What the damping ratio tells you
The damping ratio (zeta, ζ) is a dimensionless number that describes how oscillations in a system decay after a disturbance. It classifies a system’s response as underdamped (oscillates before settling), critically damped (returns to rest fastest without oscillating), or overdamped (returns to rest slowly without oscillating).
The formula
The damping ratio is ζ = c / cc, where c is the actual damping coefficient and cc = 2√(mk) is the critical damping coefficient (m is mass, k is spring constant). A ζ less than 1 means underdamped, exactly 1 means critically damped, and greater than 1 means overdamped.
This calculator is for general mechanical and control-systems engineering education.
Last reviewed August 2026