ONE FORMULA, ONE ANSWER
Mass Spring Damping Ratio Calculator
Check viscous damping relative to critical damping in a linear vibration model. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Mass spring damping ratio ζ
Enter values and select Calculate.
ζ = c / (2 √(m k))
Assumptions
Use c≥0 and m,k>0. Assume one linear degree of freedom with viscous damping. Dry friction and nonlinear dampers are excluded. The damping coefficient written b in the reference is named c here.
Displayed values are floating-point approximations. Measurement uncertainty and design safety factors are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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