Compute black hole temperature, power, lifetime, and peak wavelength. Switch units, inspect constants, and export. Built for quick checks, study tasks, and comparisons today.
| Example | Mass | Temperature (K) | Power (W) | Lifetime (years) |
|---|---|---|---|---|
| 1.0e5 kg black hole | 1.00000e+5 kg | 1.22690e+18 | 3.56162e+22 | 2.66544e-9 |
| 1.0e8 kg black hole | 1.00000e+8 kg | 1.22690e+15 | 3.56162e+16 | 2.66544 |
| 1.0e11 kg black hole | 1.00000e+11 kg | 1.22690e+12 | 3.56162e+10 | 2.66544e+9 |
| 1 solar mass black hole | 1.98847e+30 kg | 6.17007e-8 | 9.00761e-29 | 2.09568e+67 |
This calculator uses the standard Schwarzschild black hole approximation.
T_H = hbar c^3 / (8 pi G M kB)P = hbar c^6 / (15360 pi G^2 M^2)tau = 5120 pi G^2 M^3 / (hbar c^4)r_s = 2 G M / c^2m_dot = P / c^2lambda_peak = b / T_HS = 4 pi kB G M^2 / (hbar c)
| Name | Symbol | Value |
|---|---|---|
| Gravitational constant | G | 6.67430e-11 m^3 kg^-1 s^-2 |
| Speed of light | c | 2.99792458e8 m/s |
| Reduced Planck constant | hbar | 1.054571817e-34 J s |
| Boltzmann constant | kB | 1.380649e-23 J/K |
| Wien displacement constant | b | 2.897771955e-3 m K |
This Hawking radiation equation calculator estimates how a black hole behaves as it emits thermal radiation. It starts with mass. Then it derives Hawking temperature, emitted power, Schwarzschild radius, evaporation time, and mass loss rate. It also reports peak wavelength and entropy scale. These outputs help learners connect gravity, quantum theory, thermodynamics, and energy transfer. That makes the tool useful for chemistry-adjacent study, physical science review, and interdisciplinary classroom work.
Mass controls every result in the Hawking radiation model. A smaller black hole has a higher temperature. It radiates more power. It loses mass faster. It also evaporates in less time. A larger black hole does the opposite. Its temperature becomes extremely low. Its power output drops sharply. Its lifetime becomes enormous. This relation is important because the Hawking equation is highly nonlinear. Simple mass changes can produce huge output differences.
Temperature shows the effective blackbody temperature associated with Hawking emission. Power estimates the total radiative output. Schwarzschild radius shows the event horizon size for a non-rotating, uncharged black hole. Lifetime estimates total evaporation time under the standard approximation. Mass loss rate converts radiated power into equivalent mass loss using E = mc². Peak wavelength uses Wien’s displacement law, which links temperature and strongest spectral region. Entropy gives another way to understand state count and horizon information.
This page is designed for fast comparison and clean interpretation. You can test gram, kilogram, Earth-mass, or solar-mass values. You can switch output units for temperature, power, lifetime, and length. You can also export results for reports, assignments, or notes. The example table shows scale effects quickly. The formula section explains the physics. The usage section explains the workflow. Together, these features turn one equation set into a practical learning and reference tool.
Because real black holes may spin or carry charge, this calculator uses the standard non-rotating, uncharged case. That keeps the results consistent and easier to compare. It is ideal for concept learning. It is not a full astrophysical simulation. Still, it gives strong intuition about black hole temperature, evaporation, and radiation scaling in practice.
Hawking radiation is the theoretical thermal emission associated with black holes. Quantum effects near the event horizon make the black hole behave like a body with temperature and radiative power.
The Hawking temperature is inversely proportional to black hole mass. When mass decreases, temperature rises quickly. That also increases power and speeds up evaporation.
No. It uses the standard Schwarzschild case. That means the black hole is treated as non-rotating and uncharged, which keeps the equations clean and widely used in teaching.
Evaporation time scales with the cube of mass. Large black holes therefore survive for extremely long periods. Stellar black holes have lifetimes far beyond the current age of the universe.
Peak wavelength is the wavelength linked to the strongest blackbody emission using Wien’s law. It helps show whether the dominant emission is extremely energetic or very weak and long-wave.
Entropy connects horizon area with the number of possible internal states. It is useful for thermodynamics discussions and helps frame Hawking radiation in a broader physical context.
Yes. It fits thermodynamics, energy transfer, radiation concepts, and unit conversion practice. It also supports cross-topic learning for physical chemistry and advanced science courses.
No. They are standard theoretical estimates based on ideal equations and constants. Real astrophysical conditions, rotation, charge, and advanced quantum gravity effects are not included.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.