Calculator Form
Enter four ring values and optional controls. Results appear above this form after submission.
Example Data Table
This sample shows how the calculator works with a practical four-value ring.
| A | B | C | D | Scale | Shift | Modulus | Target | Sum | Mean | Balance Gap | Symmetry % |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 12 | 18 | 15 | 9 | 1.25 | 1 | 7 | 60 | 54.00 | 13.50 | 0.00 | 100.00 |
Formula Used
This calculator assumes a quad ring contains four ordered values: A, B, C, and D.
- Ring Sum:
A + B + C + D - Arithmetic Mean:
(A + B + C + D) / 4 - Product:
A × B × C × D - Range:
max(A,B,C,D) − min(A,B,C,D) - RMS:
sqrt((A² + B² + C² + D²) / 4) - Population Variance: average of squared deviations from the mean
- Opposite Sums:
A + CandB + D - Balance Gap:
|(A + C) − (B + D)| - Symmetry Score:
100 × (1 − BalanceGap / (|A+C| + |B+D|)) - Determinant:
(A × D) − (B × C) - Norms:
L1 = |A|+|B|+|C|+|D|,L2 = sqrt(A²+B²+C²+D²) - Rotation: cyclic left shift by 0 to 3 places
- Mod Ring: each value reduced with a positive modulus rule
- Target Achievement:
(Ring Sum / Target) × 100
How to Use This Calculator
- Enter the four ring values in the A, B, C, and D fields.
- Add a scale factor if you want to magnify or reduce all values.
- Select a rotation shift to inspect the same ring in another order.
- Enter a modulus when modular wraparound values are needed.
- Set a target sum if you want gap and achievement analysis.
- Choose display precision for cleaner result formatting.
- Press Calculate Quad Ring to show results above the form.
- Use the CSV and PDF buttons to export the result table.
Frequently Asked Questions
1. What is a quad ring here?
Here, a quad ring means four ordered numbers arranged in a loop. The calculator studies totals, spread, symmetry, balance, and cyclic behavior.
2. Why are opposite sums important?
Opposite sums compare A with C and B with D. Their difference reveals whether the ring is balanced across the loop.
3. What does the symmetry score show?
The symmetry score converts the balance gap into a percentage. Higher values mean the two opposite sides are closer in combined size.
4. When is the geometric mean unavailable?
The geometric mean is shown only when all values are positive, or when all are nonnegative with a zero product. Negative values make it unsuitable here.
5. What does rotation shift do?
Rotation shift moves the ring order cyclically. It helps you inspect the same data from a different starting point without changing the set itself.
6. Why use modulus in a math ring?
Modulus is useful for wraparound systems, periodic data, clocks, residues, and cycle-based patterns. It converts each value into a modular equivalent.
7. What does the Plotly graph compare?
The graph compares original values, scaled values, and rotated values. This makes pattern changes easier to see than reading a table alone.
8. Can I export the result table?
Yes. After calculating, use the CSV button for spreadsheet-friendly data and the PDF button for a shareable report layout.