Enter the Dividend
Enter the first number, also called the dividend. This is the number that will be divided.
Example: 17
ModCalculator.org makes modulo calculations simple. Enter a dividend and a divisor, and the calculator instantly finds the modulo result, quotient, and remainder with an easy-to-follow breakdown.
Try the Mod Calculator →17 divided by 5 leaves a remainder of 2.
The modulo operation finds the remainder left after one number is divided by another.
In the expression a mod b, the value a is divided by b. The amount left over after division is the modulo result.
You only need two numbers. The calculator handles the calculation and displays the important values automatically.
Enter the first number, also called the dividend. This is the number that will be divided.
Enter the second number. This is the divisor or modulus used in the modulo operation.
Click the calculate button. The calculator divides the first number by the second and determines the remainder.
View the modulo result together with the quotient, remainder, and calculation breakdown.
Here is the same calculation broken down manually.
17 ÷ 5 = 3.4
The whole-number quotient is 3.
5 × 3 = 15
17 − 15 = 2
These examples show how modulo returns the remainder after division.
| Expression | Division | Quotient | Remainder | Result |
|---|---|---|---|---|
| 10 mod 3 | 10 ÷ 3 | 3 | 1 | 1 |
| 17 mod 5 | 17 ÷ 5 | 3 | 2 | 2 |
| 20 mod 4 | 20 ÷ 4 | 5 | 0 | 0 |
| 25 mod 7 | 25 ÷ 7 | 3 | 4 | 4 |
| 100 mod 9 | 100 ÷ 9 | 11 | 1 | 1 |
The final value left after division. This is the main result of the mod calculation.
The quotient shows how many complete times the divisor fits into the dividend.
The remainder is the amount left after the complete groups have been removed.
The breakdown helps you understand how the result was produced rather than only displaying the final answer.
Modulo calculations can require extra care when negative numbers or decimal values are involved.
Different programming languages can handle negative modulo values differently. ModCalculator.org displays the convention used by the calculator clearly with the result.
The calculator also supports decimal input, allowing you to find remainders for values that are not limited to whole numbers.
Modulo is useful in mathematics, computer programming, scheduling, cryptography, and repeating patterns.
Developers use modulo for even and odd checks, loops, indexes, pagination, and repeating patterns.
Clocks repeat after a fixed number of hours, making them a common real-world example of modular arithmetic.
Modular arithmetic plays an important role in many encryption and number-theory techniques.
Mod, short for modulo, refers to the remainder left after dividing one number by another.
10 mod 3 equals 1 because 3 fits into 10 three complete times, giving 9, with 1 left over.
A result of 0 means the first number is evenly divisible by the second number and there is no remainder.
No. Division usually focuses on the quotient, while modulo focuses on the remainder after division.
Yes. ModCalculator.org supports positive, negative, and decimal inputs, although negative modulo conventions can vary between mathematical systems and programming languages.