In short
- Use the free CCT calculator below to convert CIE x, y to CCT and Duv, or a CCT and Duv target back to x, y.
- CCT alone does not describe a white. Two LEDs can both measure 3000 K and still look different: one greenish, one pinkish. The second number, Duv, tells you how far the color sits above or below the blackbody (Planckian) locus.
- Both come from chromaticity. Measure the spectrum, compute CIE x, y, convert to the CIE 1960 (u, v) diagram and find the nearest point on the Planckian locus. That point’s temperature is the CCT; the signed distance is Duv.
- McCamy’s formula is a quick estimate, not a test method. It has no Duv and drifts by tens of kelvin off the locus. Use a locus-based method for specifications and production limits.
Correlated color temperature (CCT) is the number on every white-LED datasheet, lamp box and luminaire specification. Yet engineers who test LEDs in production soon learn that CCT is only half of the answer. This guide explains how to calculate CCT and Duv from CIE x, y chromaticity, compares the common calculation methods, works through a numerical example, and gives you a CCT calculator that returns both values in your browser.
What CCT and Duv mean
A blackbody (Planckian) radiator changes color in a well-defined way as it heats up: from deep orange near 1800 K, through warm white around 2700–3000 K, to bluish white above 6500 K. Plotted on a chromaticity diagram, those colors form a curve: the Planckian locus.
Real light sources, and white LEDs in particular, almost never sit exactly on that curve. The correlated color temperature is the temperature of the blackbody whose color is closest to the source. “Closest” is measured in the CIE 1960 uniform chromaticity scale (u, v), which the colorimetry standards use for this purpose because distances there correspond better to perceived color differences than in x, y. Lines of constant CCT, the isotemperature lines, are perpendicular to the locus in this diagram.
Duv is the signed distance from the source’s chromaticity to the locus in the same (u, v) diagram. ANSI C78.377 defines it and the sign convention: positive above the locus (towards green), negative below it (towards magenta or pink). Because CCT collapses a two-dimensional color into one number, every isotemperature line contains a whole range of different-looking whites; Duv is the coordinate along that line.
CCT is only meaningful close to the locus. The usual limit is a distance of 0.05 in (u, v); beyond that, a “color temperature” no longer describes the color and you should report chromaticity coordinates instead.
How to calculate CCT and Duv from x, y
- Measure the spectrumRecord the spectral power distribution with a calibrated spectroradiometer, usually with an integrating sphere for total flux or a defined geometry for intensity. Wavelength accuracy matters (see below).
- Compute X, Y, Z and x, yWeight the spectrum with the CIE 1931 2° color-matching functions and sum. Then x = X/(X+Y+Z) and y = Y/(X+Y+Z).
- Convert to (u, v)u = 4x / (−2x + 12y + 3), v = 6y / (−2x + 12y + 3). (The CIE 1976 coordinates are u′ = u and v′ = 1.5 v.)
- Find the nearest locus pointSearch the Planckian locus for the temperature T whose (uT, vT) is closest to (u, v). That temperature is the CCT.
- Compute Duv with its signDuv = √[(u − uT)² + (v − vT)²], positive if the point lies above the locus and negative if below.
Step 4 is where the methods differ. The locus itself is computed from Planck’s law and the color-matching functions; the question is how quickly and accurately each method finds the closest point.
CCT calculation methods compared
| Method | How it works | Duv? | Typical accuracy | Use it for |
|---|---|---|---|---|
| McCamy (1992) | Cubic polynomial in n = (x − 0.3320)/(0.1858 − y) | No | Within about 10 K on the locus from 2700 to 6500 K; up to about 40 K at |Duv| = 0.02; over 100 K near 10 000 K (IZAK calculation) | Quick estimates, displays, sanity checks |
| Robertson (1968), original table | Interpolation between tabulated isotemperature lines | Yes | Errors up to about 150 K over 1500–40 000 K in the same 2023 comparison | Legacy software |
| Robertson, 1% table | Same algorithm with a denser table | Yes | Within 0.1 K and 0.000001 Duv over 1500–40 000 K, |Duv| ≤ 0.05 in a 2023 comparison of 40 methods | Recommended for standards and fast production code |
| Ohno (2014) combined method | Table search plus triangular or parabolic refinement | Yes | Within about 1 K for 1000–20 000 K, |Duv| ≤ 0.03 | Lab and production software |
| Direct search on the computed locus | Compute the locus from Planck’s law and minimize the distance numerically | Yes | Limited only by numerical precision; slower | Reference calculations, the calculator on this page |
We checked McCamy against an exact locus calculation. On the locus it stays within about 10 K between 2700 and 6500 K, but at 4000 K and Duv = −0.02 it reads 38 K high, at 2000 K and Duv = −0.02 it reads 77 K low, and at 10 000 K it is more than 100 K off even on the locus. For a pass/fail limit that is tens of kelvin wide, any of the locus-based methods is good enough. McCamy is not: it cannot give Duv, and Duv is exactly the quantity that separates a good white from a greenish or pinkish one at the same CCT.
