Contrast Efficiency — How Much of Your Palette Is Actually Usable

You know K — the minimum step distance for WCAG AA contrast across the palette. Now the next question: is that K good or bad?

A palette with K=6 out of 12 steps uses up half its range just to clear the accessibility bar. A palette with K=4 out of 12 steps is more compact — more room for secondary roles like borders and hover states.

But how do you know if K=6 in a 12-step palette is expected, or a sign that the palette is poorly built?

You compare against the theoretical ideal.

The Ideal Density

For a perfectly constructed achromatic ramp (pure grays from white to black), there is a theoretical minimum contrast span density. This lower bound is approximately:

λ ≈ 0.501

Meaning: no matter how well you build a palette, the minimum distance for WCAG 4.5:1 will consume at least 50.1% of the range. This is a physical limit — it comes from the math of relative luminance.

The density of your palette is:

D = K / (N − 1)

For K=6 in a 12-step palette: D = 6/11 ≈ 0.545

For K=4 in a 12-step palette: D = 4/11 ≈ 0.364 — below λ, which means something is off (likely the palette skips usable contrast range by concentrating shades in safe zones).

The Efficiency Score

Contrast efficiency η measures how close your palette's density is to the theoretical ideal:

η = 1 − (D − λ) / (1 − λ)    when λ < D < 1
η = 1                          when D ≤ λ  (better than ideal)
η = 0                          when D ≥ 1  (no accessible pair exists)

For D = 0.545 and λ = 0.501:

η = 1 − (0.545 − 0.501) / (1 − 0.501) = 1 − 0.044/0.499 ≈ 0.91

Score: 91 — close to ideal, a small penalty for the density gap above λ.

What a Low Score Looks Like

A palette might score low on contrast efficiency if:

• Shades are concentrated near the middle — many similar mid-tones, weak contrast at both ends
• The ramp skips lightness quickly in the highlights but slowly in the shadows, creating uneven density
• Too many "dark mode only" dark shades with no accessible light counterpart at a reasonable K

In practice: a palette where you need to jump 8 steps out of 12 to get readable text has D = 8/11 ≈ 0.73, giving η ≈ 0.55. More than 40% of efficiency is lost.

Efficiency and Palette Density

High contrast efficiency means the palette is dense — many shades are packed into the contrast space efficiently. The accessible range covers a large portion of the ramp.

Low contrast efficiency means the palette is sparse — most contrast is concentrated at the extremes (near-white and near-black), with a dead zone in the middle where nothing achieves 4.5:1 against anything else.

Dense palettes support richer component design. The text role, border role, hover state, and selected state all derive from K — and a smaller K relative to N means those derived roles have more room to breathe.

→ Lightness Linearity