TeXipedia

rho

Represents density or mass density in physics and engineering contexts, commonly used as a variable in mathematical equations.

Overview

A versatile Greek letter widely used across multiple scientific disciplines, particularly in physics and engineering calculations.

  • Frequently denotes density in fluid mechanics and material science
  • Used to represent correlation coefficients in statistics
  • Common in electrical engineering to indicate resistivity
  • Appears in quantum mechanics for density matrices
  • Serves as a standard variable in mathematical proofs and theoretical physics equations

Examples

Density function in physics equations

ρ(r)=M4πr2\rho(r) = \frac{M}{4\pi r^2} 
\rho(r) = \frac{M}{4\pi r^2}

Correlation coefficient in statistics

ρX,Y=Cov(X,Y)σXσY\rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} 
\rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y}

Resistivity formula in electrical engineering

ρ=RAL\rho = \frac{RA}{L} 
\rho = \frac{RA}{L}