CCT calculator: x, y to CCT and Duv
Enter CIE 1931 x, y chromaticity to get CCT, Duv and u′, v′, or switch modes to convert a CCT and Duv target back to x, y. The calculator computes the Planckian locus from Planck’s law and the CIE 1931 2° color-matching functions and finds the closest point numerically.
Worked example: an LED sold as 3000 K
A spectroradiometer measurement of a warm-white LED module gives x = 0.4380, y = 0.3960. Here is the calculation step by step.
1. Convert to (u, v). The denominator is −2(0.4380) + 12(0.3960) + 3 = 6.876. So u = 4 × 0.4380 / 6.876 = 0.2548 and v = 6 × 0.3960 / 6.876 = 0.3455 (u′ = 0.2548, v′ = 0.5183).
2. Quick estimate with McCamy. n = (0.4380 − 0.3320) / (0.1858 − 0.3960) = −0.5043, and CCT ≈ 449n³ + 3525n² + 6823.3n + 5520.33 = 2918 K.
3. Exact locus search. The closest point on the Planckian locus is at 2915 K, and the distance to it is 0.0034 with the point below the locus, so Duv = −0.0034. Here McCamy is only 3 K away, because the point is close to the locus and in the range where the formula works well.
4. Interpret. The module is about 85 K warmer than a 3000 K target and slightly on the pink side of the locus. Whether it passes depends on the limits in your specification: a nominal 3000 K category in a binning standard covers a window of CCT and Duv, not a single number. If the specification states only “3000 K ± 100 K”, this module passes, yet it could look visibly different from a module at 3000 K with Duv = +0.006.
The table shows why Duv belongs in every white-point specification. All three points have exactly the same CCT:
| Point | CCT | Duv | x | y | Appearance |
|---|---|---|---|---|---|
| A | 3000 K | +0.006 | 0.4459 | 0.4227 | Greenish-yellow white |
| B | 3000 K | 0.000 | 0.4369 | 0.4041 | On the blackbody locus |
| C | 3000 K | −0.006 | 0.4284 | 0.3865 | Pinkish white |
Points A and C are about 0.036 apart in y, a difference that is easy to see when the two sources are side by side. Vision experiments have also shown that many observers judge white light slightly below the locus (Duv around −0.015 on average in one study) as the most natural, so a negative Duv is not automatically a defect. It must simply be specified and controlled.
Using CCT and Duv in LED production test
In production the calculation is easy; the measurement is what decides whether the numbers are right. Six points cause most disagreements between a supplier’s and a customer’s CCT values.
ANSI C78.377 defines nominal white categories as quadrangles in the chromaticity diagram, each with a target CCT and Duv and their tolerances. The 2024 edition extends the range down to 1800 and 2000 K. Write both limits into your test.
In our model of a three-band warm-white spectrum at 3000 K, a 1 nm wavelength-scale error in the spectroradiometer shifts the computed CCT by about 25 K. Check the wavelength scale with a line source regularly.
LED chromaticity moves with junction temperature and current. A short pulsed test and a thermally stabilized test can give different results; state which one the limits apply to.
Many white LEDs change color with angle. Total-flux measurements in an integrating sphere and on-axis intensity measurements are not interchangeable; use the geometry the specification calls for.
Stray light in a compact spectrometer adds signal where the LED has little, often in the blue and deep red, and pulls x, y. Subtract a dark spectrum and validate against a reference source.
Agree the method (a locus-based method with Duv) and the color-matching functions with your customer or supplier. Different methods can disagree by tens of kelvin on the same data.
Further reading
Radiometry and LED inspection on the IZAK Knowledge hubStart with radiometry and photometry basics, then see how an integrating sphere is used for LED inspection and how sensors are chosen in our optical sensors in radiometry review.For custom radiometers and spectroradiometers with a defined spectral range, field of view and calibration, see our radiometry design consultation and the multi-channel spectro-radiometer.
Frequently asked questions
QCan I calculate CCT from x, y with a simple formula?
QWhat is a good Duv value for a white LED?
QWhy do two instruments report different CCTs for the same LED?
References
- CIE 015:2018, Colorimetry, 4th edition.
- ANSI C78.377-2024, Electric Lamps — Specifications for the Chromaticity of Solid-State Lighting Products.
- C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Research & Application 17(2), 142–144 (1992).
- Y. Ohno, “Practical use and calculation of CCT and Duv,” LEUKOS 10(1), 47–55 (2014).
- K. Smet, M. Royer, D. Baxter et al., “Recommended method for determining the correlated color temperature and distance from the Planckian locus of a light source,” LEUKOS 20(2), 223–237 (2024).
- Y. Ohno and M. Fein, “Vision experiment on acceptable and preferred white light chromaticity for lighting,” CIE x039:2014, 192–199 (2014).
Tzachi Sabati
CEO, IZAK Scientific
Physicist specializing in photonics and quantum technologies, with deep expertise in quantum sensors and advanced optical systems. Leads the Advanced Quantum Lab course at the Technion, bridging academic excellence with industry innovation. At IZAK Scientific, provides cutting-edge photonics-based solutions, developing customized inspection and sensing systems for R&D and production. Passionate about advancing quantum sensing applications and integrating novel technologies to meet industry needs.
