What color is magenta: the one screen color with no wavelength, measured

Magenta is #FF00FF. Red at full, blue at full, green at nothing. It is the sixth corner of the sRGB cube, the M in CMYK, and the color CSS also answers to when you type fuchsia, which is the same three bytes and measures 0.00 CIEDE2000 units away from magenta because it is literally the same number.

That is the easy half of the answer. The interesting half is that magenta is the only one of those six sRGB corners that no wavelength of light can make. Point a spectrometer at a rainbow and you will find red, orange, yellow, green, blue and violet. You will not find magenta, anywhere, at any width, at any brightness. It is not there.

Every claim in this piece is computed from the CIE 1931 2-degree color matching functions at 1 nm resolution, rendered to sRGB under a D65 white point, and compared with CIEDE2000. Where a number appears below, it came out of that pipeline rather than out of a textbook.

How close does a wavelength get

The test is simple. Take every wavelength from 380 to 700 nm, render each one to sRGB at the same luminance as magenta so the comparison is about hue and saturation rather than brightness, and measure the color difference. Then do the same for the other five corners of the cube, so there is something to compare against.

Blue lands at 3.44 units from 467 nm, which is close enough that most people would call it a match. Red manages 5.36 at 622 nm. The best magenta can do is 23.64 units, and the wavelength that gets there is 463 nm, which is a blue. Not a red, not a purple. A blue, failing by a margin of roughly ten just noticeable differences.

Cyan at 21.48 is nearly as bad, but for a different reason. Cyan has a wavelength, 490 nm or so, and that wavelength simply sits a long way outside what an sRGB screen can display, which is a gamut problem rather than a physics problem. Magenta has no wavelength to be outside the gamut in the first place.

The line of purples

The reason has a shape. Plot every wavelength on a CIE chromaticity diagram and you get a horseshoe. The curved part is the spectrum, from violet at one tip round through green to red at the other. The two tips do not meet. The straight line drawn between them, closing the shape, is called the line of purples, and nothing on it corresponds to a wavelength. It is a bookkeeping edge, not a measured one.

Magenta sits on that line. So does every color whose ray from the white point exits through it. Counting them is a matter of sampling the cube and testing each one:

• 22.81 percent of the sRGB gamut is extra-spectral, from a sample of 636,055 colors. Nearly a quarter of what a monitor can show has no wavelength.
• Packing the cube with non-overlapping 2.3-unit balls, the way the JND measurement does, the extra-spectral region holds 27.7 percent of all distinguishable colors. It is slightly over-represented, not under.
• On the saturated HSL hue wheel it runs from 274 to 339 degrees, a 66-degree arc, or 18.3 percent of the circle.
• In perceptual Lab hue the wedge spans 77.3 degrees, from 301.8 through zero to 19.1.

That last figure is worth sitting with. Somewhere between a fifth and a quarter of the colors a person can name, sort or match are colors that light cannot deliver on its own. They only exist as mixtures. If you have ever played the hue sorting mode and felt that the pinks and purples behave differently from the rest of the wheel, this is why. That stretch of the circle is not a continuation of the spectrum. It is the join.

Magenta is what green is not

Every extra-spectral color can be described by what is missing rather than by what is present. Draw a line from magenta through the white point and out the other side and it lands on the spectral curve at 549 nm, with an opposition error of 0.155 degrees. That wavelength renders as #00AD00, a middling leaf green.

So magenta is the color of white light with its green taken out, and the measurement backs the phrasing up. Cut a notch out of a D65 spectrum at 549 nm and watch what comes back:

The hue barely moves. Across notches from 20 to 120 nm wide it drifts from 325.1 to 323.0 degrees, a range of two degrees, while the chroma climbs from 25 to 145. Widening the notch does not change which color you get, only how much of it. Magenta is not a point on a scale between red and blue. It is a single direction, and the width of the missing band is the volume knob.

The ceiling is higher than the screen, incidentally. Optimising the notch width freely, the most saturated magenta a pure subtraction from D65 can produce has a chroma of 165.9 at a 168 nm notch. Screen magenta is 115.6. A real surface can be a great deal more magenta than #FF00FF, which the monitor simply cannot show you.

So does magenta exist or not

Magenta gets called an invented color, a trick, a thing your brain makes up. That framing is half right and it is the wrong half that tends to get repeated. No wavelength is magenta, true. But plenty of real physical surfaces are, and there is nothing imaginary about them.

Here is the proof as a measurement rather than an argument. Take a flat white reflector and carve one Gaussian absorption band into it. Search the centre, width and depth for the combination that best matches #FF00FF under D65. The answer is a notch centred at 540 nm, 110 nm wide at half maximum, 99 percent deep.

Every value on that curve sits between 0 and 100 percent, so a real pigment could have it, and the result renders as #EB45ED, which is 3.42 CIEDE2000 units from screen magenta. Just above the threshold where two colors start to look different, and far closer than the 23.64 that the best single wavelength managed.

