Settling Time Calculator
Declared exponential-envelope settling bound−lnε/(ζωn), not exact oscillatory crossing or universal4/(ζωn).Actual0<ε<1. Actual independently established compatible SI units/model context; conditional arithmetic, not code compliance, engineering design or safe operation approval.
Description
A specified exponential envelope reaches a chosen fraction according to its decay rate.
A specified exponential envelope reaches a chosen fraction according to its decay rate.1
This tool calculates that settling-envelope time without locating the exact crossings of an oscillatory response.
When to use Settling Time Calculator
Use this tool to calculate that settling-envelope time without locating the exact crossings of an oscillatory response.
How to use Settling Time Calculator and how it works
- Prepare callerSpecifiedEnvelopeFraction, dampingRatio, naturalAngularFrequencyPerSecond, with the units, conventions and assumptions below.
- Enter the required fields and run Settling Time Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerSpecifiedEnvelopeFraction | Caller Specified Envelope Fraction. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| dampingRatio | Dimensionless damping ratio zeta on the tool-specific branch below. | number | Required; strictly positive; finite; other constraints below |
| naturalAngularFrequencyPerSecond | Natural Angular Frequency Per Second. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Supply tolerance epsilon strictly between zero and one and positive damping ratio zeta and natural angular frequency omega in radians per second. Return -ln(epsilon)/(zeta*omega) in seconds. The implementation accepts zeta above or equal to one, but this envelope estimate is not an exact settling-time solution for every damping regime or system.
settlingSeconds=-ln(tolerance)/(dampingRatio*naturalAngularFrequency) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Envelope-based settling-time estimate in seconds. | number |
{
"input": {
"callerSpecifiedEnvelopeFraction": 0.02,
"dampingRatio": 0.5,
"naturalAngularFrequencyPerSecond": 2
},
"output": {
"result": {
"value": 3.912023005428146
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Vibration Transmissibility Calculator for a complementary operation: An ideal single-degree-of-freedom transmissibility depends on damping and excitation-to-natural-frequency ratio.
Use Step Response Overshoot Calculator for a complementary operation: Ideal underdamped second-order step overshoot depends on damping ratio within a restricted branch.
References
-
Settling Time Calculator — tool.io
Similar or alternative tools
- Vibration Transmissibility Calculator
An ideal single-degree-of-freedom transmissibility depends on damping and excitation-to-natural-frequency ratio.
- Step Response Overshoot Calculator
Ideal underdamped second-order step overshoot depends on damping ratio within a restricted branch.