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Luhn Algorithm Calculator

Luhn (mod 10) check digit

Client-side computation for analysis, verification, and learning. Do not paste production secrets into untrusted sites; prefer local tooling for key material.

Educational / engineering use. RSA mode uses tiny primes for illustration only—not for real key generation.

Full number (with check digit) — validate
Body without check digit — compute check digit

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What is Luhn Algorithm Calculator?

A simple checksum formula used to validate identification numbers like credit cards and IMEI codes. It works by doubling every second digit from the right and summing all digits to check divisibility by 10.

Luhn Formula

Σ(i=1..n)di0(mod10)Σ(i=1..n) d_i ≡ 0 (mod 10)

Where digits at even positions from the right are doubled; if the doubled value exceeds 9, subtract 9.

di=2di9if2di>9;2diotherwised_i = { 2d_i − 9 if 2d_i > 9 ; 2d_i otherwise }

Luhn Step-by-Step

  1. Read digits from right to left.
  2. Double every second digit.
  3. If doubled value > 9, subtract 9.
  4. Sum all processed digits.
  5. Validate that sum mod 10 = 0 (or compute check digit).

Luhn Worked Example

Card number: 4539 1488 0343 6467

Step 1: Double every second digit from the right.

Step 2: If doubled digit > 9, subtract 9.

Step 3: Sum all processed digits.

Computed sum = 70

Check:70mod10=0>Valid.Check: 70 mod 10 = 0 -> Valid.

Where Luhn Algorithm Calculator Is Applied

  • Credit and debit card number validation (Visa, Mastercard, Amex)
  • IMEI number verification for mobile devices
  • National ID numbers in some countries
  • Canadian Social Insurance Numbers
  • NPI (National Provider Identifier) in US healthcare
  • ISBN-10 book identifier validation

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