Planck's Law of Radiation Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/3/2026
Planck's law gives the spectral radiance B(λ,T) = (2hc²/λ⁵) ÷ (exp(hc/(λkT)) − 1), where λ is the wavelength and T is the blackbody's absolute temperature. For the Sun (T≈5778 K) at 500 nm, this gives about 2.64×10¹³ W·sr⁻¹·m⁻³, a classic value cited in radiation physics.
Explanation
Planck's law precisely describes how a blackbody — an idealized object that perfectly absorbs and re-emits all the energy it receives — distributes its thermal radiation across different wavelengths, at a given temperature. It is historically the formula that marked the birth of quantum physics: Max Planck had to introduce the assumption that energy is exchanged in discrete amounts ("quanta") to get a formula that matched experimental data, thereby resolving what was known as the "ultraviolet catastrophe" — the complete failure of classical theories to correctly predict radiation at short wavelengths. This law is in fact the master formula from which two other well-known radiation laws are derived: by finding at which wavelength the spectral radiance reaches its maximum for a given temperature, you get exactly Wien's displacement law; and by summing (mathematically, integrating) this radiance over every possible wavelength, you get the total radiated power described by the Stefan-Boltzmann law. The Sun, with a surface temperature of about 5,778 K, therefore emits most of its radiation in the visible and near-infrared range, which is no coincidence: it's precisely in that range of wavelengths that the human eye evolved to be sensitive. For other foundational relationships in classical physics, see also our Coulomb's law calculator and our Newton's second law calculator, both from the pre-quantum physics that Planck's law helped move beyond.
Example: the Sun at its peak emission wavelength
Inputs
Temperature T = 5,778 K (the Sun's surface). Wavelength λ = 501.518 nm, close to the maximum predicted by Wien's law.
Calculation
B = (2×h×c² ÷ λ⁵) ÷ (exp(h×c ÷ (λ×k×T)) − 1), with h, c, and k the usual physical constants.
Result
This gives B ≈ 2.64×10¹³ W·sr⁻¹·m⁻³ — slightly higher than the value obtained at 500 nm or 510 nm, confirming the maximum does sit at this wavelength, independently predicted by Wien's law.
Frequently asked questions
Why is Planck's law said to have "saved" classical physics?
Before Planck, the classical theory of radiation (the Rayleigh-Jeans law) predicted that the energy radiated by a blackbody should become infinite at short wavelengths (in the ultraviolet), which is physically absurd and completely contradicted by experiment. By assuming energy could only be exchanged in discrete packets proportional to frequency (E=hf), Planck obtained a formula that matched measurements perfectly at every wavelength — unintentionally laying the first cornerstone of quantum mechanics.
Is the Sun a true blackbody?
Not exactly, but its emission spectrum resembles that of an ideal blackbody at about 5,778 K closely enough that this approximation is widely used in astrophysics. Reality is slightly more complex (absorption lines from elements present in the solar atmosphere, local temperature variations), but the blackbody model remains an excellent starting point for understanding and calculating stellar radiation.
What happens at very long wavelengths, like microwaves?
At long wavelengths (and/or low frequencies), the exponential in the formula gets close to 1, and Planck's law naturally simplifies to the classical Rayleigh-Jeans approximation — the same limit classical theory managed to predict correctly, before failing at short wavelengths. The cosmic microwave background, the relic radiation that fills the entire universe at just 2.7 K, in fact follows a blackbody curve very precisely, one of the most famous experimental confirmations of this law.