Calculator Inputs
Example Data Table
These sample values are illustrative and rounded for easy comparison.
| Temperature (K) | Peak Wavelength (µm) | Total Emissive Power (W/m²) | Approx. Visible Fraction (%) | Example Interpretation |
|---|---|---|---|---|
| 300 | 9.6592 | 459.3003 | 0.0000 | Room-temperature thermal infrared emitter. |
| 1200 | 2.4148 | 117,573.2022 | 0.3400 | Hot industrial furnace surface. |
| 2500 | 1.1591 | 2.2149e+6 | 9.5000 | Bright incandescent source region. |
| 5800 | 0.4996 | 6.4160e+7 | 43.5000 | Sun-like surface approximation. |
Formula Used
1) Planck’s Law for Spectral Radiance
Bλ(T) = [2hc² / λ⁵] / [ehc/(λkT) − 1]
This gives spectral radiance in W·sr⁻¹·m⁻³ for an ideal radiator at temperature T.
2) Spectral Emissive Power
Mλ(T) = ε π Bλ(T)
The calculator treats the surface as a Lambertian graybody using emissivity ε.
3) Wien’s Displacement Law
λpeak = b / T
Here b = 2.897771955 × 10−3 m·K. Higher temperatures shift the peak toward shorter wavelengths.
4) Stefan–Boltzmann Law
M = εσT⁴
This returns total emissive power density in W/m² across all wavelengths.
5) Photon Energy
E = hc / λ
The tool reports photon energy at the selected analysis wavelength and at the Wien peak wavelength.
6) Band Power by Numerical Integration
Band exitance is estimated using trapezoidal integration of Mλ over the chosen wavelength interval.
This helps estimate how much total radiated energy lies inside your selected spectral band.
How to Use This Calculator
- Enter the source temperature in kelvin.
- Set emissivity between 0 and 1 to model a non-ideal surface.
- Provide the emitting surface area in square meters.
- Choose the wavelength range for the graph and selected-band integration.
- Set an analysis wavelength for point-by-point radiance and photon energy outputs.
- Choose enough sample points for a smooth spectral curve.
- Press the calculate button to display results above the form.
- Use the CSV and PDF buttons to export the summary table.
FAQs
1) What does this calculator plot?
It plots spectral emissive power versus wavelength for your chosen temperature and emissivity. The curve shows where emitted energy concentrates across the spectrum.
2) What is the difference between a blackbody and a graybody?
A perfect blackbody has emissivity of 1 at all wavelengths. A graybody uses emissivity below 1, so it emits less energy while keeping the same basic spectral shape here.
3) Why does the peak wavelength move left when temperature rises?
Wien’s law states that peak wavelength is inversely proportional to temperature. As temperature increases, the strongest emission shifts toward shorter wavelengths and higher photon energies.
4) Why can visible output be nearly zero at room temperature?
Room-temperature objects radiate mainly in the infrared, not the visible band. Their peak wavelength is far longer than visible light, so visible power becomes extremely small.
5) Does emissivity change total power only, or the curve too?
In this graybody model, emissivity scales the spectral values and total power together. The curve shape stays similar, but every plotted value drops proportionally.
6) Which wavelength range should I choose?
Pick a range that covers the expected peak and surrounding tails. For cool objects, extend farther into infrared. For hot sources, include shorter wavelengths too.
7) Are radiance and emissive power the same quantity?
No. Radiance includes directional information per steradian, while emissive power is hemispherical output per unit area. This calculator reports both for clearer interpretation.
8) Can I use this for stars, furnaces, and filaments?
Yes. It works well for idealized thermal emitters and graybody approximations. Real materials can have wavelength-dependent emissivity, so measured spectra may differ from this simplified model.