Blackbody Radiation Calculator for spectral radiance, peak wavelength, exitance and net heat loss. Enter a temperature, or work it out from its peak wavelength or radiant exitance.
Pick nm or µm for wavelength, THz or GHz for frequency, or cm⁻¹ for wavenumber.
Band, Area & Distance
Step-by-Step Working
- T = 5,772 K
- λ = 500 nm = 5 × 10⁻⁷ m
- x = hc ÷ (λkT) = 0.0143878 ÷ (5 × 10⁻⁷ × 5,772) = 4.98537
- B = ε × 2hc² ÷ λ⁵ × 1 ÷ (eˣ − 1) = 2.62385 × 10¹³ W/(m²·sr·m)
- Per nm: 2.62385 × 10¹³ × 1 × 10⁻⁹ = 26,239 W/(m²·sr·nm)
Reference Temperatures
| Source | Temp (K) | Peak λ | Blackbody Exitance (ε = 1) | In Band |
|---|---|---|---|---|
| CMB | 2.725 | 1.063 mm | 3.129 × 10⁻⁶ W/m² | 0% |
| Body (37 °C) | 310.1 | 9.343 µm | 524.7 W/m² | 5.253 × 10⁻²¹% |
| Boiling water | 373.1 | 7.766 µm | 1.099 kW/m² | 1.045 × 10⁻¹⁶% |
| 1,000 K | 1,000 | 2.898 µm | 56.7 kW/m² | 0.0005949% |
| 3,000 K | 3,000 | 965.9 nm | 4.593 MW/m² | 10.9% |
| Yours · Sun | 5,772 | 502 nm | 62.94 MW/m² | 43.77% |
| 10,000 K | 10,000 | 289.8 nm | 567 MW/m² | 39.1% |
Planck Spectrum
Blackbody Radiation Calculator and Planck’s Law
The blackbody radiation calculator works out the light and heat a body gives off from its temperature alone. At its core is Planck’s law, which gives the spectral radiance B, the power leaving each square meter of surface into each steradian, per unit of wavelength.
$$B_\lambda(T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{hc/(\lambda k T)} – 1}$$
Here h is the Planck constant, c is the speed of light, k is the Boltzmann constant, λ is the wavelength and T is the absolute temperature in kelvin. This is the black body radiation formula most people mean, and the blackbody radiation calculator evaluates it at the wavelength you enter. Since 2019 all three constants have exact SI values, as listed in the NIST CODATA table.
Worked Example: the Sun at 500 nm
The tool loads with the Sun’s effective temperature of 5,772 K from the NASA Sun Fact Sheet and green light at 500 nm. First the exponent: hc ÷ (λkT) works out to about 4.99.
$$B = \frac{2hc^2}{(5 \times 10^{-7})^5} \cdot \frac{1}{e^{4.99} – 1} = 2.624 \times 10^{13}\ \text{W/(m}^2\text{ sr m)}$$
Dividing by 10⁹ gives the spectral radiance per nanometer, 26,239 W/(m²·sr·nm), which is the figure the blackbody radiation calculator shows. The line under it gives the spectral exitance, π × B, which is 82,430 W/(m²·nm) leaving the surface in all directions. It also gives the photon rate, 6.604 × 10²² photons per second, per square meter, per steradian and per nanometer.
Wavelength, Frequency or Wavenumber
Spectroscopy often works in frequency or wavenumber instead of wavelength. Pick THz or GHz, or cm⁻¹, in the unit menu and the blackbody radiation calculator switches to the matching form of Planck’s law.
$$B_\nu(T) = \frac{2h\nu^3}{c^2} \cdot \frac{1}{e^{h\nu/(kT)} – 1}$$
The frequency form gives W/(m²·sr·Hz), and the wavenumber form gives W/(m²·sr·cm⁻¹). All three describe the same physical spectrum. They just spread it over different units, so their curves peak at different places.
What Blackbody Radiation Is
A blackbody is an ideal object that absorbs every bit of radiation that falls on it, at every wavelength. It is called “black” because it reflects nothing. When it is warm, it also emits the most radiation any surface can at that temperature, and the spectrum depends only on temperature.
In simple terms, blackbody radiation is the glow every object gives off because of its heat. Another name for it is thermal radiation, and the lab version is often called cavity radiation, since a small hole in a closed, evenly heated box behaves almost exactly like a blackbody.
Gustav Kirchhoff introduced the idea of a black body in 1860. Classical physics then predicted that a blackbody should give off endless energy at short wavelengths, a failure later called the ultraviolet catastrophe. Max Planck solved this “blackbody problem” in 1900 by assuming energy comes in packets of size hν, the first step toward quantum theory.
