Specify modulus, weights, and output rules.
Initialising algorithm engine for Custom Modulus Calculator...
How Custom Modulus Calculator Works?
The Custom Modulus Calculator works by applying a user-chosen modulus, weight list, direction, and output rule to any numeric payload. The tool reproduces most weighted check digit schemes without code.
- 1Choose the modulus m (for example 7, 10, 11, 23, 31, 37, 43, 89, or 97).
- 2Enter the weight list and choose left-to-right or right-to-left application.
- 3Choose the product rule: plain product or digit-sum of the product (Luhn style).
- 4Choose the output rule: remainder r, complement m − r, or (m − r) mod m.
- 5Map output values above 9 to letters or symbols with a character table.
Custom Modulus Calculator Formula
The Custom Modulus formula is Check = g( Σ h(dᵢ × wᵢ) mod m ), where h is the product rule and g is the output rule.
S = Σ h(dᵢ × wᵢ)
r = S mod m (CUSTOM MODULUS)
Check = g(r) ∈ { r, m − r, (m − r) mod m } → mapped through the character tablemis the modulus.his identity or digit-sum.gis the output rule.wᵢis the weight for digit i.
S = 195 r = 8 Check = 3
Custom Modulus Calculator Conversion Table
The Custom Modulus conversion table lists the parameter sets that reproduce well-known schemes.
| Scheme | Modulus | Weights | Direction | Output rule |
|---|---|---|---|---|
| GS1 GTIN | 10 | 3, 1 | Right | (10 − r) mod 10 |
| Luhn | 10 | 2, 1 + digit-sum | Right | (10 − r) mod 10 |
| ISBN-10 | 11 | 10…2 | Left | (11 − r) mod 11, 10 = X |
| ABA routing | 10 | 3, 7, 1 | Left | (10 − r) mod 10 |
| NHS number | 11 | 10…2 | Left | 11 − r, 11 = 0, 10 invalid |
| Spanish NIF | 23 | none | — | r → letter table |
| Finnish HETU | 31 | none | — | r → 31-character table |
| Code 39 | 43 | 1 | — | r → Code 39 set |
| ABN | 89 | 10, 1, 3…19 | Left | valid when r = 0 |
| IBAN | 97 | ISO 7064 | Left | 98 − r |
What is Custom Modulus Calculator?
A Custom Modulus Calculator is a general check digit engine where the user defines the modulus, weights, and output mapping. The tool suits schemes that no dedicated calculator covers.
Most check digit schemes differ in 4 parameters: modulus, weights, direction, and output mapping. Setting those 4 values reproduces the scheme exactly.
What are the uses of Custom Modulus Calculator?
There are 4 main uses of the Custom Modulus Calculator, including in-house schemes, legacy data, and teaching.
- In-house identifier schemes: Companies check proprietary part or member numbers.
- Legacy data recovery: Analysts test parameter sets until historic records validate.
- Specification testing: Engineers confirm a written specification before writing code.
- Teaching modular arithmetic: Teachers show how each parameter changes the result.