What this calculator does
Every object emits radiation according to its temperature, and Planck's law describes exactly how much at each wavelength. Working it out was the problem that started quantum mechanics: classical physics predicted infinite emission at short wavelengths, which plainly does not happen.
The temperature dependence is fierce. At 500 nm, in the middle of visible light, a 10,000 K surface emits nearly a thousand times the spectral radiance of a 3,000 K one, which is why hot stars look blue-white and cool ones dull red.
The formula
Planck's law gives spectral radiance from wavelength and temperature using Planck's constant, the speed of light and Boltzmann's constant. Integrating across all wavelengths gives the Stefan-Boltzmann total, which scales with temperature to the fourth power.
| Term | Meaning |
|---|---|
| Spectral radiance | Power emitted per unit area, per unit solid angle, per unit wavelength. |
| Blackbody | An idealised perfect absorber and emitter, which real surfaces approximate to varying degrees. |
| Total emissive power | The Stefan-Boltzmann figure, summing emission across every wavelength. |
The inputs explained
| Field | What to enter |
|---|---|
| Wavelength (λ) (nm) | The wavelength of interest in nanometres. Visible light runs from about 400 to 700. |
| Temperature (T) (K) | The absolute temperature in kelvin. The Sun's surface is about 5,778 K. |
When to use it
Understanding stellar colour
The wavelength of peak emission shifts with temperature, which is why star colour indicates surface temperature.
Estimating thermal emission
The Stefan-Boltzmann total gives the radiated power per square metre at any temperature.
Working with infrared imaging
Objects near room temperature emit almost entirely in the infrared, which is what thermal cameras detect.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does temperature change emission at 500 nm?
Green-light emission from surfaces at three temperatures.
| Temperature | Spectral radiance at this wavelength | Total emissive power (Stefan-Boltzmann, σT⁴) |
|---|---|---|
| 3,000 K | 2.6027e+2 W/(sr·m²·nm) | 4,593.00 kW/m² |
| 5,778 K | 2.6376e+4 W/(sr·m²·nm) | 63,200.70 kW/m² |
| 10,000 K | 2.2726e+5 W/(sr·m²·nm) | 567,037.44 kW/m² |
Questions
Why did this problem start quantum mechanics?
Classical theory predicted emission rising without limit at short wavelengths, the so-called ultraviolet catastrophe. Planck could only match the observed spectrum by assuming energy comes in discrete packets, which he proposed reluctantly and which turned out to be correct.
Why does spectral radiance rise so steeply with temperature?
At a fixed short wavelength, emission is governed by an exponential term that is very sensitive to temperature. Doubling the temperature moves far more of the distribution into the short-wavelength region.
Is anything really a blackbody?
Nothing perfectly, but many things come close. A small hole in a heated cavity is nearly ideal, and stars are a good approximation. Real surfaces are handled by multiplying by an emissivity factor between 0 and 1.
Why is the Sun yellow-white rather than green?
Its peak is near 500 nm, which is green, but it emits across the whole visible range at once. The eye combines that broad mixture as white, which sunlight slightly warmed by the atmosphere renders yellowish.
For the total radiated power alone, see the Stefan-Boltzmann law calculator. For the wavelength of peak emission, see the Wien's displacement law calculator.