Calculator Inputs
Example Data Table
| Mass (kg) | Temperature (K) | Power (W) | Energy in 1 hour (J) | Lifetime (years) |
|---|---|---|---|---|
| 1.0e5 | 1.227e18 | 3.562e22 | 1.282e26 | 2.665e-9 |
| 1.0e8 | 1.227e15 | 3.562e16 | 1.282e20 | 2.665e0 |
| 1.0e11 | 1.227e12 | 3.562e10 | 1.282e14 | 2.665e9 |
| 5.0e11 | 2.454e11 | 1.425e9 | 5.129e12 | 3.332e11 |
Formula Used
This calculator uses standard formulas for a non rotating, uncharged black hole.
- Hawking temperature:
T = ħc³ / (8πGMkB) - Radiated power:
P = ħc⁶ / (15360πG²M²) - Total energy over time:
E = P × t - Schwarzschild radius:
rs = 2GM / c² - Mass loss rate:
dM/dt = -P / c² - Evaporation lifetime:
τ = 5120πG²M³ / (ħc⁴) - Peak wavelength guide:
λmax = b / T
How to Use This Calculator
- Enter a black hole mass value.
- Select the mass unit you want to use.
- Enter a time span for energy emission.
- Select the matching time unit.
- Choose the energy output unit.
- Set your preferred number notation and decimal places.
- Press Calculate to show results above the form.
- Use CSV or PDF export after calculation.
About Hawking Radiation Energy
Why Hawking Radiation Matters
Hawking radiation describes the slow quantum emission from a black hole horizon. This calculator helps you estimate energy output from a chosen mass. It also reports temperature, power, radius, mass loss rate, and expected lifetime. That makes it useful for physics students, teachers, and researchers reviewing black hole evaporation.
A black hole is not fully dark in quantum theory. Particle pairs can appear near the event horizon. One partner can escape. The other can fall inward. The escaping particle carries energy away. Over time, the black hole loses mass. Smaller black holes radiate more strongly. Larger black holes radiate far more slowly.
What This Calculator Shows
The main result is emitted Hawking radiation energy over a selected time span. The tool also calculates Hawking temperature in kelvin and electron volts. It estimates radiated power in watts, Schwarzschild radius in meters, and mass loss rate in kilograms per second. Peak wavelength is included as a simple thermal guide. Lifetime is also shown in seconds and years.
Interpreting the Output
Very massive black holes have tiny power values. Their temperatures are extremely low. Their lifetimes are enormous. Small black holes behave differently. They become hotter, brighter, and shorter lived. Because of that trend, the mass field controls every major result. Changing the time field only changes total emitted energy. It does not change the black hole temperature or power.
Practical Uses and Limits
This Hawking radiation energy calculator is ideal for classroom exercises, astrophysics notes, and quick validation checks. It is based on standard simplified formulas for a non rotating, uncharged black hole. Real emission spectra are more complicated. Greybody factors, spin, and charge can change exact values. Even so, the calculator gives a strong first estimate and a clear comparison framework.
Flexible Input Design
You can enter mass in kilograms, grams, Earth masses, or solar masses. You can select seconds, minutes, hours, days, or years for duration. That makes the calculator easier to test across many scales. Export tools also help you save numeric results for assignments, reports, and comparison tables without rewriting values by hand.
Sample tables show output shifts when black hole mass changes dramatically.
FAQs
1. What does this calculator estimate?
It estimates Hawking radiation energy over a chosen time. It also reports temperature, power, radius, mass loss rate, thermal photon energy, and evaporation lifetime.
2. Does a larger black hole radiate more energy?
No. Larger black holes are colder and less luminous. Power falls with the square of mass, so very massive black holes emit extremely weak Hawking radiation.
3. Why does the tool show temperature in eV too?
Electron volts are common in physics. Showing temperature as an equivalent energy scale makes it easier to compare Hawking radiation with particle and radiation processes.
4. Is this valid for rotating or charged black holes?
Not exactly. This version uses the simple Schwarzschild case. Rotation, charge, and greybody effects can change detailed emission rates and spectral behavior.
5. What changes when I increase the time span?
Only the total emitted energy changes directly. Temperature, power, and radius depend on mass, not on the duration you selected.
6. Why are many outputs shown in scientific notation?
Black hole quantities often become extremely large or small. Scientific notation keeps the table readable and avoids misleading rounding.
7. How does the PDF option work?
The PDF button creates a simple result document in your browser using the current table values. It is useful for quick saving and sharing.
8. Can I use solar mass input directly?
Yes. Choose the solar mass option, enter the value, and the calculator converts it to kilograms before running all physics formulas.