Free · Division and rounding

Signed Division, Quotient and Remainder

Find a truncating quotient, signed remainder and decimal quotient, with ordinary division inverses.

Formula & worked example
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Calculator inputs

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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For 13 divided by 5, the quotient is 2, remainder 3 and decimal result 2.6.

dividend = divisor × quotient + remainder

Worked example

Enter these known values and leave the other values blank.

Dividend (A): 13
Divisor (B): 5

Division (C): 2.6
Quotient: 2
Remainder: 3

Assumptions and limitations

The integer quotient truncates toward zero. The remainder has the dividend sign and satisfies dividend = divisor × quotient + remainder.
The divisor is nonzero. Decimal inputs remain available; integer examples illustrate long division. Quotient magnitude must remain below 10^50.

Common questions

What happens with negative numbers?

The quotient truncates toward zero; the signed remainder completes the same division identity.

Can I solve for the divisor or dividend?

Clear that unknown and enter the decimal result with the other independent input. Quotient and remainder are forward-only.

References

Translate truncating integer division into exact local decimal arithmetic. Compute the signed remainder from dividend minus divisor times quotient, correcting the captured modulo result that breaks this identity for negative dividends. Bound quotient magnitude below 10^50; preserve all ordinary division inverses and the hidden trigger equation.

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