Sensitivity Analysis Solver Calculator

Model input uncertainty with clear percentage-driven scenarios quickly. Measure derivatives, elasticities, and output swings instantly. See which variables drive decisions across every tested scenario.

Solver Inputs

Choose a model, enter baseline values, and apply percentage shocks to estimate mathematical sensitivity.

Variable 1

Variable 2

Variable 3

Variable 4

Example Data Table

Model Constant / Scale Variable Base Value Coefficient / Exponent Shock %
Linear 12 x 50 0.8 10
Linear 12 y 30 1.1 15
Linear 12 z 18 -0.6 12
Linear 12 w 10 0.3 20

Example baseline result for the linear setup: Y = 12 + (0.8×50) + (1.1×30) + (-0.6×18) + (0.3×10) = 77.2.

Formula Used

Linear model: Y = c + Σ(aᵢxᵢ) Multiplicative model: Y = c × Π(xᵢ^aᵢ) Partial derivative: Linear: ∂Y/∂xᵢ = aᵢ Multiplicative: ∂Y/∂xᵢ = Y(aᵢ / xᵢ) Normalized sensitivity coefficient: Sᵢ = (∂Y/∂xᵢ) × (xᵢ / Y) Central elasticity approximation: Eᵢ ≈ (Y_high - Y_low) / (2 × Y_base × shock_fraction)

The solver computes a baseline output first. It then changes one variable at a time by the chosen shock percentage while keeping all others fixed. That creates one-way sensitivity outputs for low and high cases.

Finally, it applies low shocks to every variable together, then high shocks to every variable together. This gives a combined range, spread percentage, strongest driver ranking, and scenario table for faster mathematical interpretation.

How to Use This Calculator

  1. Select either the linear or multiplicative model based on your mathematical structure.
  2. Enter the constant or scale value that anchors the full equation.
  3. Name each variable, then provide its baseline value, coefficient or exponent, and percentage shock.
  4. Choose the number of decimal places you want in the report.
  5. Press Submit. The result panel will appear above the form and below the header.
  6. Use the CSV and PDF buttons to export the report for records, presentations, or review.

Baseline Structure Review

Sensitivity analysis begins with a baseline equation representing expected conditions. This solver calculates that output from either a linear or multiplicative model. The choice matters because it changes how shocks move through the system. Linear structures keep marginal effects constant, while multiplicative structures scale effects with size. Analysts should confirm the form matches the process before testing scenarios.

Interpreting One Way Shocks

One way shocks move a single variable up and down by a chosen percentage while other assumptions remain fixed. This isolates pressure and exposes unstable inputs quickly. A ten percent change in demand, price, time, or rate can reveal whether the model behaves predictably. Wider output intervals suggest the need for tighter monitoring, validation, or forecasting controls.

Reading Normalized Sensitivity

Raw derivatives describe local change, but normalized sensitivity coefficients improve comparison across variables with different units. They scale influence relative to baseline output and input level. That makes ranking more useful when one variable is measured in dollars and another in percentages. Elasticity approximations estimate the percentage response in output for a percentage change in input.

Combined Scenario Range

The all low and all high cases provide a disciplined stress range for planning. They do not guarantee a worst case, yet they show the output band created when assumptions move together. Finance teams can compare the spread against margin targets. Engineers can compare it against tolerance limits. Researchers can compare it against acceptable variance. A large combined spread signals the need for narrower assumptions or deeper segmentation.

Practical Decision Thresholds

Sensitivity analysis becomes useful when it drives thresholds for action. A variable with the greatest swing should receive the strongest review discipline. A cost input may justify weekly monitoring, while a weaker driver may only require monthly checks. Ranking variables reduces reporting noise and directs attention toward the assumptions that most shape decision quality.

Reporting and Governance Use

Exportable tables and charts improve review quality across teams. Analysts, auditors, and managers can inspect the same assumptions, scenario rules, and output ranges in a repeatable format. Over time, archived reports reveal whether model risk is shrinking or growing. That makes sensitivity analysis a calculation exercise and a governance tool for consistent decisions under uncertainty across teams.

FAQs

What does the strongest driver mean?

It identifies the variable with the largest output swing after applying the chosen low and high shock levels. It highlights where the model is most sensitive.

When should I use the linear model?

Use the linear model when each variable adds a fixed marginal effect to the result. It works well for additive equations and straightforward approximation studies.

When is the multiplicative model better?

Choose it when variables scale the result proportionally, such as growth, rate, elasticity, or compounded factor relationships. Base values must stay positive.

Why are normalized coefficients useful?

They make comparisons easier when variables use different units. A standardized view helps rank importance across inputs without relying only on raw derivative size.

What does the combined spread show?

It shows how far the output can move when all variables shift together to their low or high shocked values. This gives a planning range around baseline.

Can I export the analysis for reports?

Yes. After submitting valid inputs, use the CSV or PDF buttons to save the table outputs and scenario summary for review or documentation.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.