Critical Damping Coefficient Calculator

How it is calculated

For a mass m on a spring of stiffness k, the tool computes three values: the critical damping coefficient cc = 2·√(k·m) in N·s/m, the natural angular frequency ωn = √(k / m) in rad/s, and the natural frequency fn = ωn / (2π) in Hz. Use SI units: mass in kilograms and stiffness in newtons per metre. Results are shown with four decimals.

The mass must be above zero and the stiffness cannot be negative; a stiffness of exactly 0 is accepted and just gives zeros. Nothing here depends on your actual damper: to judge a real system, divide its damping coefficient c by cc, giving the damping ratio ζ = c / cc. Below 1 the motion oscillates, at 1 it is critically damped and above 1 it creeps back without overshoot.

Common mistakes

• Entering mass in grams or stiffness in N/mm. The units must be kg and N/m; a spring rated 5 N/mm is 5000 N/m, and skipping that conversion makes cc about 32 times too small.
• Confusing ωn in rad/s with fn in Hz. They differ by 2π: 20 rad/s is only about 3.18 oscillations per second.
• Treating cc as the damping your system has. It is the target value for no overshoot, so compare your real damper's c with it to get the damping ratio.
• Using the weight in newtons instead of the mass in kilograms. A 20 N weight is about 2.04 kg, not 20 kg.
• Applying it to a system with several masses or springs as if it were one. The tool assumes a single mass on a single spring; combine the springs to an equivalent stiffness first.