Finite Difference Calculator
One series per line (comma / space / semicolon separated, negatives and decimals supported). Each series gets its own staircase difference table and conclusion.
Difference mode:
Stop when:
Polynomial formula:
Calculation Result
Download CSV
| No. | Original | Order | Difference sequence | First Term | Detail |
|---|
Introduction to the tool and how to use it
Online sequence difference tool: enter one sequence per line (comma or space separated; negative numbers, decimals, and large integers are supported), and it automatically generates each order of differences plus a stepped difference table.
Input format: one sequence per line, for example
Parameters: difference mode offers forward difference Δ (default), backward difference ∇, or central difference; the stop condition can be stop when an order is all zeros (default), stop when an order is all equal, or compute through the highest order (1 to 50).
Conclusion: if the k-th difference is constant, it reports that the sequence is degree-k polynomial and gives the first difference value; when an order is all zeros, it indicates the corresponding polynomial degree; failure to converge suggests an exponential, periodic, or random sequence. Constant requires at least 3 values in that order, otherwise verification is flagged as impossible. With polynomial general term enabled, degrees up to 3 are reconstructed by Newton forward difference formula.
Input format: one sequence per line, for example
1, 4, 9, 16, 25; a line with fewer than 2 terms reports too few terms. One sequence holds at most 500 terms and one run at most 200 lines; exceeding these shrinks to the cap automatically with a notice.Parameters: difference mode offers forward difference Δ (default), backward difference ∇, or central difference; the stop condition can be stop when an order is all zeros (default), stop when an order is all equal, or compute through the highest order (1 to 50).
Conclusion: if the k-th difference is constant, it reports that the sequence is degree-k polynomial and gives the first difference value; when an order is all zeros, it indicates the corresponding polynomial degree; failure to converge suggests an exponential, periodic, or random sequence. Constant requires at least 3 values in that order, otherwise verification is flagged as impossible. With polynomial general term enabled, degrees up to 3 are reconstructed by Newton forward difference formula.
How to use
- Paste the sequences into the input box, one per line.
- Choose the difference mode, stop condition, and highest order.
- Click the Run button.
- Review the stepped difference table and the polynomial conclusion, then copy or export.
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