Difference Between Degrees and Radians (With Table)

The two most common units of measuring angles are degrees and radians. Both the units are interconvertible and have their own domain where they can be used. The most popular situation in which both of them can be seen together is trigonometry where the symbols (0) and pie are quite common.

Degrees vs Radians

The difference between degrees and radians is that degrees measure how much the head is tilted whereas radians measure the angle based on the distance travelled. Degrees are sometimes unreliable because they are based on the Sun’s rotation whereas Radians make use of the equations and therefore seem more reliable.

The measurement of plane angles whose full rotation is said to be 360o is known as degrees. It is considered to be the SI accepted unit due to its faults while measuring angles. One rotation is 2 pie and therefore one degrees is often said to be pie/1800

It is often defined as the ratio and is therefore considered dimensionless. It is represented by rad and mathematically is given by dividing the length of the arc by the length of the radius. In simple terms, it is the angle made by a radius on the circle with an arc of the same length. 

Comparison Table Between Degree and Radian

Parameters of ComparisonDegreeRadian
DefinitionIt is the measurement of the plane angles and the whole is 360oIt is the ratio between the radius and arc suspended
SI acceptanceAlthough not being the SI unit, it is still said to be acceptedIt was supplementary before 1995 but now is known to be a derived unit. 
Bigger unitThe degree is almost equal to pie/180 and is comparatively very small.The unit is bigger in comparison and is almost ⅙ of a circle which is almost 57 degrees. 
Physical representationIt is defined as the amount of the head tilt.It is generally measured by the use of actual distance travelled.
ReliabilityIt is quite unreliable because of its dependency on the rotation of the Sun.It is far more reliable since it uses equations to find out the angle.
Usage of the unitsIn daily life, we prefer to use degrees as a form of representing the angles as it is easy to understandIn most of the calculations that are done, it is used to get an answer that is more precise and apt. 

What is Degree?


A degree is the most common unit used to express the measurement of angles and is based on the rotation of the Sun. It is generally used in daily life for reporting the angles and also at places where the calculation can have some round-ups.

Originally it was used because it was comparable to the number of days in the year and many scientists also at that point reported that the Sun moves a degree each day on the elliptical orbit. Due to this many of the calendars like Persian calendars had only 360 days.

Another theory for choosing the number 360 was that it had 24 divisors and was divisible by all numbers in 1-10 except 7 and the number of divisors helped in dividing the world into 24 time zones which developed the 24 hour time system and also helped in situating the time zones almost 150 to the longitudes. 

The degree is a very small unit and can be used directly but it can also be used in the form of 45.999o or the DMS notation can be used in which it is said that 1 degree is equal to 60 arc minutes which further is 60 arcseconds. Both of them are represented by a single prime (‘) and double prime (“) respectively. 

What is Radian?

Radian is a ratio and is said to be the angle subtended on the circle by the radius with the same length. In simpler terms, it is defined as a ratio between the displacement length of the arc and the radius.

titha =s/r

The unit is the SI unit and was accepted after 1995 as a derived unit because before that it was treated as a supplementary unit. It is said to be a pure number because of the fact that it is a ratio and it can never be imaginary.

Mathematically a radian is equal to one and therefore most of the time the representation that is radian is omitted and at all places where an angle is mentioned without any units it is assumed to be radians and if it is in degrees the symbol is mentioned.

It is the preferred way of measuring the angles because of its naturalness and the way it can cover a circle in only six parts if it is folded along an arc and this is true for every circle of different radii. 

Main Differences Between Degree and Radian

  1. A degree is an angle measurement unit whose whole is said to be 360 and measures plane angle whereas radian is the ratio between the length of the arc and the radius.
  2. A Degree is not the SI unit but is accepted by the norms whereas radians is the SI unit and has been redefined from supplementary unit to derived unit over the years.
  3. A Degree is comparatively small as it is almost 1/360th part of the circle and in comparison to that radian is 1/6th part of a circle and approximately equal to 57o.
  4. Physically, it is the amount of head tilt whereas radian is expressed by the distance travelled on the circle. 
  5. Degrees are less reliable in some terms because they measure on the basis of the rotation of the Sun. In comparison to this radian uses mathematical formulae and equations for the determination of the angles. 
  6. Degrees are generally used in daily life as well non-complex calculations as it is easy to represent and determine whereas radians are used in complex equations due to its precision.

Conclusion

Both of the units have their own importance and can be used at different places. The degree is a measurement of plane angles whereas radians can also be used in reporting the angles of 3-D figures like cones. The symbol “o” is a must while writing an angle in this form whereas the term radian or rad may or may not be mentioned as its mathematical value is 1.

References

  1. https://aip.scitation.org/doi/abs/10.1063/1.5054435
  2. https://eric.ed.gov/?id=EJ1158633
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