Blackbody Radiation - Planck, Wien, and Stefan-Boltzmann
A blackbody absorbs all incident radiation and emits thermal radiation with a spectrum that depends only on temperature. Planck's law gives the complete spectrum, Wien's law predicts peak wavelength, and Stefan-Boltzmann gives total power.
Did our AI summary help? Let us know.
Hotter objects emit at shorter wavelengths—Sun peaks at ~500 nm (green), candle at ~1600 nm (IR) Total power scales as T⁴—doubling temperature increases power by 16× CMB at 2.725 K is the most perfect blackbody spectrum ever measured Planck resolved the UV catastrophe by proposing quantized energy E = hν
Ready to run the numbers?
Why: Blackbody radiation underpins astrophysics (star temperatures), thermal imaging, lighting design, and the cosmic microwave background. Planck's quantum hypothesis (1900) resolved the UV catastrophe and launched quantum mechanics.
How: Wien's law (λ_max = b/T) gives peak wavelength. Stefan-Boltzmann (M = εσT⁴) gives total power. Planck's law B(λ,T) provides the complete spectral distribution. All use NIST physical constants.
Run the calculator when you are ready.
☀️ Sun
5778 K
🧑 Human Body
37°C
💡 Incandescent
2700 K
⭐ Sirius A
9940 K
🔴 Betelgeuse
3500 K
🕯️ Candle
1800 K
🌋 Lava
1200°C
🌌 CMB
2.725 K
Inputs
1.0 = perfect blackbody
BLACKBODY RADIATION RESULTS
Temperature: 5778 K
Calculation Steps
Visualizations
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
The Sun is a near-perfect blackbody at 5778 K—its spectrum matches Planck's law so closely it calibrates telescopes
— Astrophysics
CMB at 2.725 K was discovered accidentally in 1965 by Penzias and Wilson—1978 Nobel Prize
— Nobel Prize History
Planck's quantum hypothesis (1900) proposed E = hν to solve the UV catastrophe, launching quantum mechanics
— Physics History
Infrared cameras detect thermal radiation using Planck's law—measuring radiance at specific wavelengths to calculate temperature
— Thermal Imaging
📋 Key Takeaways
- • Wien's Law: Hotter objects emit at shorter wavelengths — the Sun (5778 K) peaks at ~500 nm (green), while a candle (1800 K) peaks at ~1600 nm (infrared)
- • Stefan-Boltzmann: Total power radiated scales as T⁴ — doubling temperature increases power by 16×, explaining why stars are so luminous
- • Planck's Law: The quantum hypothesis resolved the UV catastrophe — energy is quantized in packets of hν, launching quantum mechanics
- • CMB at 2.725 K: The cosmic microwave background is the most perfect blackbody spectrum ever measured — the cooled remnant of the Big Bang
💡 Did You Know?
🔬 How It Works
Blackbody Radiation Fundamentals
A blackbody is an idealized object that absorbs all incident radiation and emits thermal radiation with a spectrum that depends only on temperature. Real objects approximate blackbodies with emissivity (ε) less than 1.0.
The Three Laws
🎯 Expert Tips
Use Wien's law to estimate temperature from color — red hot (~1000 K) peaks at ~2900 nm (IR), white hot (~6000 K) peaks at ~480 nm (blue)
Remember T⁴ scaling — a 1000 K object radiates 16× more power than a 500 K object, not 2×
Emissivity matters for real objects — polished metals (ε ≈ 0.1) radiate much less than black paint (ε ≈ 0.95)
CMB temperature (2.725 K) corresponds to peak wavelength ~1.06 mm — in the microwave region, hence "cosmic microwave background"
📊 Blackbody Laws Comparison
| Law | Formula | What It Predicts | Temperature Dependence |
|---|---|---|---|
| Wien's Displacement | λ_max = b / T | Peak wavelength | Inverse (1/T) |
| Stefan-Boltzmann | M = εσT⁴ | Total power radiated | T⁴ (very strong) |
| Planck's Law | B(λ,T) = (2hc²/λ⁵) × 1/(e^(hc/λkT) - 1) | Complete spectrum | Complex (quantum) |
| Rayleigh-Jeans | B(λ,T) ≈ 2ckT/λ⁴ | Classical limit (long λ) | T (linear) |
❓ Frequently Asked Questions
What is a perfect blackbody?
A perfect blackbody absorbs all incident radiation and emits thermal radiation with a spectrum that depends only on temperature. Real objects approximate blackbodies with emissivity (ε) between 0 and 1. A perfect blackbody has ε = 1.0.
Why does doubling temperature increase power by 16×?
Stefan-Boltzmann law shows M ∝ T⁴. If T doubles, M increases by 2⁴ = 16×. This strong temperature dependence explains why stars are so luminous and why thermal radiation dominates at high temperatures.
What was the ultraviolet catastrophe?
Classical physics predicted that blackbodies should emit infinite energy at short wavelengths (UV). Planck resolved this in 1900 by proposing quantized energy (E = hν), launching quantum mechanics.
How do astronomers determine star temperatures?
By measuring the star's spectrum and finding the peak wavelength using Wien's law (T = b/λ_max). Blue stars (~30,000 K) are hottest, red stars (~3000 K) are coolest.
What is the cosmic microwave background?
The CMB is radiation from the early universe, now cooled to 2.725 K. It has the most perfect blackbody spectrum ever measured, peaking at ~1.06 mm wavelength (microwave region).
How do thermal cameras work?
They detect infrared radiation using Planck's law. By measuring radiance at specific wavelengths, they calculate temperature without contact. Objects at room temperature (~300 K) peak at ~10 μm (long-wave IR).
Why don't we see objects glow until they're very hot?
Objects below ~500°C emit almost entirely in the infrared (invisible). Above ~500°C, they begin glowing red as visible light becomes significant. The Sun (5778 K) peaks in the visible range.
What is emissivity and why does it matter?
Emissivity (ε) is the ratio of an object's radiation to that of a perfect blackbody at the same temperature. Polished metals have low ε (~0.1), while black surfaces have high ε (~0.95). Real objects radiate less than ideal blackbodies.
📊 Blackbody Radiation by the Numbers
📚 Official Sources
⚠️ Disclaimer
This calculator is for educational and design purposes. Real objects have emissivity less than 1.0 and may deviate from ideal blackbody behavior. For critical applications in thermal engineering, astrophysics, or lighting design, consult appropriate references and verify calculations with experimental data.
Related Calculators
Angular Resolution Calculator
Calculate the resolving power of optical systems using Rayleigh criterion and diffraction limits.
PhysicsAperture Area Calculator
Calculate aperture area for circular and non-circular apertures in optical and photography systems.
PhysicsBinoculars Range Calculator
Calculate field of view, magnification, exit pupil, and effective range for binoculars and spotting scopes.
PhysicsBragg's Law Calculator
Calculate X-ray diffraction angles, d-spacings, and wavelengths using Bragg's Law for crystallography.
PhysicsBrewster's Angle Calculator
Calculate Brewster's angle, Fresnel coefficients, and polarization effects at optical interfaces.
PhysicsDiffraction Grating Calculator
Calculate diffraction angles, wavelengths, and spectral analysis for diffraction gratings.
Physics