\[m_p=\sqrt{\frac{\hbar c}{G}}\]
Variables
mpPlanck mass (kg)
hbar[ℏ]reduced Planck constant (J·s)
cspeed of light (m/s)
Ggravitational constant (m³/kg·s²)
Description
What is this formula?
The Planck mass formula calculates a fundamental mass scale obtained by combining quantum mechanics, gravity, and relativity constants. It defines a characteristic scale where quantum gravitational effects become important.
When to use it
Use this formula when studying quantum gravity, black hole physics, cosmology, and Planck-scale phenomena.
Example
Data:
ℏ=1.055×10^-34 J·s
c=3×10^8 m/s
G=6.674×10^-11 m³/kg·s²
Formula:
mp=√((ℏc)/G)
Substitution:
mp=√(((1.055×10^-34)(3×10^8))/(6.674×10^-11))
Result:
mp≈2.18×10^-8 kg
Applications
- Quantum gravity
- Black hole physics
- Cosmology
- String theory
- Fundamental physics
- Early universe models