The Closest Thing to a Perfect Blackbody
The best natural blackbody known is the cosmic microwave background, the leftover glow of the early universe. NASA’s COBE mission found its spectrum to be a nearly perfect blackbody at 2.725 K, so close that the data could not be told apart from the theoretical curve.
Stars are close to blackbodies too, which is why astronomers quote a star’s effective temperature. The CMB is the first row of the tool’s Reference Temperatures table, with a peak wavelength of 1.063 mm.
Peak Wavelength and Wien’s Law
Hotter bodies peak at shorter wavelengths. Wien’s displacement law gives the wavelength of the peak directly, so card 1 of the blackbody radiation calculator doubles as a black body peak wavelength calculator.
$$\lambda_{max} = \frac{b}{T}$$
The constant b is exactly 2.897771955 × 10⁻³ m·K. For the Sun at 5,772 K, the peak sits at 502 nm, in the blue-green part of the visible range. A body at 300 K, close to room temperature, peaks at 9.66 µm in the infrared.
The same card gives the height of that peak, 26,240 W/(m²·sr·nm) for the Sun, and the peak per unit frequency. That frequency peak is 339.3 THz, which corresponds to about 884 nm, not 502 nm, because the two curves spread the spectrum differently. The peak in photon count per unit wavelength falls at 635.8 nm, which the Temperature From Peak λ mode lists.
Black Body Temperature Formula
Wien’s law also runs backward. If you know where a spectrum peaks, pick Temperature From Peak λ and the tool returns T = b ÷ λmax. A peak at 10 µm, the default, means a temperature of 289.8 K.
This is how astronomers estimate the surface temperature of stars from their color. It is also the idea behind thermal cameras, which read the infrared that warm objects give off.
The peak wavelength also affects how sharply a telescope sees the source, since longer wavelengths blur more for the same mirror, as the angular resolution calculator shows. The aperture area calculator gives how much of that light the mirror collects.
Blackbody Spectrum by Temperature
This table runs the blackbody radiation calculator at a range of temperatures. The visible share is the fraction of total output between 380 nm and 750 nm, the tool’s default band.
| Temperature | Peak Wavelength | Exitance (ε = 1) | Visible Share |
|---|---|---|---|
| 2.7255 K (CMB) | 1.063 mm | 3.13 µW/m² | 0% |
| 300 K (room) | 9.66 µm | 459 W/m² | 0% |
| 310.15 K (37 °C) | 9.34 µm | 525 W/m² | 0% |
| 373.15 K (boiling water) | 7.77 µm | 1,099 W/m² | 0% |
| 1,000 K | 2.90 µm | 56.7 kW/m² | 0.0006% |
| 2,000 K | 1.45 µm | 907 kW/m² | 1.28% |
| 3,000 K | 966 nm | 4.59 MW/m² | 10.9% |
| 5,772 K (Sun) | 502 nm | 62.9 MW/m² | 43.8% |
| 10,000 K | 290 nm | 567 MW/m² | 39.1% |
The visible share peaks near the Sun’s temperature, then falls again as hotter bodies push most of their output into the ultraviolet. Below about 798 K (525 °C), known as the Draper point, objects give off too little visible light to glow, and the tool says so in its result note.
Stefan-Boltzmann Law and Radiated Power
Adding up Planck’s law over every wavelength gives the total power leaving each square meter, the radiant exitance M. It rises with the fourth power of temperature, so doubling T raises the output 16 times.
$$M = \varepsilon \sigma T^4$$
The Stefan-Boltzmann constant σ is exactly 5.670374419 × 10⁻⁸ W/(m²·K⁴). At 5,772 K, a blackbody gives off 62.94 MW from each square meter. Card 2 also gives the total radiance, M ÷ π, and the irradiance at a set distance from the source. The Planck Spectrum panel draws the full curve for your temperature, a quick simulation of how the output spreads across wavelengths.
The Full Formula for Stefan’s Law
A real object also absorbs radiation from its surroundings. The full form of Stefan’s law gives the net power a surface of area A loses to surroundings at temperature Tₛ.
$$P_{net} = \varepsilon \sigma A \left(T^4 – T_s^4\right)$$
This is what a net radiation or thermal radiation calculator needs. Open Band, Area and Distance in the tool and enter the area and the surrounding temperature, 2 m² and 300 K by default. Card 4 then shows the power radiated, the power absorbed back and the net loss or gain.
For example, a 1 m² blackbody plate at 100 °C in a 300 K room radiates 1,099 W and absorbs 459 W. Its net loss is about 640 W, far less than the radiated figure alone suggests.
