Check monotonic patterns across custom number lists. Measure changes, tolerance effects, and turning points accurately. Use responsive inputs, exports, examples, formulas, and helpful guidance.
Use commas, spaces, semicolons, or new lines between numbers. The calculator checks each adjacent pair and applies your chosen tolerance.
For a sequence a₁, a₂, ..., aₙ, the calculator evaluates adjacent differences using:
Δᵢ = aᵢ₊₁ − aᵢ
A reversal occurs whenever nonzero difference signs switch from positive to negative, or from negative to positive.
| Example Sequence | Tolerance | Expected Classification | Why |
|---|---|---|---|
| 2, 4, 7, 10, 15 | 0 | Strictly increasing | Every adjacent difference is positive. |
| 3, 3, 5, 5, 9 | 0 | Non-decreasing | Equal ties appear, but no decrease occurs. |
| 12, 9, 9, 5, 2 | 0 | Non-increasing | No step rises above the previous value. |
| 1, 4, 3, 6, 5 | 0 | Not monotonic | Positive and negative differences both appear. |
A monotonic sequence keeps moving in one direction or stays level. It can rise throughout, fall throughout, or remain flat within the tolerance you selected.
Strict monotonicity allows no equal neighboring values. Weak monotonicity permits ties, so a sequence may stay the same temporarily while still counting as non-decreasing or non-increasing.
Tolerance helps when data includes rounding noise, sensor error, or very small fluctuations. Values changing less than the tolerance are treated as effectively equal during the test.
Yes. You can test strict decreasing, non-increasing, or let automatic classification decide whether the sequence trends upward, downward, stays constant, or breaks monotonicity.
A sequence fails when one or more adjacent differences violate the chosen rule. For example, a negative step breaks increasing behavior, while a positive step breaks decreasing behavior.
The trend score summarizes directional balance. Positive values suggest more upward moves, negative values suggest more downward moves, and values near zero indicate mixed behavior.
A reversal is counted whenever meaningful differences switch direction. Flat steps within tolerance are ignored, so only actual sign changes between rising and falling moves are counted.
Yes. The page includes CSV and PDF download buttons after a successful calculation, letting you save the summary, pairwise differences, and any violation notes.
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.