Describe the Pattern Calculator

Calculator Form

Sequence Values

Sequence Label

Start Position

Forecast Count

Moving Average Window

Decimal Places

Comparison Tolerance

Outlier Z-Score Threshold

Accepted Separators

Example Data Table

Example Sequence	Likely Pattern	Expected Next Values	Reason
5, 10, 15, 20	Arithmetic	25, 30	Each term increases by 5.
2, 4, 8, 16	Geometric	32, 64	Each term doubles.
3, 1, 3, 1, 3, 1	Repeating cycle	3, 1	The two-value cycle repeats.
1, 4, 9, 16, 25	Quadratic-like	36, 49	Second differences remain constant.

Formula Used

Arithmetic difference: d = x_n - x_n-1. If differences stay nearly equal, the sequence is treated as arithmetic.

Geometric ratio: r = x_n / x_n-1. If ratios stay nearly equal, the sequence is treated as geometric.

Mean: x̄ = (sum of values) / n.

Sample variance: s² = Σ(x - x̄)² / (n - 1).

Standard deviation: s = √s².

Z-score: z = (x - x̄) / s.

Moving average: average of the last selected window of values.

Linear trend: y = a + bx, where b is the slope and R² shows fit quality.

Quadratic-like check: when second differences remain nearly constant, the next values extend that same second-difference step.

How to Use This Calculator

Enter at least two numeric values in order.
Use commas, spaces, semicolons, or new lines as separators.
Add a label if you want named output.
Set the starting position for the first value.
Choose how many future values you want projected.
Set decimal places for clean reporting.
Choose a moving average window for smoothing.
Adjust tolerance when values are close but not exact.
Set the z-score threshold for outlier marking.
Press Describe Pattern to show the result above the form.
Review the summary, graph, and detailed table.
Use CSV or PDF export for saving results.

Frequently Asked Questions

1. What does this calculator identify?

It checks for constant, arithmetic, geometric, repeating, alternating, quadratic-like, and trend-based patterns. It also summarizes spread, central tendency, outliers, and projected next values.

2. Does it work with decimals and negative values?

Yes. You can enter integers, decimals, and negative numbers. The parser accepts common separators and treats the entered values as a numeric sequence.

3. What is comparison tolerance?

Tolerance controls how strictly the calculator compares differences or ratios. A larger tolerance can treat nearly equal steps as the same pattern when small noise exists.

4. When is a pattern called arithmetic?

If consecutive differences remain nearly constant, the sequence is treated as arithmetic. The next values are then projected by adding the same step repeatedly.

5. How are projected values estimated?

The calculator continues the detected rule first. If no clear exact rule exists, it uses a linear trend projection based on the entered positions and values.

6. What does the z-score threshold do?

It marks values that sit far from the sequence mean. Larger absolute z-scores indicate points that may be unusually high or low relative to the rest.

7. Why is there a moving average column?

Moving averages smooth short-term variation. That helps you see the broader direction of the sequence, especially when the raw values fluctuate.

8. What files do the export buttons create?

The CSV button downloads a spreadsheet-friendly report. The PDF button downloads a compact printable summary with the main metrics, description, and analysis rows.