This is a "big" question, because as you may imagine, a dye for turning dark hair light is different from one turning light hair dark (or some bright color). Different color dyes have different chemical formulas of course. Another complication is that many dyes are only formed in the process of dyeing the hair and the formulas for the final dye are not known for sure. So I will just give you the most simple answer.

The most simple, and apparently also the first, hair dye is hydrogen peroxide. Hydrogen peroxide, chemical formula H₂O2 or H-O-O-H, can be used to "bleach" hair. That means, it will turn dark hair lighter. This happens because the hydrogen peroxide destroys the natural color of the hair by oxidizing it. So strictly speaking, turning dark hair light is not dyeing the hair, it is "un-dyeing" the hair. This process may oxidize not only the natural color in the hair but also the proteins that make up the structure of the hair, leaving it brittle or "damaged". More modern hair dyes for lightening hair will have additives designed to minimize this undesirable side effect, which is one reason why the list of ingredients on a hair dye package is long.

Let me also give you some starting points for further reading. You can find the chemical formula of the active ingredient in the popular natural hair dye henna at this site. And you can look at this other site for some formulas of ingredients in other hair dyes.

Hair dye is made of many different chemical things we call compounds. (By the way, water is a chemical compound.)

Many permanent hair dyes use three components: ammonia (NH₃), hydrogen peroxide (H₂O₂), and p-phenylenediamine or something very similar to it. p-phenylenediamine has the chemical formula C₆H₈N₂ and another extremely common ingredient that can be used in place of p-phenylenediamine is 2,5-diaminotoluene, with the formula C₇H₁₀N₂. Both compounds are made of a ring with 6 carbon atoms, with things sticking out of the ring. The chemistry of hair dye relies on the three components working together to lighten natural hair and for the dye to diffuse inside the fiber, so hair dyes does not have a single chemical formula because it is made of at least three things.

That’s such a great question! Some of the most common chemicals in hair dye include ammonia (which gives it that smell), peroxide, and some other really confusing-sounding compounds (like p-phenylenediamine and toluene-2,5-diamine).

The process is actually a bunch of different chemical reactions happening in sequence rather than one specific chemical formula applied at once. First, ammonia and hydrogen peroxide combine and cause the natural hair color to lighten and provide a “blank canvas” for the dye. It practically bleaches your hair. Ammonia also opens hair pores so that the dye can later enter and penetrate deep into the hair to create long lasting and fuller color.

Next, compounds called “intermediates” and “coupler compounds” undergo the oxidation process, to create chemicals that are heavier in a molecular sense, making it harder to wash them out of your hair. So the chemicals bleach, then they open the hair pores, and then create heavy color that gets locked inside.

The different colors of hair dye are created from using slightly different variations of the coupler compounds.

Great question Victoria! You've asked a question which led to the creation of a billion dollar industry! The chemical formula for hair dye is not just one formula. Most permanent hair dyes are a combination of several chemicals. The primary chemical is called paraphenylenediamine (PPD). The formula is C₆H₄(NH₂)₂ . Check out the structure of PPD here.

When PPD is mixed with other chemicals like hydrogen peroxide, it produces dye molecules. By itself this mixture makes a brown dye. To make other colors you would need to add more chemicals. Lets say you want pink hair! Simply mix in a special combination of chemicals which produce blue, red and green dye. By changing the amounts of each color in the mix, you can make any fashionable color you wish!

Assuming permanent hair dyes , there are different formulae for the coloring molecules (at least one for each color) as well as multiple chemicals within the dye.

The molecules which give the new color to hair are composed of a primary intermediate which then bonds to another molecule called a coupling agent. The primary intermediate is sort of a "starting block" and is either paraphenylenediamine , para-aminophenol, or 2,5-diaminotoluene. All of these are similar, being essentially benzene rings with some of the hydrogens replaced with other functional groups.

The coupling agents that bind to these are too numerous to list, but each leads to a different final color.

In addition to these, hair dyes contain hydrogen peroxide and ammonia (or sometimes ethanolamine). Hydrogen peroxide is responsible for oxidizing the primary intermediate to enable the binding to the coupling agent and also lightens the existing color so the new color will be more visible. The reaction between the primary and the coupling agent occurs in pH above 7 (neutral). Ammonia is included to raise the pH to allow this to happen. Ammonia also "opens" the structure of the hair to allow the dye to diffuse in. Instead of ammonia, ethanolamine can be used but the coloring with this is less permanent.

Most dyes have a one or more benzene rings (C₆H₆), attached to other groups, including alcohol (OH) or amine (NH₂) groups.

Here are lots of links to keep you busy with your question - good luck!

1. This is the first hit - it has lots of good stuff.
2. And - The PPD derivative 2,5-diaminotoluene or p-aminophenols are also sometimes used as alternative primary intermediates. Primary intermediates only produce dye molecules when exposed to an oxidizing agent. For this reason, hydrogen peroxide is included in almost all hair dyes.
3. Also here.
Some of the most common and dangerous ingredients used in hair dyes are;
• ammonia,
• peroxide,
• p-phenylenediamine,
• diaminobenzene,
• toluene-2,5-diamine,
• resorcinol etc.
4. Another one.
5. Finally, Wikipedia is usually good.