ΔE turns a measured color difference into a decision. This page calculates it three ways – ΔE76, ΔE94 and ΔE2000 – from two sets of CIE L*a*b* values, and explains what the number does and does not tell you about the samples behind it.
What is ΔE?
ΔE (delta E, written ΔE* or ΔE*ab) is a single number describing how far apart two colors are. It is calculated from the difference between two sets of coordinates in a color space, most often CIE L*a*b*, where L* describes lightness and a* and b* describe the red–green and yellow–blue axes. Two samples measured on the same instrument under the same conditions produce two points in that space, and ΔE is the size of the gap between them.
- ΔE is a measured difference. It reports what the instrument recorded, which is not the same thing as what a customer will see.
- ΔE is relative. The same number describes a different visual event in a pale neutral and in a saturated red.
- ΔE needs its context. The formula, illuminant, observer, measurement geometry and sample preparation all change the number.
How to read a ΔE value
The bands below are a rough guide to how a difference of a given size is usually perceived on flat, uniform, adjacent samples viewed under controlled lighting. They describe perception, not acceptance. Every one of them shifts with the material, the finish and the viewing relationship.
| ΔE (any formula) | Typical perception | What it usually means in production |
|---|---|---|
| Below 1 | Usually not visible on flat adjacent samples under controlled light | Inside most commercial tolerances for critical parts, though large areas, gloss and low-chroma neutrals can still show it |
| 1 to 2 | Small; visible to some observers on close comparison | Commonly accepted for parts viewed separately, and often at or beyond the limit for parts viewed side by side |
| 2 to 3.5 | Visible when samples are compared directly | Outside a tight commercial tolerance unless the specification for the product allows it |
| 3.5 to 5 | Clearly visible | Usually a rejection against a tight specification; may pass where color is not critical |
| Above 5 | Large; reads as a different color rather than a shade variation | Clear mismatch |
Treat “ΔE below 1 is invisible” with care
It is repeated everywhere and it is not reliable. Visibility depends on the color region, the material, gloss and texture, the size of the area, whether the parts sit next to each other, the lighting and who is looking. Use perception data from your own product and application to set a limit, and record the measurement conditions alongside it.
ΔE76, ΔE94 and ΔE2000 compared
The three formulas answer the same question with different assumptions about how the eye works. ΔE76 treats the L*, a* and b* axes as equally important, which overstates differences in saturated colors. ΔE94 and ΔE2000 apply weighting that reduces the influence of chroma and hue differences as samples become more saturated, and ΔE2000 also corrects for the blue region and for the interaction between chroma and hue.
| Formula | What it does | Where it is normally used |
|---|---|---|
| ΔE76 (ΔE*ab) | Straight-line distance in CIE L*a*b*. Simple, symmetrical and unweighted. | Legacy specifications, quick internal checks and older color software defaults |
| ΔE94 (ΔE*94) | Weighted for chroma and hue, with parametric factors chosen for the application. | Textiles with 2:1:1 weighting, and older automotive and coatings specifications |
| ΔE2000 (ΔE00) | The current CIE recommendation. Weighting plus corrections for the blue region and the chroma–hue interaction. | New specifications in automotive, paint, plastics, printing and general manufacturing |
Which formula should I use?
Choose in this order, and write down what you chose.
- Follow the specification. If the customer, contract or standard names a formula, use that one, including its parametric factors and rounding rule.
- If nothing is specified, use ΔE2000. It is the current CIE recommendation and the closest single number to average visual assessment for small differences.
- Use ΔE94 with 2:1:1 weighting for textiles where the specification is written in those terms. Many textile specifications are written in ΔE*CMC(2:1) instead, which is a different formula again.
- Keep ΔE76 where an existing tolerance is already expressed in ΔE*ab, or where a rough internal check is enough.
- Record the formula, the parametric factors and the rounding rule wherever the tolerance is written down. A number without its formula cannot be checked.
ΔE tolerance examples by application
There is no universal acceptable ΔE. The figures below are the kind of starting point that appears in published guidance and day-to-day industry practice. They are not limits you can adopt without validating them against your own visual decisions, process capability and measurement uncertainty.
| Application | Commonly quoted starting point | What drives the limit |
|---|---|---|
| Paints & coatings | Roughly 0.5 to 1.5 for panels viewed together | Gloss, texture and film build. Metallic and pearlescent finishes need multi-angle measurement as well. |
| Plastics | Roughly 0.5 to 1.5 for moulded parts | Whether parts are assembled next to each other, plus gloss, texture and color region. |
| Textiles | Roughly 1.0 to 2.0 with 2:1:1 weighting | Shade, fibre, structure and end use. Frequently written as ΔE*CMC(2:1) rather than ΔE2000. |
| Printing & packaging | Per-patch aims and tolerances, often under 2 | The press standard in use. ISO 12647 workflows specify measured aims per patch rather than one global number. |
| General manufacturing | Roughly 1.0 to 2.0 | Customer expectation and how the product is viewed. Derive the limit from visual approval evidence. |
A tolerance also needs an uncertainty budget
If repeat measurements of the same sample vary by 0.3, a limit of 0.5 leaves very little room for a real decision. Measure repeatability without moving the sample, then with repositioning, then between operators and instruments. A review or retest band near the limit reduces both false acceptance and false rejection.