This is not a contrived shape either. It is roughly what a bougainvillea bract, a magenta dye or the magenta ink in a printer actually does: reflect the two ends of the spectrum, swallow the middle. So magenta is not a hallucination. It is an ordinary reflectance curve with two humps, and the only unusual thing about it is that a prism cannot make one, because a prism produces one wavelength at a time and magenta needs two places at once.

The rainbow that starts in magenta

Now the part that made this worth writing. Render the visible spectrum to sRGB, wavelength by wavelength, and look at the short end.

The first seventeen bands are identical. Not similar, identical. Here is the same region at 2 nm resolution so there is no hiding in the sampling:

At this luminance every wavelength from 380 to 446 nm renders as exactly #FF00FF. That is 67 nm, a little over a fifth of the 380 to 700 nm span, collapsed onto one pixel value. The whole spectrum yields only 148 distinct hex codes at 1 nm sampling, and the violet sixth of it contributes one.

The cause is arithmetic rather than optics. Convert 400 nm to linear sRGB and the three channels come out at 0.165, negative 0.142, and 1.000. The green channel is negative, which is the formal way of saying the color lies outside the triangle a monitor can reach. No display can emit negative green, so the value gets clipped to zero, and red plus blue with no green is #FF00FF by definition.

Which leaves a genuinely funny result. Magenta is the one color the spectrum cannot produce, and it is also the color your screen paints over the part of the spectrum it cannot produce. Every rendered rainbow, every spectrum diagram in every textbook that was laid out in sRGB, begins with a band of the one color that is not in a rainbow. If you have ever wondered why the violet end of a picture of a rainbow looks pinkish while the violet end of a real one looks like a deepening blue, that is the answer. The pink is a clipping artefact.

It also explains a recurring confusion about indigo and violet. CSS names a color violet, #EE82EE, and it is not spectral violet at all. It is extra-spectral, with the nearest wavelength 29.36 units away at 466 nm. The word points at one thing in a physics lab and a different thing in a stylesheet, and the two are not close.

Print magenta is a different color entirely

One more gap worth measuring, because it catches people who move work between screen and paper. Magenta is a subtractive primary, which means it has a definition in ink as well as in light, and the two do not agree.

The standard press magenta and the screen magenta are 20.98 CIEDE2000 units apart. Their hue angles differ by 29.5 degrees, and 357.7 degrees is effectively red. The ink is darker by twelve L* points and carries about two thirds of the chroma. When a magenta looks disappointing coming off a press, that is not a calibration failure, it is the gap between two things sharing a name. The wider version of this problem is laid out in RGB versus CMYK.

The named colors that have no wavelength

Running the extra-spectral test across the 141 CSS named colors, 21 of them, or 14.9 percent, turn out to have no wavelength:

blueviolet, darkmagenta, darkorchid, darkviolet, deeppink, fuchsia, hotpink, indigo, lavenderblush, lightpink, magenta, mediumorchid, mediumvioletred, orchid, palevioletred, pink, plum, purple, rebeccapurple, thistle, violet

Pink is on that list. So is purple, and so is violet. Three of the most ordinary color words in English, and none of them names something a prism can produce. The list also confirms something the color psychology measurements kept running into, which is that our color vocabulary was built around what surfaces look like, not around what light does. Nobody naming pink was consulting a spectrum.

What to take away

• Magenta is #FF00FF, and fuchsia is the same three bytes. The two words are interchangeable in CSS at 0.00 units apart.
• No wavelength is magenta. The closest is 463 nm at 23.64 CIEDE2000 units, roughly ten JNDs of failure, and magenta is the only one of the six sRGB corners in that position.
• 22.81 percent of the sRGB gamut and 27.7 percent of distinguishable colors are extra-spectral. This is a large region, not a curiosity at the edge.
• Magenta is white minus green, specifically minus 549 nm. Widening the missing band changes saturation by a factor of six and hue by two degrees.
• A physically valid surface, flat white with a 110 nm notch at 540 nm, renders 3.42 units from magenta. It is a real color of real objects, just not of light on its own.
• Every wavelength from 380 to 446 nm clips to exactly #FF00FF on a screen, so a rendered spectrum opens on the one color a spectrum cannot contain.
• Press magenta is 20.98 units and 29.5 hue degrees from screen magenta, near enough to red.

If you want to feel the extra-spectral wedge rather than read about it, the hex guessing mode is the direct test, because guessing #FF00FF from memory means reasoning about an absence rather than a wavelength. The name that color mode gets at the vocabulary side of it, where pink, purple, magenta and violet all compete for the same 77 degrees. For the neighbourhood in detail there are shades of pink and shades of purple, and for how this wedge distorts the standard twelve-spoke wheel, there is what happens when you measure the color wheel. The complementary relationship that puts magenta opposite green is worked through in complementary colors.