Modulo Calculator
Modulo arithmetic returns the remainder after division and is used in cycles, schedules, array indexing and number theory.
How to use this calculator
- Enter a dividend and a non-zero divisor. The calculator shows a normalized remainder and corresponding quotient.
- Check the labels and units before using a result outside this page.
- Change one input at a time if you want to compare scenarios.
Formula and method
a = qd + r, with a normalized remainder 0 ≤ r < |d|
- a = qd + r, with a normalized remainder 0 ≤ r < |d|
- Programming languages differ on how they define remainders for negative inputs; this tool uses a non-negative normalized remainder.
Worked examples
Worked example
Compute 29 modulo 6.
29 = 4 × 6 + 5, so the remainder is 5.
29 = 4 × 6 + 5, so the remainder is 5.
Understanding the result
Modulo arithmetic returns the remainder after division and is used in cycles, schedules, array indexing and number theory.
Programming languages differ on how they define remainders for negative inputs; this tool uses a non-negative normalized remainder.
Important notes
Programming languages differ on how they define remainders for negative inputs; this tool uses a non-negative normalized remainder.
Displayed outputs are rounded for readability; preserve full precision when continuing a calculation.
Frequently asked questions
What does this modulo calculator show?
Modulo arithmetic returns the remainder after division and is used in cycles, schedules, array indexing and number theory.
Which inputs should I check first?
Enter a dividend and a non-zero divisor. The calculator shows a normalized remainder and corresponding quotient.
Can the result be used as a final professional specification?
Programming languages differ on how they define remainders for negative inputs; this tool uses a non-negative normalized remainder.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.