ONE FORMULA, ONE ANSWER
Logarithmic Decrement Calculator
Calculate logarithmic decrement from same-direction free-decay peaks. 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
Logarithmic decrement per cycle δ
Enter values and select Calculate.
δ = ln(x₁/x₂)/n
Assumptions
Required: x₁≥x₂>0 and positive integer n for same-direction peaks of linear viscously damped free vibration. n counts full cycles. Forced response, nonlinear friction, noise estimation and additional damping-ratio output are excluded.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
- Northwestern Keten Group · Free vibration and logarithmic decrement
- NASA · M. J. Casiano · NASA/TM-2016-218227
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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