\[l_p=\sqrt{\frac{\hbar G}{c^3}}\]
Variables
lpPlanck length (m)
hbar[ℏ]reduced Planck constant (J·s)
Ggravitational constant (m³/kg·s²)
cspeed of light (m/s)
Description
What is this formula?
The Planck length formula calculates the smallest fundamental length scale predicted by modern physics. It combines gravity, relativity, and quantum mechanics into a single quantity.
When to use it
Use this formula when studying quantum gravity, Planck-scale physics, cosmology, and theoretical physics.
Example
Data:
ℏ=1.055×10^-34 J·s
G=6.674×10^-11 m³/kg·s²
c=3×10^8 m/s
Formula:
lp=√((ℏG)/c^3)
Substitution:
lp=√(((1.055×10^-34)(6.674×10^-11))/(3×10^8)^3)
Result:
lp≈1.616×10^-35 m
Applications
- Quantum gravity
- String theory
- Cosmology
- Black hole studies
- Fundamental physics
- Early universe models