Blackbody Radiation Calculator
Calculate peak wavelength, total power, and other blackbody radiation properties
Common values: Room temp ≈ 300 K, Sun ≈ 5778 K, Earth ≈ 288 K
How to Use This Calculator
Enter the Temperature
Input the temperature of the blackbody in Kelvin. Remember that Kelvin = Celsius + 273.15. For example, the Sun's surface is approximately 5778 K.
Select Calculation Type
Choose what you want to calculate: peak wavelength (Wien's law), total radiated power per unit area (Stefan-Boltzmann law), or use Wien's displacement law directly.
Calculate
Click the "Calculate" button to get the result. The calculator will show the peak wavelength in nanometers or the total radiated power in watts per square meter.
Formulas
Wien's Displacement Law
λ_max = b / T
Where:
- λ_max = Wavelength of maximum emission (in meters)
- b = Wien's displacement constant = 0.0028978 m·K
- T = Temperature (in Kelvin)
Stefan-Boltzmann Law
P = σ × T⁴
Where:
- P = Total power radiated per unit area (in W/m²)
- σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/(m²·K⁴)
- T = Temperature (in Kelvin)
Example Calculation (Sun's Surface):
Temperature = 5778 K
Peak Wavelength (Wien's Law):
λ_max = 0.0028978 / 5778 = 5.01 × 10⁻⁷ m = 501 nm
Total Power (Stefan-Boltzmann):
P = 5.67 × 10⁻⁸ × (5778)⁴ = 6.33 × 10⁷ W/m²
About Blackbody Radiation Calculator
A blackbody is an idealized physical object that absorbs all incident electromagnetic radiation and emits radiation at all wavelengths. The spectrum of radiation emitted by a blackbody depends only on its temperature, described by Planck's law. This calculator uses two fundamental laws of blackbody radiation: Wien's displacement law (which determines the peak wavelength) and the Stefan-Boltzmann law (which determines total radiated power).
When to Use This Calculator
- Astronomy: Calculate the peak wavelength and luminosity of stars based on their surface temperatures
- Thermal Physics: Understand how temperature relates to emitted radiation in thermal systems
- Engineering: Design heating systems, thermal imaging devices, and radiative cooling systems
- Climate Science: Study Earth's radiation budget and greenhouse effect
- Educational Purposes: Learn about quantum mechanics and thermal radiation principles
Why Use Our Calculator?
- ✅ Multiple Calculations: Calculate peak wavelength, total power, or use Wien's law
- ✅ Accurate Constants: Uses precise physical constants for calculations
- ✅ Instant Results: Get blackbody radiation properties immediately
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works perfectly on all devices
Common Applications
Stellar Astronomy: Astronomers use blackbody radiation calculations to determine stellar temperatures, sizes, and distances. By measuring the peak wavelength of a star's spectrum, they can calculate its surface temperature using Wien's law.
Thermal Imaging: Thermal cameras detect infrared radiation emitted by objects. Understanding blackbody radiation helps engineers design and calibrate thermal imaging systems for medical, industrial, and security applications.
Climate Science: Earth radiates energy as a blackbody. Calculations help scientists understand the planet's energy balance, greenhouse effect, and climate change by analyzing how Earth's temperature relates to its radiation output.
Tips for Best Results
- Always use temperature in Kelvin (K = °C + 273.15)
- Peak wavelength decreases as temperature increases (hotter objects emit at shorter wavelengths)
- Total radiated power increases dramatically with temperature (proportional to T⁴)
- Real objects are not perfect blackbodies but approximate them - use emissivity factors for real materials
- Remember that the Sun's peak emission is in the visible range (around 500 nm), which is why we see it as yellow-white
Frequently Asked Questions
What is a blackbody?
A blackbody is an idealized object that absorbs all radiation incident on it and emits radiation at all wavelengths. Real objects approximate blackbodies - for example, the Sun is a near-blackbody, and stars are often modeled as blackbodies in astronomy.
Why does peak wavelength decrease with temperature?
According to Wien's displacement law, the peak wavelength is inversely proportional to temperature. As temperature increases, the object emits more energy at shorter wavelengths. This is why hot objects glow red, then white, then blue-white as they get hotter.
What's the difference between Wien's law and Stefan-Boltzmann law?
Wien's law tells you the wavelength where maximum emission occurs, while Stefan-Boltzmann law tells you the total power radiated across all wavelengths. Both are needed to fully characterize blackbody radiation.
Why is the Stefan-Boltzmann law proportional to T⁴?
The T⁴ dependence comes from integrating Planck's law over all wavelengths and all directions. This means that doubling the temperature increases radiated power by a factor of 16 (2⁴), making temperature extremely important for radiative heat transfer.
Do real objects behave like blackbodies?
Real objects are not perfect blackbodies. They have an emissivity factor (ε) ranging from 0 to 1, where 1 is a perfect blackbody. Most real materials have emissivities between 0.8 and 0.95. The formulas can be modified by multiplying by emissivity for real materials.