Balanced Number Checker

Compare sums of decimal digit halves, ignoring an odd central digit; arbitrary-length canonical decimal text preserves exact identity, unlike palindrome checks.

Description

A balanced decimal integer has equal sums in its digit halves.

A balanced decimal integer has equal sums in its digit halves. An odd central digit is omitted, so balance differs from palindromic digit symmetry.^[1]

Compare sums of decimal digit halves, ignoring an odd central digit; arbitrary-length canonical decimal text preserves exact identity, unlike palindrome checks.

When to use Balanced Number Checker

Use this tool to compare sums of decimal digit halves, ignoring an odd central digit; arbitrary-length canonical decimal text preserves exact identity, unlike palindrome checks.

Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.

How to use Balanced Number Checker and understand its results

Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
Enter decimalInteger using the field table and calculation rules, then run the tool.
Read leftHalfDigitSum, rightHalfDigitSum, isBalanced. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
decimalInteger	Decimal integer	string	Required

Enter canonical unsigned ASCII decimal text of 1–128 digits, with no leading zeros except "0". Sum both halves excluding any central digit and return sums and the equality flag. A single digit has two empty halves and is balanced.

balanced = sum(left floor(length/2) digits) = sum(right floor(length/2) digits)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
leftHalfDigitSum	Left half digit sum	number
rightHalfDigitSum	Right half digit sum	number
isBalanced	Is balanced	boolean

json

{
  "input": {
    "decimalInteger": "123321"
  },
  "output": {
    "leftHalfDigitSum": 6,
    "rightHalfDigitSum": 6,
    "isBalanced": true
  }
}

Limitations and assumptions

Signs, grouping, whitespace and non-ASCII digits are rejected. The text is not converted to a potentially lossy numeric integer.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Extremely large text inputs are rejected. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Vampire Number Checker: Find all unordered equal-digit factor fangs whose combined decimal multiset matches candidate; both trailing-zero fangs excluded, 1–6 digit bounded search and odd lengths false. For a complementary task, use Factorial Digit Count Calculator: Count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit.

References

Balanced Number Checker — tool.io

Similar or alternative tools

Vampire Number Checker
Find all unordered equal-digit factor fangs whose combined decimal multiset matches candidate; both trailing-zero fangs excluded, 1–6 digit bounded search and odd lengths false.
Factorial Digit Count Calculator
Count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit.