\[E_p=\sqrt{\frac{\hbar c^5}{G}}\]
Variables
EpPlanck energy (J)
hbar[ℏ]reduced Planck constant (J·s)
cspeed of light (m/s)
Ggravitational constant (m³/kg·s²)
Description
What is this formula?
The Planck energy formula calculates a fundamental energy scale obtained from quantum mechanics, relativity, and gravity constants. It represents an energy level where quantum gravitational effects are expected to become dominant.
When to use it
Use this formula when studying quantum gravity, Planck-scale physics, high-energy systems, and theoretical cosmology.
Example
Data:
ℏ=1.055×10^-34 J·s
c=3×10^8 m/s
G=6.674×10^-11 m³/kg·s²
Formula:
Ep=√((ℏc^5)/G)
Substitution:
Ep=√(((1.055×10^-34)(3×10^8)^5)/(6.674×10^-11))
Result:
Ep≈1.96×10^9 J
Applications
- Quantum gravity
- High-energy physics
- Cosmology
- Black hole studies
- Fundamental physics
- Early universe models