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I hope this is the right stack exchange site for this. I saw a few other questions on here about HDMI monitors.

I'm looking at two different HDMI monitors and one of the biggest spec differences is the $200 dollar one has a 50,000,000:1 contrast ratio while the $180 one has a ratio of 1000:1. The gap seems very significant, but both are highly rated. Will I notice a difference if I get the one with the smaller contrast ratio?

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The contrast ratio is Brightest Possible/Darkest Possible. The Brightest possible is limited by the display brightness (typically 200 - 300 nits). The contrast ratio is really dictated by the denominator. So the monitors that claim 50,000,000 are saying that they can get really dark. The number quoted is a "dynamic" contrast ratio. In this mode, the backlighting is reduced when the overall brightness of the pixels displayed on the monitor are very low. So basically you can come up with any number you want. In the extreme, if you turn off the backlighting then effectively the denominator is zero so the contrast ratio is infinity.

Practically, your contrast ratio is limited by viewing flare. This is the ambient light that reflects off the monitor. Look at your monitor screen with the power off. This is as black as it will ever be. No exactly zero light, is it? So you would never realize even 1000:1 unless your setup is in complete darkness. Even then the limiting factor becomes how much light from the monitor reflects off your face and other objects back to the monitor.

Some context, a typical outdoor scene has a contrast ratio of 1000:1 a very high contrast scene would be 4000:1. In this case it is the numerator that contributes most to the contrast ratio. A scene with 50,000,000:1 would never occur in nature. It is also beyond anything your visual system could accommodate.

Bottom Line: Contrast ratio could be a very useful number evaluating the quality of a monitor, but marketing has made this value useless for accessing the quality.

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