Worked calculation example
Two readings of the same coating, measured on the same instrument with the same settings:
| Reading | L* | a* | b* |
|---|---|---|---|
| Reference (standard) | 55.00 | 12.00 | 18.00 |
| Batch (sample) | 53.50 | 13.20 | 16.40 |
The component differences are ΔL* = −1.50, Δa* = +1.20 and Δb* = −1.60, so the batch is slightly darker, slightly redder and slightly less yellow than the reference. The three formulas give three different numbers for the same pair:
ΔE76
2.50
Unweighted distance in L*a*b*
ΔE94 (1:1:1)
2.10
Weighted for chroma and hue
ΔE2000
2.28
Current CIE recommendation
A ΔE2000 of 2.28 is a visible difference when the two samples are compared side by side. Whether it is acceptable depends on the product, the finish, the viewing relationship and the tolerance specified for the job. On adjacent panels under a tight coatings specification it would normally be a rejection; on parts viewed separately it might sit inside tolerance. Note also the spread between 2.10, 2.28 and 2.50 for one pair of samples, which is why a tolerance must always name its formula.
How the formulas are calculated
All three formulas start from the same two sets of L*a*b* values and the same component differences: ΔL* is the lightness difference, ΔC* the chroma difference and ΔH* the hue difference. What separates them is how much weight each component is given.
ΔE76 – unweighted distance
ΔE*ab = √( (ΔL*)² + (Δa*)² + (Δb*)² ). This is the straight-line distance between the two points in CIE L*a*b*, with every axis weighted equally. It is symmetrical: swapping the two samples gives the same answer.
ΔE94 – weighted for chroma and hue
ΔE*94 = √( (ΔL* / (kL · SL))² + (ΔC* / (kC · SC))² + (ΔH* / (kH · SH))² ), where SL = 1, SC = 1 + K1 · C*₁ and SH = 1 + K2 · C*₁. The graphic arts parametric factors are kL = kC = kH = 1, K1 = 0.045 and K2 = 0.015; the textile recommendation uses kL = 2, K1 = 0.048 and K2 = 0.014. Because the weighting depends on the reference sample only, ΔE94 is not symmetrical.
ΔE2000 – weighting plus rotation
ΔE00 = √( (ΔL′ / (kL · SL))² + (ΔC′ / (kC · SC))² + (ΔH′ / (kH · SH))² + RT · (ΔC′ / (kC · SC)) · (ΔH′ / (kH · SH)) ). The a* axis is first rescaled by G = 0.5 · (1 − √(C̄&sup7; / (C̄&sup7; + 25⁷))), after which chroma and hue are recalculated. SL, SC and SH are weighting functions of lightness, mean chroma and the T term, and RT = −sin(2Δθ) · RC adds the rotation term that improves agreement with visual assessment in the blue region. This calculator uses kL = kC = kH = 1, the parametric-factor-free form recommended by CIE 224.
Color measurement FAQ
Is a lower ΔE always better?
No. ΔE measures size, not direction or cause. Two samples can share the same ΔE with one too dark and the other too yellow, and those are different production problems. A sample can also sit inside a ΔE limit while failing a separate hue or lightness requirement, which is why many specifications add limits on ΔL*, ΔC* or hue angle alongside the total.
Should I use ΔE2000 or ΔE76?
Use whichever formula the specification names. If none is named, ΔE2000 is the current CIE recommendation and the better single-number predictor of visual difference. ΔE76 remains common in older specifications and is easier to explain, but it overstates differences in saturated colors and understates nothing in the neutral region.
Can I compare a ΔE2000 result with a ΔE94 tolerance?
No. The formulas weight lightness, chroma and hue differently and apply different corrections, so the numbers are not interchangeable. A tolerance is only valid for the formula it was written for. Where a supplier and a customer use different formulas, agree a conversion or a single formula for the contract rather than comparing raw numbers.
Why do two instruments give different ΔE values for the same pair of samples?
Geometry, aperture size, UV condition, calibration state and inter-instrument agreement all affect the underlying L*a*b* values. Two readings can be perfectly repeatable on one instrument and still differ between instruments. Compare values measured on the same instrument under the same settings, and check inter-instrument agreement before exchanging data with a supplier.
Does ΔE account for gloss, texture or metamerism?
Not on its own. ΔE is calculated from a single measurement condition. Gloss, texture, sparkle and metamerism need extra measurement or assessment: a SCI and SCE comparison, multi-angle measurement, a gloss or haze reading, and visual assessment under more than one illuminant.
Does this calculator send my measurements anywhere?
No. The calculation runs entirely in your browser with JavaScript. Nothing is uploaded to this site and nothing is stored in your browser. If you copy the page address after entering values, those values are carried in the address so the recipient sees the same calculation, so avoid sharing a link that contains confidential production data.