Quick answer: A MacAdam ellipse describes a colour-matching region around a target colour. SDCM expresses that tolerance in ellipse steps: fewer steps mean a tighter allowed colour spread around the same centre. Wikipedia's MacAdam ellipse article describes this use of standard-deviation steps in LED lighting.
Use this guide to compare colour-consistency claims when choosing LEDs for a shared space. It explains what the step number measures, why matching labels do not establish an exact colour match, and what the cited lamp and downlight specifications actually require.
What does a MacAdam ellipse measure?
It describes variation around a colour coordinate, rather than brightness or electrical power. According to ENERGY STAR Lamps V2.1, a standardized colour ellipse is specified by its centre coordinates, CIE x and y, and its number of standard-deviation steps, with reference to ANSI C78.376.
That makes the centre essential to a useful comparison. A small tolerance around one target colour does not establish a match with a small tolerance around a different target. Read the target and the tolerance together.
According to Wikipedia, the ellipse describes the spread of repeated colour matches: a one-times ellipse contains about 39% of match points, a two-times ellipse about 86%, and a three-times ellipse about 99%. These percentages describe match points, not the percentage of buyers who will notice a difference between lamps. They are also not manufacturing pass rates.
What do SDCM and the step number mean?
SDCM means Standard Deviation Colour Matching; in LED colour specifications it expresses tolerance using MacAdam-ellipse steps. A smaller step count defines a tighter region when the centre and underlying ellipse are the same. See Photometric Testing's explanation and Wikipedia.
The following reference compares assumed bins with the same centre, orientation and base ellipse. It is a geometric comparison, not a recommendation or a visibility test. Let r be the one-step distance from the centre to the boundary along a chosen line.
| Assumed tolerance | Centre-to-boundary distance | Opposite-boundary span | What the comparison establishes |
|---|---|---|---|
| 3 steps | 3 × r = 3r | 3r + 3r = 6r | Tightest allowed region of these choices |
| 5 steps | 5 × r = 5r | 5r + 5r = 10r | Wider allowed region around the same centre |
| 7 steps | 7 × r = 7r | 7r + 7r = 14r | Widest allowed region of these choices |
Worked example: a bin limit is not a pairwise limit
Assumed inputs: two LEDs sit exactly on opposite boundaries of the same seven-step ellipse, along a line through its centre. Each is seven one-step distances from the centre.
- Formula: separation = distance from the first LED to the centre + distance from the centre to the second LED.
- Substitution: separation = 7r + 7r.
- Result: separation = 14r, or 14 one-step distances along that line.
Both LEDs satisfy the assumed bin boundary, yet their separation is twice the centre-to-boundary limit. This is an extreme geometric case, not a prediction of the spread in a delivered batch. Actual LEDs could sit much closer together within the same allowed region.
Can you see a difference within an ellipse?
There is no single visibility label that the supplied sources consistently assign to each step. Photometric Testing describes a one-step ellipse as a region within which the eye cannot discern a colour difference, while Wikipedia says a three-times ellipse is generally taken as a just-noticeable chromaticity difference.
The useful distinction is that roughly one step describes the standard deviation of colour matches, while roughly three steps is a commonly cited just-noticeable threshold. Those descriptions should not become a promise that every observer will see, or fail to see, a particular pair of LEDs. The differing thresholds are explicit in the lab explanation and Wikipedia account.
For a purchase where matching matters, use the step count to compare the permitted spread, then compare samples in the intended arrangement. Do not translate each step into a universal label such as “invisible,” “slightly visible” or “obvious.”
What do the cited ENERGY STAR specifications require?
The cited documents use seven-step colour regions, but their requirements must be read by product type and version. According to ENERGY STAR Lamps V2.1, reported CCT must correlate to a nominal CCT, and nine out of ten units must fall within a seven-step MacAdam ellipse or ANSI quadrangle for the designated CCT.
According to ENERGY STAR Downlights V1.0, a downlight must offer at least one listed nominal CCT and fall within its corresponding seven-step chromaticity quadrangle under ANSI C78.377-2017 (R2022). The same document specifies Ra ≥ 80 and R9 > 0.
These are requirements from the named document versions, not a claim about the current certification status of any product. Also preserve the distinction between an ellipse and a quadrangle: the downlight provision names a quadrangle. Calling every permitted region an exact ellipse would erase that distinction.
The separate chromaticity and rendering requirements are useful when shopping. Colour consistency and colour rendering need separate comparisons; the cited downlight document does not replace one with the other. Our CRI calculator compares a CRI input against the site's application planning figures. It does not calculate SDCM or verify an LED's chromaticity measurements.
How should you compare LED colour claims?
Compare the target coordinate and the allowed spread together. According to ENERGY STAR Lamps V2.1, the standardized ellipse description combines centre coordinates with the step count; the count alone is incomplete.
- Match the intended target. Compare the nominal colour temperature, then the specified centre where available.
- Compare the tolerance. For the same centre and base ellipse, prefer the smaller allowed region when your priority is a tighter match.
- Identify the region. Read whether the claim describes an ellipse or a chromaticity quadrangle before comparing limits.
- Separate rendering from matching. Compare the rendering figures alongside the colour-consistency claim, rather than treating either as a complete light-quality score.
- Compare actual samples. A tolerance gives a permitted boundary; it does not disclose where every supplied LED lies inside it.
For the rest of your lighting plan, the LEDask calculator hub links to tools for output, layout and power calculations.
FAQ
Is SDCM different from MacAdam steps?
In this context, they express the same colour-tolerance concept. SDCM stands for Standard Deviation Colour Matching, as explained by Photometric Testing.
Is a three-step LED more consistent than a five-step LED?
Its allowed region is smaller if the centre and base ellipse are the same: the corresponding centre-to-boundary distances are 3r and 5r. That compares specification limits, not the measured separation of any particular pair of LEDs.
Does seven-step binning mean every pair is seven steps apart or less?
No. With the assumed opposite-boundary positions in the worked example, the separation is 7r + 7r = 14r; the bin limit measures distance from the centre.
Does ENERGY STAR require four-step colour consistency?
That is not the requirement in the cited documents. According to Lamps V2.1, nine out of ten units must meet the designated seven-step ellipse or ANSI quadrangle provision; Downlights V1.0 specifies the corresponding seven-step quadrangle.
Does matching nominal CCT guarantee matching colour?
No: a nominal category still allows a region of chromaticity values. According to ENERGY STAR Lamps V2.1, units are assessed against the ellipse or quadrangle for the designated CCT, rather than required to share one exact coordinate.
Jack Shi
Founder & editor, LEDaskJack Shi builds and writes LEDask, an independent LED-lighting tools project operated by clooms. He designs the calculators, checks their formulas and reference values against published engineering data, and writes the guides across the site.
