If you are looking for the Best Permanent Bright Hair Color, there is an important distinction to make first.
Many of the hair dyes famous for extremely vivid pink, blue, purple, green and other unconventional shades are actually semi-permanent, not permanent. Brands such as Arctic Fox and Good Dye Young, for example, specifically describe their vivid ranges as semi-permanent and recommend lightened hair for the strongest results.

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For a genuinely permanent bright hair color, you have fewer choices, particularly if you want a shade that looks noticeably vivid rather than simply being a brighter version of brown or blonde.
What makes the Best Permanent Bright Hair Color different?
Permanent hair color uses an oxidative coloring process, generally involving colorant and developer. Because the color is formed within the hair rather than simply sitting on its surface, it can last considerably longer than direct dyes.
That does not mean permanent color never fades. Bright shades, especially reds, purples and fashion-inspired tones, can lose some intensity with repeated washing, heat styling and exposure to the elements. The underlying color remains, but the original vibrancy can diminish.
Another important point is that permanent dye cannot necessarily turn very dark hair into an intensely bright fashion color in one step. If you want something like vivid pink, electric purple, turquoise or neon green, achieving the brightness shown on the box may require lightening the hair first.
Best Permanent Bright Hair Color #1: L’Oréal Préférence Vivids
One particularly interesting option is L’Oréal Paris Préférence Vivids. The current Préférence collection includes a range of permanent hair colors as well as a dedicated Vivids collection with 14 striking shades.
This makes it worth considering if your priority is a bold color with permanent-dye technology, rather than a temporary or semi-permanent fashion color.
The range is particularly relevant if you want a dramatic change but still want to use a conventional permanent hair-color system.
The Best Permanent Hair Dye #2: L’Oréal Féria
L’Oréal Paris Féria is another option for people who want permanent color with a brighter, more multidimensional appearance.
The range includes shades such as Ruby Rush, Red Velvet and Midnight Violet alongside more conventional colors. Féria is designed around multi-tonal results rather than a flat-looking single color, which can make bright shades appear particularly noticeable.
If your idea of bright hair is rich red, vibrant violet, intense burgundy or another dimensional shade, Féria can make more sense than a direct fashion dye.
Examples of Permanent Hair Color #3: Clairol Bold & Bright
Clairol Bold & Bright is another permanent option specifically aimed at vivid color. Its current collection includes shades such as Intense Passion Plum and Intense Cherry. The range is designed around strong color and includes technology intended to help maintain vibrancy. (Clairol)
This is particularly interesting if you want something bright without necessarily going into the extremely unconventional neon territory associated with direct fashion colors.
Dyes Site:ChickAboutTown.com/Best Cover Permanent Hair Dye Brands #4: Garnier Olia Vivid Garnet
For someone who wants bright red, Garnier Olia has a permanent Vivid Garnet shade.
Olia is ammonia-free and uses an oil-powered color formula. The Vivid Garnet shade is designed to give an intense red result and can provide grey coverage as well. Garnier notes that the resulting color depends on the starting hair color, which is important when choosing any permanent dye.

Photo credits: Wella Professionals, Reddit