# Whats the difference between radians and degrees?

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829
Hello,
as in degree we can see by device measure a circle in 360*, but in case of radian?

#### bertus

Joined Apr 5, 2008
20,573

#### bertus

Joined Apr 5, 2008
20,573
Hello,

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Bertus

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829
Why we take phase angle in TanQ in // LR circuits?
TanQ=Xr/Xl

#### pgs

Joined Dec 20, 2015
6
You can 'see' radians in a circle but it is not as easy as say degrees, gradians, Biebers or Clintons (last two made up for example purposes below)

One way to think about it is to look at a circle and break it up into a certain amount of sectors or 'cheeses'. Then call the internal angle a name, thus:

- A circle broken into 360 equal sized sectors has an internal angle 1/360 of a circle. Let us call that angle a 'degree'
- A circle broken into 400 equal sized sectors has an internal angle 1/400 of a circle. Let us call that angle a 'gradian'
- A circle broken into 37 equal sized sectors has an internal angle of 1/37 of a circle. Let us call that angle a 'Bieber'
- A circle broken into 11.6 equal sized sectors has an internal angle of 1/11.6 of a circle.
Let us call that angle a 'Clinton'. If you look at this circle there will be 11 equal sized cheeses and a smaller section left over equal to 0.6 of a cheese.
- A circle broken into 6.28 equal sized sectors has an internal angle of 1/6.28 of a circle.
Let us call that angle a 'NrRadian'). If you look at this circle there will be 6 equal sized cheeses and a smaller section left over equal to 0.28 of a cheese.
- A cirlce broken into 2 x pi (6.283185307...) equal sized sectors has an internal angle of 1/(2 x pi).
Let us call that angle a radian. If you look at this cirlce there will be 6 equal sized cheeses and a smaller section left over equal to [(2 x pi) - 6] or (0.283185307...) of a cheese.

In terms of circles:

There are 360 degrees that make up a whole circle
There are 400 gradians that make up a whole circle
There are 37 'Biebers' that make up a whole circle
There are 11.6 'Clintons' that make up a whole circle
There are 6.28 'NrRadians' that make up a whole circle
There are (2 x pi) radians that make up a whole circle. This is usually just called "2 pi radians".

Approximate degree quivalents:

1 degree = 1 degree
1 Bieber = 9.729729... degrees
1 Clinton = approx. 31.03 degrees
1 NrRadian = approx. 57.32 degrees
1 radian = approx. 57.29577951... degrees (put 360/(2 x pi) into your calculator)

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#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829
1 radian = approx. 57.29577951... degrees (put 360/(2 x pi) into your calculator)
I will remeber this
thanks

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829
Why we take phase angle in TanQ in // LR circuits?
TanQ=Xr/Xl

#### pgs

Joined Dec 20, 2015
6
A slight omission above. Error underlined and emboldened below:

- A cirlce broken into 2 x pi (6.283185307...) equal sized sectors has an internal angle of 1/(2 x pi) of a circle.
Let us call that angle a radian. If you look at this cirlce there will be 6 equal sized cheeses and a smaller section left over equal to [(2 x pi) - 6] or (0.283185307...) of a cheese.

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829
how do you learn it?
but is there any reason of converting radian?

#### pgs

Joined Dec 20, 2015
6
The use of the radian is because of the properties of a circle. Don't forget that our lovely decimal system cannot define the world perfectly and we can get stuck if we use only that system. It isn't very good with irrational numbers for example...

Pi is one of those irrational numbers...

For any perfect circle, Pi = Circumference/Diameter = C/D = C/(2 x r) = 3.141592.... The number does not repeat and goes on forever.

Your question is the wrong way round perhaps. Why would you want to covert a ratio of circumference to diameter into clumsy decimal numbers? The answers are all irrational and cannot be wirtten down!

Surely best to keep the pi symbol going and just know it represents that ratio. Yes, think of it as about 3.14 in decimals if you want, but don't forget it isn't exactly that.

So,

The circumference is about 3.14 times bigger than the diameter of a (perfect) circle
The circumference is pi times bigger than the diameter of a (perfect) circle

If it is best to keep that last ratio for accuracy when calculating circumferences and areas, then the logical extension is to use it for angles within circles too...

Think of a sector of a circle (the cheeses talked about earlier). The angle created has somethng to do with ratio between the length of the arc (which is part of the circumference of a circle) and the length of the straight sides (the radius of the circle).

If we take a ratio of arc length to radius we will have an answer that gives a clue as to the angle: The bigger the 'arc:radius' ratio, then the bigger the angle. The 'unit' of that angle is defined in 'radians'.

When the length of the arc of the sector is the same as the radius (straight lines of the sector) of the circle, the angle is called 1 radian. Our decimal number system falls apart now because the angle is an irrational when we use it.

That angle is about 57.29577951... degrees.

Arcs are part of the circumference and so are a fraction of (pi x d) or (pi x 2r). If the radius has a unit of 1, then the circumference of the circle is 2 x pi (C = pi x 2r). So, any arc length is a proportion of this. A full 'rainbow like' arc is half a circle and so has a length of 1 x pi. The angle (that you may know as 180 degrees) is called 1 pi radian because it is 1 pi in length. The angle of a whole circle is therefore 2 pi radians.

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#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829
How to remeber this thanks for help
Actualy i am learning LCR / RL /Rc etc circuit in that it come...phase angle

thanks

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829

#### KeepItSimpleStupid

Joined Mar 4, 2014
4,104
Many things will talk about the radian frequency ω. ω=2π*f (2 * PI * frequency in Hz)

#### KeepItSimpleStupid

Joined Mar 4, 2014
4,104
Yep. The Radian is also a unitless number.

#### RRITESH KAKKAR

Joined Jun 29, 2010
2,829

#### KeepItSimpleStupid

Joined Mar 4, 2014
4,104
Why? Because there are 2*PI radians in a circle and that really doesn't have units. It's just a number.

It's not like an AMP being Coulombs/s.