Wien's Displacement Law: Peak Blackbody Wavelength & Temperature

Specify which spectral peak you mean

Wien’s wavelength displacement law is lambda_max×T=b, with b≈2.897771955E−3 m K. It locates the maximum of spectral radiance per unit wavelength, B_lambda. The maximum of a spectrum per unit frequency, B_nu, is different: converting its peak frequency using c/nu does not give this lambda_max.

A blackbody emits a broad spectrum. A peak near 500 nm does not mean the object looks green, and the peak alone does not determine perceived colour or correlated colour temperature. The inverse calculation below is an ideal blackbody peak-temperature estimate, not a general colour-temperature measurement for LEDs or arbitrary light sources.

Temperature to peak wavelength

Enter absolute temperature in kelvin in B2, initially 5778. If your input is Celsius, convert it first with =CelsiusCell+273.15. C2 contains the unrounded peak in nanometres; C3 contains the peak in micrometres.

The adopted constant is 2897771.955 nm K, equivalent to 2897.771955 micrometre K. Use the formula below in C2 and =IF(ISNUMBER(C2),C2/1000,C2) in C3. Do not round C2 before subsequent conversions or classification.

=IF(NOT(ISNUMBER(B2)),"Enter numeric temperature",IF(B2<=0,"Requires Kelvin T > 0",2897771.955/B2))

Check the example values

At 5778 K, the ideal blackbody peak is about 501.52 nm. At 9940 K, it is about 291.53 nm. These are example temperatures, not precise observational determinations for named stars.

At 310.15 K (37 degrees Celsius), the example peak is about 9343.13 nm or 9.34313 micrometres. This illustrates a body-temperature blackbody; actual skin temperature and wavelength-dependent emissivity need not equal the assumptions of the example.

To display two decimals, apply a number format or use =IF(ISNUMBER(C2),ROUND(C2,2),C2) in another cell. C2 and C3 retain their full computed values.

Compare the peak with a stated visible interval

C4 uses 380 through 750 nm, inclusive, as an approximate visible interval for this tutorial. Visible sensitivity has no universal abrupt cutoff; these thresholds are a classification convention.

Shorter-than-visible examples may be ultraviolet, and longer-than-visible examples may be infrared, but the formula does not label all shorter wavelengths UV or all longer wavelengths infrared. At extreme temperatures other electromagnetic bands are possible. The labels describe the location of the peak, not all emitted radiation.

The classification uses unrounded C2. A value just below 380 nm can display as 380.00 nm when rounded yet correctly remain outside the selected interval.

=IF(NOT(ISNUMBER(C2)),C2,IF(C2<380,"Shorter than visible (<380 nm)",IF(C2<=750,"Visible interval (380-750 nm)","Longer than visible (>750 nm)")))

Invert a wavelength-domain peak to temperature

Enter a positive peak wavelength in nanometres in E2, initially 500. F2 contains the formula below and returns 5795.54391 K. For a wavelength measured in micrometres, multiply by 1000 before entering it here.

E2 is independent of B2. To check a round trip, set E2 to =C2; F2 should reproduce B2 to floating-point precision. The inversion assumes a blackbody-like wavelength-domain spectral peak, not an emission line, a detector-response maximum or a frequency-domain peak.

=IF(NOT(ISNUMBER(E2)),"Enter numeric peak wavelength",IF(E2<=0,"Requires wavelength > 0 nm",2897771.955/E2))

Further reading

• NIST CODATA — Wien wavelength displacement law constant
• Marr & Wilkin — A better presentation of Planck’s radiation law