Short answer
A tolerance is a volume in colour space around the standard, and the real decision is its shape. A box of plus-or-minus limits on L*, a* and b*, or a single ΔE*ab sphere, is easy to state but fits vision badly: in a saturated colour the eye accepts more than twice as much chroma difference as hue difference, and near grey it accepts little of either. CMC, CIE94 and CIEDE2000 define ellipsoids that change size and orientation with the colour, which is what lets one number serve a whole range, provided the formula, its parameters and the measuring condition are written beside it.
Writing 'ΔE ≤ 1' draws a surface around the standard, and every batch inside it is accepted. With plain ΔE*ab that surface is a sphere: a unit of lightness, a unit of chroma and a unit of hue are treated as equally serious everywhere. With separate limits on ΔL*, Δa* and Δb* it is a box whose faces are lined up with the red–green and yellow–blue axes. Neither matches how differences are seen. Visual acceptability around a colour is roughly an ellipsoid: long in the lightness and chroma directions, short in the hue direction, and larger for saturated colours than for near-neutrals. The modern formulas are attempts to draw that ellipsoid, so choosing a formula is choosing a shape.
The corner of a box of ±1 in each coordinate is 1.73 ΔE*ab from the centre, and what that corner means depends entirely on where the box sits. The first table works it out for five illustrative standards. Around a mid grey the corner scores 2.0 by CIEDE2000 and 2.3 by CMC(2:1): a sample that passes every component limit is twice as far out as a limit of one would allow. Around a saturated orange the same corner scores 0.9 and 0.65. One box is therefore loose for neutrals and needlessly tight for saturated colours, and because its faces follow a* and b*, it cannot separate a harmless chroma shift from an objectionable hue shift when the colour does not happen to lie on an axis.
The second table shows how far a sample can move along lightness, chroma and hue before each formula reaches 1.0. CMC at its usual 2:1 setting allows roughly two CIELAB units of lightness in the mid-tones, more for pale colours and less for dark ones, because that setting doubles its lightness axis. The choice reflects its textile origin: buyers tolerate a slightly lighter or darker piece more readily than an off-shade one. CIEDE2000 allows between about 1.0 and 1.6 units of lightness across the same five standards. Both stretch the chroma allowance dramatically as chroma rises, to about 3 units by CMC and about 4.5 by CIEDE2000 for the orange, while holding hue much tighter. Equal numbers in two formulas therefore describe different volumes, and a limit cannot be carried from one to the other by multiplying.
The size of the ellipsoid is a commercial decision, and the dependable way to make it is empirical. Collect samples the customer has accepted and rejected, measure them, and find the limit that separates the two groups; one instrument maker suggests at least ten to twenty samples and cautions that a customer will sometimes accept a larger difference than one they rejected, which is why the visual check stays in the loop. ASTM's practice for establishing colour and gloss tolerances takes the same position from the other side: it describes how to arrive at tolerances and declines to say how large they should be. A limit copied from another product, customer or industry has skipped this step.
A tolerance that names only a formula and a figure is still incomplete. It needs the formula's parameters (the l:c ratio for CMC, the weighting factors for CIE94 or CIEDE2000, any commercial factor), the illuminant and observer, the instrument geometry and specular mode, the reference it is measured against, and whether the figure applies to one reading, an average or a percentile of many. Component limits on lightness, chroma and hue are worth adding beside the total, because they show the direction of a failure and stop a pure hue shift hiding inside an acceptable total. ASTM D2244 puts the general point bluntly: differences calculated in different systems are not directly comparable.
The formulas themselves, and why the same pair of colours scores differently in each, are set out on the ΔE page in the measurement section.
| Standard | ΔE*ab | ΔE CMC(2:1) | ΔE00 |
|---|---|---|---|
| Mid grey | 1.73 | 2.26 | 2.00 |
| Pale cream | 1.73 | 1.38 | 1.49 |
| Saturated orange | 1.73 | 0.65 | 0.92 |
| Saturated red | 1.73 | 0.71 | 1.03 |
| Deep blue | 1.73 | 1.12 | 1.41 |
| Standard | CIELAB position | CMC lightness | CMC chroma | CMC hue | ΔE00 lightness | ΔE00 chroma | ΔE00 hue |
|---|---|---|---|---|---|---|---|
| Mid grey | L* 50, C* 0, h 0° | 2.18 | 0.64 | 0.64 | 1.00 | 0.68 | 1.02 |
| Pale cream | L* 88, C* 15, h 90° | 2.82 | 1.44 | 0.86 | 1.58 | 1.71 | 0.81 |
| Saturated orange | L* 62, C* 75, h 55° | 2.43 | 3.05 | 1.10 | 1.18 | 4.48 | 1.71 |
| Saturated red | L* 45, C* 70, h 30° | 2.06 | 2.97 | 1.57 | 1.05 | 4.25 | 1.84 |
| Deep blue | L* 30, C* 45, h 285° | 1.61 | 2.44 | 1.39 | 1.28 | 3.09 | 1.26 |
Why: The box was sized on saturated colours; near neutral, a small a* or b* shift is a visible hue.
