Results & Analysis

Histogram

Each output generates a histogram showing how results are distributed across iterations. The x-axis shows possible values; the y-axis shows frequency.

Insight badge

A label above the histogram indicates the distribution shape (Normal-like, Right-skewed, Bimodal, etc.). This helps you quickly understand the characteristics of your output and whether it matches expectations.

Outlier Handling

To keep histograms readable, Carlo uses a robust range based on the 1st and 99th percentiles (P1–P99) of your simulation results. Values outside this range are considered outliers.

Why exclude outliers?

Extreme values can compress the histogram scale, making the bulk of your data hard to interpret. By focusing on P1–P99, the histogram shows 98% of outcomes at an appropriate resolution.

What happens to outliers?

Outliers are excluded from histogram bins entirely—they don't inflate edge bin heights. When outliers exist, you'll see a note below the chart.

Statistics

Large Simulations

For simulations with more than 50,000 iterations, Carlo optimizes memory usage by storing a representative sample of individual data points while computing statistics from all iterations.

What stays exact

Core statistics (mean, standard deviation, min, max) are calculated using all iterations with Welford's online algorithm, ensuring mathematical accuracy regardless of simulation size.

What uses sampling

Histograms and percentiles are computed from a representative sample of up to 10,000 data points, selected using reservoir sampling to maintain statistical validity. This approach allows Carlo to run simulations with 100,000+ iterations in your browser without memory issues.

Probability Calculator

Answer questions like "What is the probability that profit exceeds $50,000?" or "What value do we exceed 90% of the time?"

Sensitivity Analysis

Sensitivity analysis identifies which input variables have the greatest impact on your outputs. This helps you focus refinement efforts on the assumptions that matter most.

How it works

Carlo uses Spearman rank correlation to measure the relationship between each input and the output across all simulation iterations. This method is robust to non-linear relationships and doesn't assume any particular distribution shape.

For each input variable, Carlo compares how its sampled values rank against how the output values rank. If high input values consistently produce high outputs (or vice versa), the correlation will be strong. If there's no consistent pattern, the correlation approaches zero.

Tornado chart

Results are displayed as a tornado chart with horizontal bars showing correlation strength. Longer bars indicate greater influence. Bars extending right (positive correlation) mean higher input values lead to higher outputs. Bars extending left (negative correlation) indicate inverse relationships—higher inputs produce lower outputs.

Interpreting correlation values

Time Series Charts

Time Series blocks generate additional visualizations showing how values evolve over time.

AI Insights

After running a simulation, Carlo can generate a 1–3 sentence AI-powered interpretation of your results. Insights are tailored to the model's domain—financial models get business-oriented language, while scientific models use precise statistical terminology.

What's included

Insights reference key statistics like skewness, goal probability, and percentile ranges, and always include the configured units (e.g., $, %) for all numeric values. The narrative follows an "Answer → Insight → Proof" hierarchy to surface the most important takeaway first.

Export

Export results for further analysis or reporting.