Blackbody Radiation Calculator
From stars to lightbulbs, see how temperature shapes the light they emit. Calculate peak color and total power for any hot object.
λ_max = b/T | P = σT⁴ | B(λ,T) = 2hc²/λ⁵ × 1/(e^(hc/λkT) - 1)
Visible: 400-700 nm
About Blackbody Radiation:
A blackbody is an idealized object that absorbs all incident radiation and emits radiation based solely on its temperature. The Sun, stars, and incandescent objects approximate blackbody radiators. Hotter objects emit more energy and at shorter wavelengths.
How the Blackbody Radiation Calculator Works
Enter the temperature of the blackbody in Kelvin, Celsius, or Fahrenheit. The calculator converts to Kelvin for all calculations. Specify whether you want peak wavelength, total power, or spectral radiance at a specific wavelength.
The calculator applies Wien's Displacement Law (λ_max = b/T) for peak wavelength and Stefan-Boltzmann Law (P = σAT⁴) for total power. For spectral radiance, it uses Planck's Law to calculate intensity at specific wavelengths.
Results show peak wavelength (with color indication), total radiated power per unit area, and a spectral distribution curve. The visible spectrum is highlighted to show what color the object would appear.
When You'd Actually Use This
Stellar temperature estimation
Determine star temperatures from their color. Blue stars are hot (30,000 K), red stars are cool (3,000 K). Our Sun peaks in green at 5,800 K.
Incandescent bulb design
Calculate filament temperature and efficiency. Tungsten filaments at 2,800 K emit mostly infrared - only 5% visible light explains their inefficiency.
Thermal imaging analysis
Understand infrared emission from objects. Room temperature objects (300 K) peak at 10 μm - far infrared, invisible to human eyes.
Industrial furnace monitoring
Estimate furnace temperature from glow color. Red hot ≈ 800°C, orange ≈ 1,000°C, yellow ≈ 1,200°C, white hot ≈ 1,500°C+.
Climate science calculations
Model Earth's radiation balance. Earth radiates as a ~288 K blackbody. Greenhouse gases trap some of this outgoing infrared radiation.
Pyrometer temperature measurement
Understand non-contact thermometers. Optical pyrometers measure temperature by detecting emitted radiation intensity at specific wavelengths.
What to Know Before Using
Blackbody is an ideal emitter.A perfect blackbody absorbs all radiation and emits according to temperature alone. Real objects emit less - characterized by emissivity (0 to 1).
Hotter objects emit more and shift bluer.Total power increases as T⁴ (dramatically). Peak wavelength shifts inversely with T. Double the temperature, halve the peak wavelength.
Peak wavelength isn't the only emission.Blackbodies emit a continuous spectrum. The peak is just the maximum. Significant energy is emitted at wavelengths on both sides of the peak.
Color perception is complex.An object peaking in green doesn't look green. Our eyes integrate the whole spectrum. The Sun peaks in green but appears white/yellow.
Pro tip: For real objects, multiply blackbody results by emissivity. Polished metals have low emissivity (~0.05). Black paint has high emissivity (~0.95). Human skin is ~0.98 in infrared.
Common Questions
Why is it called "black" body?
A blackbody absorbs all incident radiation (appears black). But when hot, it emits radiation. A perfect absorber is also a perfect emitter.
What wavelength does room temperature peak at?
At 20°C (293 K), peak wavelength is about 9.9 μm - far infrared. This is why thermal cameras operate in the 8-14 μm range.
Do humans emit blackbody radiation?
Yes, approximately. At 37°C, we emit infrared radiation peaking around 9.3 μm. This is what thermal cameras detect.
What's the Stefan-Boltzmann constant?
σ = 5.67 × 10⁻⁸ W/(m²⋅K⁴). It relates temperature to radiated power. The T⁴ dependence means small temperature changes cause large power changes.
Why don't we glow in the dark?
We do glow - in infrared! Our eyes can't see infrared. At ~2,000 K, objects start glowing visibly (red hot). We're far too cool at 310 K.
What's Wien's displacement constant?
b ≈ 2.898 × 10⁻³ m⋅K. Peak wavelength (meters) = b / T (Kelvin). Hotter objects have shorter peak wavelengths.
How does this relate to the UV catastrophe?
Classical physics predicted infinite UV emission from hot objects - the "UV catastrophe." Planck's quantum hypothesis resolved this, founding quantum mechanics.
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