Fix: Use an ellipsoidal formula, or set separate, tighter chroma limits for near-neutral standards.
Why: The two formulas accept different volumes, most obviously in lightness.
Fix: Re-derive the limit from the archive of accepted and rejected batches in the new formula.
Why: One is using CMC 2:1 and the other 1:1, or different illuminant and observer settings.
Fix: Write the formula, its parameters and the colorimetric condition into the specification line.
Each statement is labelled by kind — established fact, a standard’s requirement, observed market data, a convention, or Colourwise’s own interpretation or analysis — with the strength of the evidence behind it.
FactModerate evidence
Visual acceptability around a colour is approximately elliptical, so a rectangular tolerance box in L*a*b* passes some samples that should fail and fails some that are acceptable; CMC, CIE94 and CIEDE2000 tolerances are ellipsoids whose size and shape change with the colour.
Source: Tolerancing: The Key to Accurate Color (white paper L10-616); Tolerancing Part 3: Color Space vs. Color Tolerance
StandardStrong evidence
ISO 105-J03:2009 calculates ΔEcmc(l:c) so that a single maximum value can be specified as a tolerance that depends on the closeness of match the end use requires and not on the colour involved or the nature of the difference.
Caveat: From the standard's public abstract, which states no numeric tolerance.
Source: ISO 105-J03:2009 Textiles — Tests for colour fastness — Part J03: Calculation of colour differences
StandardStrong evidence
ASTM D2244-25 states that colour differences calculated in different systems are not directly comparable, and that the purchaser and seller must agree both the permissible tolerance and the procedure for calculating it.
Colourwise analysisStrong evidence
A sample at the corner of a ±1 box in ΔL*, Δa* and Δb* is 1.73 ΔE*ab from the standard; for a mid grey that corner scores 2.0 by CIEDE2000 and 2.3 by CMC(2:1), and for a saturated orange 0.9 and 0.65.
Based on: Calculated by Colourwise with its implementations of CIEDE2000 and CMC(l:c) for five illustrative CIELAB standards; see the first table on this page.
Caveat: The reference colours are illustrative choices, and only one of the box's eight corners is evaluated.
Source: The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations; Modification to the JPC79 colour-difference formula
Colourwise analysisStrong evidence
For a limit of 1.0, CMC(2:1) allows about 2.2 CIELAB units of lightness difference at a mid grey but only 0.64 of chroma, and about 3 units of chroma at a saturated orange; CIEDE2000 allows about 1.0, 0.7 and 4.5 respectively.
Based on: Colourwise found, by bisection along each axis, the distance in ΔE*ab at which each formula reaches 1.0; see the second table on this page.
Caveat: Half-axes along single directions; the full acceptance volume is not exactly an ellipsoid in CIELAB for CIEDE2000.
Source: The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations; Modification to the JPC79 colour-difference formula
StandardStrong evidence
AATCC EP14 covers both CIEDE2000 and CMC(l:c) for small colour differences and recommends CIEDE2000 as the primary method on the ground that it agrees slightly better with visual evaluation.
Source: AATCC EP14-2021e2 Evaluation Procedure for Small Color Differences
FactLimited evidence
One instrument maker puts agreement between instrumental pass/fail and visual assessment at about 75 % for an L*a*b* box, about 85 % for L*C*h limits, about 95 % for CMC 2:1 and about 98 % for CIEDE2000.
Caveat: Stated in a manufacturer's white paper without a reference, sample or method. Useful as an ordering of the methods, not as measured rates.
Source: Tolerancing: The Key to Accurate Color (white paper L10-616)
Reviewed 6 October 2026. Colourwise summarises its sources in its own words and does not reproduce standards text or proprietary colour data. Spotted an error? Tell us.