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Blackbody Wavelength and Frequency Peaks

Find the separate wavelength-density and frequency-density peaks of ideal blackbody radiation, with editable temperature inverses and exact SI constants.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

At 1,000 K the ideal wavelength-density spectrum peaks near 2,897.772 nm and the frequency-density spectrum peaks near 58.7893 THz. These are separate spectral maxima.

λ_peak = bλ/T; ν_peak = bνT. Ideal bλ ≈ 0.002897771955 m·K and bν ≈ 5.878925757 ×10¹⁰ Hz/K.

Worked example

Enter these known values and leave the other values blank.

Absolute blackbody temperature
1000 K
Peak per wavelength interval
2898 nm
Peak per frequency interval
58.79 THz

Assumptions and limitations

  • This is ideal thermal blackbody radiation at one equilibrium temperature. Real materials can have wavelength-dependent emissivity and additional emission lines; the calculator does not model those effects.
  • The wavelength result maximizes spectral density per wavelength interval. The frequency result maximizes density per frequency interval. They are different spectral maxima: multiplying these two peak coordinates does not give the vacuum speed of light.
  • Temperature must exceed 0 K. Celsius or Fahrenheit values can be zero or negative provided their absolute temperature is positive. Unit conversion uses T[K] = T[°C] + 273.15 and T[°F] = 1.8 T[K] − 459.67.
  • The ideal coefficients derive from exact SI h, k and c and the nonzero maxima of Planck’s spectrum. Displayed precision does not remove uncertainty in a measured temperature or the idealization of a real emitter.
  • The wavelength displacement coefficient is fixed at its ideal Planck-spectrum value. Temperature and the two peak coordinates are the three editable quantities.
  • The three visible quantities remain editable with all 19 unit choices. The RPM option is a cycles-per-minute expression of frequency, not rotation of a thermal emitter.
  • Zero or negative absolute temperature, wavelength, frequency or coefficient is outside this model. Missing values remain incomplete. Unit changes preserve the underlying quantity; inconsistent locked inputs produce a conflict.

Common questions

Why is frequency not c divided by the displayed peak wavelength?

A density per wavelength interval and a density per frequency interval weigh the same radiation differently. Changing the spectral variable changes where its density is largest. The two peak coordinates belong to different representations.

What happens if temperature doubles?

With the ideal wavelength coefficient fixed, the wavelength peak halves and the frequency peak doubles.

Can I use a negative Celsius temperature?

Yes, if it is above −273.15 °C. For example, −20 °C equals 253.15 K and is a positive absolute temperature.

Can I infer temperature from either peak?

Yes. Enter a known wavelength-density peak or frequency-density peak and leave temperature blank. Use the corresponding spectral representation; the two peaks are not the coordinates of one monochromatic wave.

References

Use the frequency peak of the Planck spectrum per frequency with exact SI h and k, replacing the captured rounded coefficient. Preserve both spectral relationships and all five inverse branches; guard zero wavelength/absolute-temperature denominators. Set the initially locked wavelength displacement coefficient from the independent Planck wavelength maximum using exact SI h, c and k. Preserve the hidden, initially locked coefficient and its captured inverse graph. Require exact-sign positive Kelvin, wavelength and frequency while retaining Celsius/Fahrenheit offsets. Use Kelvin as the equivalent internal temperature reference to avoid subtracting and re-adding the Celsius offset for Kelvin inputs close to absolute zero. Validate known wavelength/temperature pairs against the hidden fixed coefficient so conflicting locked values cannot silently appear consistent.

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