Einstein Coefficient Calculator
Enter the transition frequency and degeneracy ratio. The Einstein Coefficient Calculator instantly computes A (spontaneous emission) and B (stimulated/absorption) coefficients.
About the Einstein Coefficient Calculator
The Einstein Coefficient Calculator is a precise, scientifically accurate tool that computes the Einstein A and B coefficients for quantum transitions between two energy levels. This Einstein Coefficient Calculator implements the fundamental relations derived by Albert Einstein in 1916–1917 that revolutionized our understanding of light-matter interaction and laid the foundation for lasers and masers. Proudly supported by Agri Care Hub.
Scientific Formulas
B₁₂ = (g₂/g₁) B₂₁ (absorption)
h = 6.62607015 × 10⁻³⁴ J s
c = 299792458 m/s
Why This Calculator Is Essential
Einstein coefficients are fundamental in: • Laser physics and masers (stimulated emission) • Astrophysics (radiative transfer in stars and galaxies) • Quantum optics and cavity QED • Atomic and molecular spectroscopy • Quantum computing (optical transitions) • Understanding blackbody radiation Einstein's prediction of stimulated emission from the B coefficient directly led to the invention of the laser — one of the most important technologies of the 20th century.
How to Use
- Enter transition frequency ν (e.g., 1.42 GHz for hydrogen 21 cm line).
- Enter degeneracy ratio g₁/g₂ (lower level / upper level).
- Click “Calculate Einstein Coefficients”.
- Get A₂₁, B₂₁, B₁₂, and radiative lifetime.
When Should You Use This Tool?
- Laser design and population inversion analysis
- Astrophysics radiative transfer modeling
- Atomic physics research
- Quantum optics experiments
- Teaching quantum mechanics and lasers
- Maser and astronomical maser studies
Scientific Foundation
The Einstein coefficients were introduced by Albert Einstein in 1916–1917 to resolve inconsistencies in Planck's blackbody radiation law. The relation A = (8π h ν³ / c³) B is exact in quantum electrodynamics. Full theory at Einstein Coefficient on Wikipedia and all quantum optics textbooks.
Conclusion
The Einstein Coefficient Calculator brings one of Einstein's greatest insights — the prediction of stimulated emission — to your browser with perfect accuracy and beautiful design. Whether you’re a student learning quantum optics, a researcher modeling astrophysical masers, or an engineer designing lasers, this tool delivers precise results every time. For more physics tools, visit Agri Care Hub.