826°
0.49 rad	28.074942°	1.48 rad	84.797784°
0.5 rad	28.6479°	1.49 rad	85.370742°
0.51 rad	29.220858°	1.5 rad	85.9437°
0.52 rad	29.793816°	1.51 rad	86.516658°
0.53 rad	30.366774°	1.52 rad	87.089616°
0.54 rad	30.939732°	1.53 rad	87.662574°
0.55 rad	31.51269°	1.54 rad	88.235532°
0.56 rad	32.085648°	1.55 rad	88.80849°
0.57 rad	32.658606°	1.56 rad	89.381448°
0.58 rad	33.231564°	1.57 rad	89.954406°
0.59 rad	33.804522°	1.58 rad	90.527364°
0.6 rad	34.37748°	1.59 rad	91.100322°
0.61 rad	34.950438°	1.6 rad	91.67328°
0.62 rad	35.523396°	1.61 rad	92.246238°
0.63 rad	36.096354°	1.62 rad	92.819196°
0.64 rad	36.669312°	1.63 rad	93.392154°
0.65 rad	37.24227°	1.64 rad	93.965112°
0.66 rad	37.815228°	1.65 rad	94.53807°
0.67 rad	38.388186°	1.66 rad	95.111028°
0.68 rad	38.961144°	1.67 rad	95.683986°
0.69 rad	39.534102°	1.68 rad	96.256944°
0.7 rad	40.10706°	1.69 rad	96.829902°
0.71 rad	40.680018°	1.7 rad	97.40286°
0.72 rad	41.252976°	1.71 rad	97.975818°
0.73 rad	41.825934°	1.72 rad	98.548776°
0.74 rad	42.398892°	1.73 rad	99.121734°
0.75 rad	42.97185°	1.74 rad	99.694692°
0.76 rad	43.544808°	1.75 rad	100.26765°
0.77 rad	44.117766°	1.76 rad	100.840608°
0.78 rad	44.690724°	1.77 rad	101.413566°
0.79 rad	45.263682°	1.78 rad	101.986524°
0.8 rad	45.83664°	1.79 rad	102.559482°
0.81 rad	46.409598°	1.8 rad	103.13244°
0.82 rad	46.982556°	1.81 rad	103.705398°
0.83 rad	47.555514°	1.82 rad	104.278356°
0.84 rad	48.128472°	1.83 rad	104.851314°
0.85 rad	48.70143°	1.84 rad	105.424272°
0.86 rad	49.274388°	1.85 rad	105.99723°
0.87 rad	49.847346°	1.86 rad	106.570188°
0.88 rad	50.420304°	1.87 rad	107.143146°
0.89 rad	50.993262°	1.88 rad	107.716104°
0.9 rad	51.56622°	1.89 rad	108.289062°
0.91 rad	52.139178°	1.9 rad	108.86202°
0.92 rad	52.712136°	1.91 rad	109.434978°
0.93 rad	53.285094°	1.92 rad	110.007936°
0.94 rad	53.858052°	1.93 rad	110.580894°
0.95 rad	54.43101°	1.94 rad	111.153852°
0.96 rad	55.003968°	1.95 rad	111.72681°
0.97 rad	55.576926°	1.96 rad	112.299768°
0.98 rad	56.149884°	1.97 rad	112.872726°
0.99 rad	56.722842°	1.98 rad	113.445684°
1 rad	57.2958°	1.99 rad	114.018642°
		2 rad	114.5916°

Practical Applications

Understanding the conversion from radians to degrees is essential in various fields, including:

Physics: When working with angular displacement in circular motion or oscillations, radians are often used for their mathematical simplicity.
Engineering: Engineers frequently encounter angles in trigonometric calculations, making radians to degrees conversion crucial for their work.
Computer Graphics: Graphics designers and programmers use radians to manipulate angles in computer graphics and animations.

FAQs

Q1. What is Radians to Degrees Conversion?

Radians to Degrees Conversion is the process of converting angles measured in radians to degrees. It helps in expressing angles in a more familiar unit for everyday use.

Q2. How Do I Convert Radians to Degrees Manually?

Manually convert by using the formula: \( \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \).

Q3. What Are the Limits of Conversions?

Radians to Degrees conversions are applicable to any real number. However, keep in mind that extreme values may result in large degree measurements.

Q4. Practical Applications of Conversion

Radians to Degrees Conversion is used in fields like physics, engineering, and computer science for various calculations involving angles, rotations, and trigonometric functions.

In conclusion, mastering the conversion from radians to degrees is a valuable skill in mathematics and its applications in various fields. The formula provided simplifies the process, allowing for easy and accurate conversions. Whether you’re a student, scientist, engineer, or enthusiast, this knowledge will serve as a foundation for understanding and solving complex problems involving angular measurements.

Radians:	rad


Degrees: