Modulo Calculator

Modulo is evaluated from Dividend and Divisor. The calculation reports Remainder, Integer Quotient and Exact Division.

Results

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About the Modulo Calculator

Modulo is treated here as a quantitative relation between Dividend and Divisor and Remainder, Integer Quotient, Exact Division and Evenly Divisible?.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
a mod b = a - b x ⌊a/b⌋
Remainder is always non-negative (0 to b - 1)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

a mod b = a - b x ⌊a/b⌋
Remainder is always non-negative (0 to b - 1)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Odd/Even Check

Inputs

dividend: 2026 divisor: 2
Remainder: 0. Integer Quotient: 1,013. Exact Division: 1,013. Evenly Divisible?: Yes - 2026 is divisible by 2

With Dividend = 2,026 and Divisor = 2 as the stated inputs, the result is Remainder = 0, Integer Quotient = 1,013 and Exact Division = 1,013. Each value corresponds to the declared output fields.

Example 2: Clock Arithmetic — Time Wrap

Inputs

dividend: 17 divisor: 12
Remainder: 5. Integer Quotient: 1. Exact Division: 1.41666667. Evenly Divisible?: No - remainder is 5

With Dividend = 17 and Divisor = 12 as the stated inputs, the result is Remainder = 5, Integer Quotient = 1 and Exact Division = 1.41666667. Each value corresponds to the declared output fields.

Example 3: Leap Year Check

Inputs

dividend: 2024 divisor: 4
Remainder: 0. Integer Quotient: 506. Exact Division: 506. Evenly Divisible?: Yes - 2024 is divisible by 4

With Dividend = 2,024 and Divisor = 4 as the stated inputs, the result is Remainder = 0, Integer Quotient = 506 and Exact Division = 506. Each value corresponds to the declared output fields.

Example 4: Credit Card Check Digit (Luhn)

Inputs

dividend: 37 divisor: 10
Remainder: 7. Integer Quotient: 3. Exact Division: 3.7. Evenly Divisible?: No - remainder is 7

With Dividend = 37 and Divisor = 10 as the stated inputs, the result is Remainder = 7, Integer Quotient = 3 and Exact Division = 3.7. Each value corresponds to the declared output fields.

Common Use Cases

  • Find the remainder of any division
  • Check if a number is odd or even (mod 2)
  • Determine leap year (year mod 4)
  • Circular array index calculation in programming