Configure weights and remainder handling.
Initialising algorithm engine for Weighted Modulus 11 Calculator...
How Weighted Modulus 11 Calculator Works?
The Weighted Modulus 11 Calculator works by multiplying digits by a repeating weight sequence, dividing the sum by 11, and turning the remainder into a check character. The calculator lets the user decide how remainders of 10 and 11 map to output characters.
- 1Enter the payload and select the weights (default 2-3-4-5-6-7 from the right).
- 2Multiply each digit by its weight and add the products into S.
- 3Compute r = S mod 11 and the raw check value 11 − r.
- 4Map a raw value of 11 to 0.
- 5Map a raw value of 10 to X, 0, a hyphen, or reject the payload, based on the selected rule.
Weighted Modulus 11 Calculator Formula
The Weighted Modulus 11 formula is Check = 11 − (Σ dᵢ·wᵢ mod 11), with special handling for results 10 and 11.
S = Σ dᵢ × wᵢ raw = 11 − (S mod 11) raw = 11 → 0; raw = 10 → X / 0 / '-' / invalid (scheme rule)
wᵢcycles 2, 3, 4, 5, 6, 7 from the rightmost digit by default.rawis the unmapped check value 1–11.
0 × 2 = 0 9 × 3 = 27 8 × 4 = 32 7 × 5 = 35 6 × 6 = 36 5 × 7 = 35 4 × 2 = 8 3 × 3 = 9 2 × 4 = 8 1 × 5 = 5 S = 195 S mod 11 = 8 raw = 11 − 8 = 3 Check character = 3
Weighted Modulus 11 Calculator Conversion Table
The Weighted Modulus 11 conversion table maps each remainder to its check character under the 3 most common rules.
| S mod 11 | Raw 11 − r | X rule (ISBN style) | 0 rule (UPU style) | K rule (Chilean RUT) |
|---|---|---|---|---|
| 0 | 11 | 0 | 0 | 0 |
| 1 | 10 | X | 0 | K |
| 2 | 9 | 9 | 9 | 9 |
| 3 | 8 | 8 | 8 | 8 |
| 4 | 7 | 7 | 7 | 7 |
| 5 | 6 | 6 | 6 | 6 |
| 6 | 5 | 5 | 5 | 5 |
| 7 | 4 | 4 | 4 | 4 |
| 8 | 3 | 3 | 3 | 3 |
| 9 | 2 | 2 | 2 | 2 |
| 10 | 1 | 1 | 1 | 1 |
What is Weighted Modulus 11 Calculator?
A Weighted Modulus 11 Calculator is a tool that computes check characters with modulus 11 and custom weights. A prime modulus of 11 detects 100% of single-digit errors and 100% of adjacent transpositions when the weights are distinct and non-zero.
Modulus 11 creates 11 possible remainders but only 10 decimal digits exist. Each scheme solves the extra value its own way: ISBN-10 uses X, the Chilean Rol Único Tributario (RUT) uses K, and the UK National Health Service (NHS) number rejects the payload.
What are the uses of Weighted Modulus 11 Calculator?
There are 4 main uses of the Weighted Modulus 11 Calculator, including book numbers, tax IDs, and health identifiers.
- Book and serial numbers: Publishers check ISBN-10 and ISSN values that end in X.
- Tax identifiers: Accountants check modulus 11 tax numbers in Chile, Portugal, and Brazil.
- Health identifiers: Health IT teams validate NHS numbers with weights 10 to 2.
- Scheme testing: Developers test remainder rules before going live with a new numbering scheme.