Which ΔE, and How Much

A tolerance quoted as “ΔE 3” is not a tolerance. There are half a dozen formulas in common use and they disagree by a factor of two on the same pair of colours. This is which one to use, and what the numbers feel like.

Six answers, one pair of colours

9R5.61 Pyrrole Orange, computed under D50 and again under F2 — one sample, one instrument, two lamps. Every formula below is measuring exactly the same difference:

Formula	Says	Where it came from
ΔE₀₀ (CIEDE2000)	8.82	the current standard, and what this library uses
ΔE₉₄ graphic arts	7.32	its predecessor, still in older specifications
ΔE₉₄ textiles	6.75	the same, with lightness weighted down
ΔE₇₆ (CIE76)	17.27	plain distance in Lab — simple, and wrong in a specific way
ΔE CMC 1:1	11.80	from the textile industry
ΔE CMC 2:1	11.57	the same, tuned for acceptability rather than perceptibility

8.82 and 17.27 describe the same two colours. A tolerance agreed without naming the formula is an argument scheduled for later.

Use ΔE₀₀

Unless a customer’s specification names another one, which happens and has to be honoured. ΔE₀₀ exists because the older formulas were demonstrably uneven: ΔE₇₆ is honest Euclidean distance in a space that is not perceptually even, so it overstates differences in saturated blues and understates them in near-neutrals. Every correction in CIEDE2000 — the lightness, chroma and hue weights, the blue-region rotation — exists to flatten one of those.

Two things about it that catch people out

It does not add up. Two steps of 2 are not a step of 4. The weights depend on where in the space you are, so distances along a path do not sum — the neutral ramp in this library steps at 1.90 to 2.00 between neighbours, and the ends are nothing like 35 × 2 apart.

It is not a threshold. There is no value below which everybody agrees and above which everybody objects. What there is: a rough scale, which is more useful.

What the numbers feel like

Anchored in this library, so each one is checkable rather than folklore:

ΔE₀₀	What it is
0.03	re-reading the same patch without moving the instrument. Below this nothing is real — it is the noise floor.
0.25	the median round trip of this library through a CMYK profile and back.
1.5	the closest any two samples in the library are allowed to be.
1.9 – 2.0	one step of the neutral grey ramp. This is what “just visibly different” looks like, side by side.
2.5	the average distance between neighbouring swatches — and the threshold the Ranges filter uses for “this process can reproduce it”.
4.0	the widest gap in the library. Nothing is further than this from its nearest neighbour.
8 – 18	what changing the lamp does to the colours that move most. Not a tolerance question — a different colour.

The library is built to a band of 1.5 to 4.0, and for most work that is all the accuracy anyone needs.

Say what you measured, as well as how much

Every ΔE quietly carries a whole measurement condition with it. Two figures are not comparable unless all of this matches:

Also part of the number	This library’s default
Formula	ΔE₀₀, k_L:k_C:k_H = 1:1:1
Illuminant	D50
Observer	2°
Measurement condition	M2 — see Optical Brighteners
Backing	white

A tolerance worth writing down reads like this: ΔE₀₀ ≤ 2.0, D50/2°, M2, white backing. Five facts, one line, and nothing left to interpret at four in the morning on a press floor.