Modulo Calculator

Modulo Calculator gives the remainder left when one number is divided by another, along with the quotient. It is the operation behind clock arithmetic, checksums, hash buckets, cycling through a list and every 'every nth item' rule: 17 mod 5 is 2 because five goes into seventeen three times with two left over.

Negative numbers are where the operation stops being obvious, and the calculator shows both answers rather than picking one. Mathematics and Python floor the quotient, which keeps the remainder's sign the same as the divisor: -17 mod 5 is 3. C, Java, JavaScript and most spreadsheet engines truncate towards zero, which keeps the remainder's sign the same as the dividend: -17 % 5 is -2. Neither is wrong, but mixing them up produces bugs that only appear on negative input.

The modular inverse is listed when one exists. It is the number that multiplies a back to 1 modulo n, and it exists only when a and n share no common factor. That condition is the whole basis of RSA and of most modular arithmetic in cryptography, which is why it is worth seeing beside the remainder.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

• Shows a mod n, quotient, remainder, truncated, remainder, floored and divides exactly? together, so you are not running it twice
• A results table you can read across
• Prints the formula with your own figures substituted in
• Updates as you type, with no button to press and no page reload
• Copy the result in one click
• Free, no sign-up, and it runs entirely in your browser

The modulo calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Finding the remainder of a division
• Checking whether one number divides another exactly
• Working out a clock or cyclic position
• Comparing how two languages handle a negative modulo