Explore Planck radiance with precise unit controls here. Create wavelength or frequency curves instantly today. Export tables to share with your team quickly anywhere.
These sample values show typical visible-range usage.
| Temperature (K) | Mode | Input | Emissivity | Output (chosen units) |
|---|---|---|---|---|
| 3000 | Wavelength | 550 nm | 1.0 | Per nm spectral radiance |
| 5778 | Wavelength | 500 nm | 1.0 | Solar-like blackbody point estimate |
| 1200 | Frequency | 30 THz | 0.8 | Infrared frequency-form radiance |
Planck's law gives blackbody spectral radiance as a function of temperature and either wavelength or frequency:
This tool also reports Wien peak wavelength λmax = b/T and integrated radiance L = (σT⁴/π)×ε.
Planck radiance tells you how much electromagnetic power an ideal blackbody emits into a given direction, per square meter, and per unit spectral interval. In practice it underpins infrared thermography, optical pyrometry, lamp design, and stellar temperature estimates. This calculator reports radiance as a function of wavelength (Bλ) or frequency (Bν).
The computation uses fixed physical constants: Planck’s constant h = 6.62607015×10−34 J·s, speed of light c = 2.99792458×108 m/s, and Boltzmann constant k = 1.380649×10−23 J/K. Exponential terms can grow rapidly, so the code evaluates exp(x)−1 safely to avoid subtractive loss for small x and overflow for large x.
Bλ(λ,T) and Bν(ν,T) describe the same spectrum but use different independent variables, so they do not have the same numeric value at matching λ and ν. If your instrument bandwidth is specified in nanometers, use the wavelength form. If it is specified in hertz, gigahertz, or terahertz, use the frequency form.
For wavelength form, the SI unit is W·sr−1·m−3, meaning per meter of wavelength. Many optics workflows prefer per nanometer or per micrometer, so the calculator converts by multiplying by 10−9 (per nm) or 10−6 (per µm). For frequency form, SI is W·sr−1·m−2·Hz−1, with convenient per GHz and per THz options.
Common reference points help you sanity-check results. A tungsten filament lamp is often around 2600–3000 K, the Sun’s effective temperature is about 5778 K, and many industrial furnaces operate near 1200–2000 K. In the visible band (roughly 380–780 nm), radiance rises strongly with temperature and shifts toward shorter wavelengths as T increases.
The calculator also returns Wien’s peak wavelength using λmax = b/T with b = 2.897771955×10−3 m·K. For example, 3000 K peaks near 966 nm (near infrared), while 5778 K peaks near 501 nm (green visible). Remember that λmax is a peak in wavelength space; frequency space peaks at a different location.
Real materials emit less than a blackbody, captured by emissivity ε between 0 and 1. Polished metals can be below 0.2 in parts of the infrared, while painted or oxidized surfaces can be 0.8–0.95. This tool scales spectral and integrated radiance by ε, which is a useful first-order model when detailed spectral emissivity curves are unavailable.
Use single-point mode for quick checks (for example, radiance at 10 µm for a thermal sensor), then enable the spectrum table to generate a curve. Choose linear spacing for narrow bands and logarithmic spacing for wide spans such as 0.2–20 µm. Export CSV for plotting and fitting, or PDF for lab notes and reports.
Bλ is radiance per unit wavelength, while Bν is radiance per unit frequency. They describe the same physical spectrum, but the numerical values differ because the spectral interval (dλ vs dν) is defined differently.
Spectral radiance is reported per unit spectral width. In wavelength form, “per meter” introduces m⁻³ after combining area and wavelength. In frequency form, the “per hertz” term appears explicitly as Hz⁻¹.
Use kelvin for the formula. Convert from Celsius with T(K) = T(°C) + 273.15. If you enter Celsius directly, results will be incorrect because Planck’s law depends on absolute temperature.
Many thermal cameras operate in 8–14 µm, while some sensors use 3–5 µm. For hot sources, include shorter wavelengths too. Log spacing is helpful if you are spanning from visible into mid-IR.
If you do not know the surface, start with ε = 1 for an upper bound. Painted, matte, or oxidized surfaces are often 0.8–0.95. Polished metals can be much lower and vary strongly with wavelength.
At very short wavelengths or low temperatures, the exponential term becomes extremely large, pushing radiance toward zero. At extremely small wavelengths with high temperature, intermediate steps may overflow. Use realistic ranges and consider log spacing for stability.
Enable the spectrum table, calculate, then download CSV. Import the CSV into your plotting tool and graph the first column (wavelength or frequency) versus the second column (radiance). Use logarithmic axes when values span many decades.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.