Calculator Inputs
Formula Used
This calculator supports two closely related sensitivity measures:
- Normalized sensitivity (elasticity):
S = (\u0394Y/Y\u2080) / (\u0394P/P\u2080). This is dimensionless and compares influence across different units. - Absolute sensitivity:
dY/dP \u2248 \u0394Y/\u0394P. This keeps the physical units of output per parameter unit.
Both use a finite-difference approximation around a baseline operating point, which is common in experimental physics and model calibration.
How to Use This Calculator
- Enter the baseline output Y\u2080 from your model, sensor, or experiment.
- Pick a method: normalized sensitivity for comparisons, or absolute sensitivity for unit-based interpretation.
- For each parameter, enter P\u2080 (baseline), P\u2081 (perturbed), and the resulting output Y\u2081.
- Press Calculate Sensitivity to view a ranked-style table of influences.
- Use Download CSV or Download PDF to save your results.
Example Data Table
Example: baseline output Y\u2080 = 100 units. Each row changes one parameter and records Y\u2081.
| Parameter | P\u2080 | P\u2081 | Y\u2080 | Y\u2081 |
|---|---|---|---|---|
| Mass (m) | 10 kg | 10.5 kg | 100 | 102 |
| Length (L) | 2 m | 2.1 m | 100 | 105 |
| Temperature (T) | 300 K | 315 K | 100 | 98 |
Article: Sensitivity Index in Physics
1) Purpose of a sensitivity index
A sensitivity index measures how strongly an output quantity Y responds to a change in an input parameter P near a baseline setting. In laboratory work it prioritizes calibration targets, and in modeling it ranks assumptions by influence.
2) Absolute versus normalized sensitivity
Two common forms are used. Absolute sensitivity approximates dY/dP and carries units of output per unit of parameter. Normalized sensitivity uses S = (ΔY/Y0)/(ΔP/P0), which is dimensionless. If P rises 5% and Y rises 2%, then S = 0.4, indicating a mild positive dependence.
3) Selecting a perturbation size
Finite differences assume the response is nearly linear over the step. In practice, 1% to 10% perturbations are common. Too small can be buried in measurement noise, while too large can mix nonlinear effects. A practical check is to compute S using two step sizes, such as 2% and 6%, and confirm the values are similar.
4) Interpreting sign and magnitude
The sign indicates direction. A negative index means Y decreases when P increases near the baseline. Magnitude indicates strength: |S| < 0.1 is weak, 0.1–1 is moderate, and |S| > 1 is strong. Sorting by |S| helps you spot the dominant drivers quickly.
5) Connecting sensitivity to uncertainty
Sensitivity links parameter uncertainty to output uncertainty. If a parameter has relative uncertainty uP/P0 and the normalized sensitivity is S, then the output’s relative change is roughly S × (uP/P0). Example: S = 1.8 and uP/P0 = 3% implies about 5.4% relative impact on Y
6) Using sensitivities for experiment planning
In sensor physics, sensitivity turns performance requirements into tolerances. Suppose a voltage output changes 0.30 V when a field changes 0.10 T, giving dY/dP ≈ 3.0 V/T. If acceptable drift is 0.02 V, the field should be stable within about 0.0067 T near that operating point.
7) Comparing many parameters fairly
Normalized sensitivity is best when parameters have different units, such as mass, length, and temperature. It supports fair comparison even when the output scale changes. If baseline P0 is near zero, elasticity becomes unstable; in that case, use absolute sensitivity or choose a meaningful reference value.
8) Reporting and traceability
Professional reporting should include the baseline Y0, the perturbation sizes, and whether values are absolute or normalized. Record units for each parameter and the output. If results change with step size, note the nonlinearity.
FAQs
1) What is a sensitivity index?
It quantifies the local influence of a parameter on an output around a baseline. Larger magnitude means stronger effect. The sign shows whether the output increases or decreases as the parameter rises.
2) When should I use normalized sensitivity instead of absolute sensitivity?
Use normalized sensitivity to compare parameters with different units or scales. Use absolute dY/dP when you need a unit-based rate, or when the baseline parameter is near zero and normalization becomes unstable.
3) What happens if P0 equals P1?
If ΔP is zero, a slope cannot be estimated. Change P1 slightly above or below P0, rerun your model or measurement, and enter the new Y1.
4) How should I structure each row?
Use one row per one-at-a-time perturbation. Keep all other parameters fixed so each index represents a clean partial effect. If parameters are coupled, interpret results as local rather than global.
5) Why does the index change when I change the step size?
Step dependence often indicates nonlinearity, noise, or numerical tolerances. Try two step sizes and look for stability. If values vary strongly, treat the system as nonlinear and consider smaller steps or curve fitting.
6) Can I rank parameters using this calculator?
Yes. Rank by the absolute value of the selected metric. Elasticity rankings reflect relative influence. For dY/dP, ranking depends on units, so compare within consistent contexts.
7) How do I interpret a negative sensitivity value?
A negative value means the output decreases as the parameter increases near the baseline. It does not imply a problem; it simply describes direction. Combine sign with magnitude to understand both trend and strength.