Blackbody Spectral Radiance Calculator

Calculator

Wavelength form: Bλ(λ,T) = (2hc²/λ⁵) · 1/(exp(hc/(λkT)) − 1) (W·sr⁻¹·m⁻²·m⁻¹).

Frequency form: Bν(ν,T) = (2hν³/c²) · 1/(exp(hν/(kT)) − 1) (W·sr⁻¹·m⁻²·Hz⁻¹).

Real emission is approximated as ε · B using constant emissivity.

1. Enter temperature in kelvin and emissivity between 0 and 1.
2. Select wavelength or frequency and provide the value with units.
3. Choose output form and matching unit scaling.
4. Optional: enable band integration and set start, end, and steps.
5. Click Calculate to show results above the form.
6. Download CSV or PDF for quick reporting.

Spectral radiance quantifies emitted power in a specific direction per area and per spectral interval. It supports band comparisons, radiometric validation, and accurate thermal modeling across instruments.

Planck’s law defines an ideal spectrum for a source at temperature T. Many surfaces approximate this behavior within limited bands, especially when temperature is stable and the surface is diffuse.

Bλ and Bν describe the same emission but use different spectral intervals. Because the axis transforms nonlinearly, curve shapes and peak locations differ. Compare data using one form consistently.

Raising temperature increases radiance sharply and shifts emission to shorter wavelengths. A quick check is Wien’s displacement: λmax ≈ 2.898×10⁻³/T (m·K). Around 300 K, λmax sits near 9–10 µm.

Emissivity scales radiance: ε·B. This calculator uses constant ε as a practical estimate. For tighter accuracy, use measured ε near your band, since emissivity can vary with finish and wavelength.

Detectors respond over ranges such as 8–14 µm or 3–5 µm. Band integration sums radiance across the interval to estimate band-limited radiance in W·sr⁻¹·m⁻². Increase steps for wide bands or hotter targets.

“Per nm” and “per µm” rescale Bλ, while “per GHz” and “per THz” rescale Bν. Matching the scaling to your plot axis prevents confusion and makes exported values consistent across reports.

Room-temperature sources should show strong mid‑IR radiance and negligible visible radiance. Sun-like temperatures near 5800 K shift power into visible and near‑IR. If outputs look wrong, re-check units, form choice, and ε.

1) What does “per steradian” mean?

It indicates direction. Radiance is given per solid angle, which supports imaging and optical throughput calculations without immediately integrating over viewing angles.

2) Why do Bλ and Bν peaks differ?

They use different spectral intervals. Converting axes redistributes energy across bins, so the maximum occurs at a different coordinate for Bλ than for Bν.

3) Which form should I choose?

Use Bλ for wavelength-based data (nm, µm). Use Bν for frequency-based data (GHz, THz). Keep one form throughout comparisons and reporting.

4) How does emissivity affect results?

It scales radiance linearly: ε·B. Lower ε reduces emission at all wavelengths in this simplified model. Real ε may vary by wavelength and surface condition.

5) How many steps are good for integration?

Start around 1000–3000. If doubling steps changes the band result, increase further. Wider ranges and higher temperatures typically require more steps.

6) Why is visible radiance tiny at 300 K?

Because the spectrum peaks near 10 µm at room temperature. Visible wavelengths are far from the peak, so emission is extremely small until temperatures reach thousands of kelvin.

7) Can I use this at extreme inputs?

Typical UV–IR engineering ranges are fine. Extreme values can overflow the exponential term. Use realistic ranges, validate with reference cases, and increase numeric care when pushing limits.