Temperature From Exitance
Pick Temperature From Exitance to solve the Stefan-Boltzmann law for T. A surface radiating 800 W/m² as a blackbody sits at 344.6 K, or about 71.5 °C.
$$T = \left(\frac{M}{\varepsilon \sigma}\right)^{1/4}$$
Lower the emissivity and the same output needs a hotter surface. Card 2 in this mode also lists the mean photon energy, which for any blackbody is about 2.70 kT.
Black Body vs Gray Body Radiation
Real surfaces radiate less than a blackbody at the same temperature. Emissivity ε, between 0 and 1, sets how much less. A gray body has the same emissivity at every wavelength, so its spectrum keeps the blackbody shape but is scaled down by ε.
The calculator treats ε as constant across the spectrum, which is the gray-body model. At ε = 0.9, a surface at 37 °C radiates 472 W/m² instead of 525 W/m². Its peak wavelength does not move, because scaling the whole curve leaves the peak in the same place.
Many real materials have an emissivity that changes with wavelength. For those, the gray-body result is a first estimate, and the tool’s result note says so whenever ε is below 1.
Light in a Chosen Band
Card 3 gives the share of total output that falls between two wavelengths, plus that band’s exitance and radiance. With the default 380 to 750 nm band, it shows how much of the output the eye can see.
For the Sun at 5,772 K, 43.77% of the radiated power falls in that visible band, or 27.55 MW/m². Change the band to 8 to 14 µm for the thermal-camera window, or to any detector’s range, to see how much signal it receives.
Band edges are entered in nm, µm or mm. The wavelength calculator and the frequency calculator convert a detector’s range from THz or other units first.
Example: Sunlight at Earth
Exitance is measured at the surface of the source. To get the irradiance at a distance d from a sphere of radius R, scale it by (R/d)². The tool does this on card 2 from the Source Radius and Distance fields, which default to the Sun’s 695,700 km and 1 AU.
$$E = \sigma T^4 \left(\frac{R}{d}\right)^2$$
That gives 62.94 MW/m² × (695,700 ÷ 149,597,871)² ≈ 1.361 kW/m², the default result on card 2. NASA’s fact sheets list the solar irradiance at Earth as 1,361 W/m², so a simple 5,772 K blackbody reproduces it closely.
Blackbody Radiation FAQs
These answers cover the questions people search most often about blackbody radiation. The figures come from the same formulas the blackbody radiation calculator uses.
What wavelength is blackbody radiation?
A blackbody emits at every wavelength, from radio waves to the ultraviolet and beyond. The temperature only decides where the peak sits and how much power each part of the spectrum carries.
Objects near room temperature peak around 10 µm in the infrared. A 3,000 K body peaks just beyond visible red at 966 nm. The Sun peaks at 502 nm, and a 10,000 K star peaks in the ultraviolet at 290 nm.
Is blackbody radiation heat?
Blackbody radiation is one way heat moves, along with conduction and convection. It needs no material in between, which is how the Sun’s energy crosses empty space to reach Earth.
At everyday temperatures nearly all of it is infrared, which is why you feel a warm stove before you see it glow. At higher temperatures part of it becomes visible light.
What happens when a blackbody becomes hotter?
Two things happen at once. The total power rises with T⁴, so a body at twice the temperature radiates 16 times more. The peak also shifts to a shorter wavelength in proportion to 1/T.
That shift is why heated metal glows dull red, then orange, then yellow-white as it warms. The whole curve also grows taller at every wavelength, so a hotter body outshines a cooler one everywhere in the spectrum.
What are examples and uses of blackbody radiation?
The Sun and other stars, a glowing stove element, molten metal and the filament in an incandescent bulb are all close to blackbody emitters. The cosmic microwave background is the most precise natural example.
Blackbody physics is used to measure star temperatures, to calibrate infrared thermometers and thermal cameras, and to design lighting and heaters. Radiation pyrometers read the temperature of a furnace or a molten pour without touching it.
What are the 7 types of radiation?
The electromagnetic spectrum is usually split into seven bands, from long to short wavelengths. They are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.
A blackbody emits in all of them, but its peak band depends on temperature. The 2.7 K CMB peaks in microwaves, a person peaks in infrared, and the Sun peaks in visible light.
Which tool is used to measure radiation?
For thermal radiation, an infrared thermometer, a radiation pyrometer or a thermal camera measures it. A bolometer or thermopile measures total radiant power, and a spectrometer records the full spectrum to compare with Planck’s law.
Ionizing radiation such as gamma rays is a different measurement, made with a Geiger counter or a dosimeter. Those devices are not used for blackbody work. More tools for light and optics sit on the optics calculators hub.