\[t_p=\sqrt{\frac{\hbar G}{c^5}}\]
Variables
tpPlanck time (s)
hbar[ℏ]reduced Planck constant (J·s)
Ggravitational constant (m³/kg·s²)
cspeed of light (m/s)
Description
What is this formula?
The Planck time formula calculates the smallest meaningful interval of time predicted by modern theoretical physics. It represents the time required for light to travel one Planck length in vacuum.
When to use it
Use this formula when studying quantum gravity, early-universe models, cosmology, and fundamental 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:
tp=√((ℏG)/c^5)
Substitution:
tp=√(((1.055×10^-34)(6.674×10^-11))/(3×10^8)^5)
Result:
tp≈5.39×10^-44 s
Applications
- Quantum gravity
- Early universe studies
- Cosmology
- String theory
- Fundamental physics
- Planck-scale models