I think the color of cyan or green will exactly depend on the exact color of red.

Because as per the literature and complementary color charts if the color is exactly red then you can get complementary color as green but if its the kind of red orange then you get the cyan.

I thick it also depends of different things including human perception as described in the below article.

http://blog.asmartbear.com/color-wheels.html

 Dear Md. Abdul Hannan ,

you can refer the details on net with following reference to solve Your question

"CIE 1931 color space"

We need to things in the right perspective when we talk about such a transdisciplinar and complex issue as color. One thing is to talk about colour regarding to light (additive system)  and other thing is to talk about color regarding to pigments and painted surfaces (subtractive system). One thing is to talk about color perception regarding to physiological , neurologic and brain activity, other thing is to talk about cognition in psychological terms.

The primary colors in the additive system (light) are Red, Green an Blue. So the complementary color to Red would be a secondary color resulting from the mixture between Green an Blue (Cyan).

The primary colors in the subtractive system (pigments) are Cyan, Yellow and Magenta (or Blue, Yellow and Red if we follow Itten). So the complementary color to Red should be the secondary color Green.

The fundamental colors to a system based on perception (NCS_Natural Color System) are Yellow, Red, Blue, Green, White and Black, because we refer to these colours to describe what you see. You don't say "this" color is a mixture between yellow and Blue, you just say its Green.

I hope it helps !

Green is complimentary to red. However it strongly depends upon red that how red it is. Cyan can be complimentary to it but it depends upon the wavelength of red.

Hope it will help you.

There is more than one answer to this question!!

If you take the colorimetric interpretation and the literal meaning of complement, being the colour that "completes" red, ie mixes to white, then you draw a line though the red chromaticity and the white pointchormaticity and see where it intersects the spectral locus in the green.  So it depends on exactly which red you are talking about and which white you are talking about.  The higher the temperature the white, the bluer will be the complementary colour.  In that a signal red and CIE Standard Illuminant D65 will give a complementary that is blue-green, you are right.

The second concept belongs with the art world and very have a very different idea of complementary colours.  I do not pretend to understand this concept!!

Complementary color: if the mix of a pair of color stimuli give achromatic color, then the two colors are complementary to each other. 

Opponent colors are based on Hering's opponent color theory which postulates three pairs of opponent color channels. Two opposing pairs of unique hues are defined for the chromatic opponent channels: Yellow-Blue, Red-Green. Unique hue is a pure without any mix of the other colors, such as unique Red: neither greenish or bluish. Mixture of a pair of chromatic opponent color is not claimed to produce achromatic. For example, mixture equal amount of unique yellow and unique blue will results in white or gray, while mixture of equal amount of unique red and unique green will be unique yellow. 

So back to your questions, 

If you want to determine whether two colors are complementary colors: you can measure the reflectance and plot them in the chromaticity diagram under one CIE standard illuminant and standard observer. Also you can plot them in the opponent based color space, like CIELAB though it is not the perfect, to check whether they are opponent or not.

You said the red i assume it is unique red, then the complementary color is cyan, and opponent color is green.

You can refer CIE Colorimetry standard and also classic books about the color vision.

As mentioned earlier the complement color depends on the definition of red color. Unfotunately our eyes are able to distinguish significantly more different "variants" of green than those of red. That is why a tiny variation of hue in red gives dramatic change of the complement "green". In theory "pure green" should be opposite to slightly bluish red (close to magenta).

It depends on your color system. Is it additive or subtractive?

For subtractive mixing, the complementary of Red is Green.

From mathematical point of view, cyan is the complement of red color. It is obtained using two unary  operators: complement and negation.

Cyan is complentary to red while green is believed to be opponent to red.

Yes, red and cyan is complementary colors. In fact I wrote a paper that tried to prove this. "The Yin and Yang of Colors" which can be found here on my RG-page

In the additive color system RED is R:255 G:0 B:0 and the complementary to this is R:0 G:255 B:255 (=cyan)

You are right. The "red-green" in the opponent theory, is actually red and cyan.

Please have a look at my symmetrical color model proposed 30 years ago: http://survivor99.com/colorforum/

Now CIELAB also uses this kind of model: http://130.149.60.45/~farbmetrik/A/FI06E.PDF

Interesting. I will take a closer look into this

A complementary color is not defined if you don't define the illuminant of reference first. If you take a narrow red light with a peak wavelength at 650nm, its complementary will be on the green side for a reference illuminant at 3000K, and on the bluish side with a reference illuminant at 7000K. On common computer screens the white point is usually near 7000K or even more, thus the complementary of the red primary is cyan, but this is just a particular case.

Stephen John Dain and Adrien Gary Lucca gave good and near-complete answers for the additive complimentary system. The complementary light spectrum (i.e. physical rather than physiological) definitely depends both on the red and on the white reference.

However, assuming the viewer's vision is accommodated to the white reference, what matters is usually the spectral content of the red relative to the reference.

So long as the reference has enough blue content that blue in a picture will appear blue, the complement of a pure red will appear cyan. A purplish red (that includes some blue) will have a greener complement; similarly, an orangy red will have a bluer complement.

The complement of red is cyan.

The complement of magenta is green.

http://survivor99.com/colorforum/