How much contrast does text need to be readable by people with low vision?

Under the Web Content Accessibility Guidelines, normal text needs a contrast ratio of at least 4.5:1 against its background, and large text needs at least 3:1. Large means 18 point text, or 14 point bold. The guidelines, known as WCAG, are a set of recommendations for improving web accessibility, primarily for people with disabilities. The contrast rule exists so that people with moderately low vision can read text.

Where does 4.5 come from? A contrast ratio of 3:1 is the minimum recommended by international and American standards for standard text and vision. People with moderately low vision need more. Visual acuity of 20/40 is associated with a contrast sensitivity loss of roughly 1.5, so such a user needs 3 times 1.5, which is 4.5 to 1. And 20/40 is commonly reported as typical visual acuity of elders at roughly age 80.

The ratio itself is simple. It compares the relative luminance, the brightness on a scale from 0 for darkest black to 1 for lightest white, of the lighter and darker colours, using (L1 + 0.05) / (L2 + 0.05). Ratios range from 1:1 to 21:1. Pure white on pure black scores the maximum: (1 + 0.05) divided by (0 + 0.05) is 21.

Larger text with wider strokes is easier to read at lower contrast, so it is allowed a lower ratio. And the rule applies to brands too: beyond logos, text with insufficient contrast because of brand guidelines is not exempt. So a pale grey chosen for style still has to reach the ratio.