Integers Calculator
Need to quickly add -15 and 27? Or verify the product of -8 × -9? This integers calculator handles all common operations with positive and negative whole numbers – without fractions or decimals. It’s built for students checking homework, developers testing logic, or anyone working with exact values.
Integer sign rules reference
Addition and Subtraction
| Case | Rule | Example |
|---|---|---|
| Same signs | Add absolute values, keep the sign | -7 + (-3) = -10 |
| Different signs | Subtract smaller absolute from larger, take sign of larger | -9 + 5 = -4 |
| Subtracting a negative | Equivalent to adding the positive | 10 − (-4) = 14 |
Multiplication, Division, and Exponentiation
| Case | Rule | Example |
|---|---|---|
| Same signs (multiply/divide) | Positive result | (-6) × (-3) = 18 |
| Different signs (multiply/divide) | Negative result | 7 × (-2) = -14 |
| Negative base, even exponent | Positive result | (-3)² = 9 |
| Negative base, odd exponent | Negative result | (-3)³ = -27 |
| Modulo (remainder) | Preserves sign of dividend | -10 mod 3 = -1 |
This calculator provides results for educational and general purposes. Always verify critical calculations manually or with a dedicated system.
The calculator above accepts two integer inputs and one operator. It computes the result immediately using standard integer arithmetic rules. Every operation gives an exact outcome – a positive, negative, or zero integer – and division by zero is blocked with a clear error.
How to Add and Subtract Integers
Addition and subtraction follow predictable sign rules. When the signs are the same, combine the absolute values and keep the sign. For different signs, subtract the smaller absolute value from the larger one and take the sign of the larger absolute value.
- Same signs:
-7 + (-3) = -10/4 − (-2) = 6 - Different signs:
-9 + 5 = -4/3 − 8 = -5
Subtracting a negative is equivalent to adding: 10 − (-4) becomes 10 + 4 = 14. The calculator automatically applies these rules, so you can focus on the logic rather than manual sign tracking.
Multiplying and Dividing Integers
Multiplication and division are simpler: the sign of the result depends only on the number of negative factors.
- Same signs give a positive result:
(-6) × (-3) = 18,(-20) ÷ (-4) = 5 - Different signs give a negative result:
7 × (-2) = -14,(-15) ÷ 3 = -5
When the operator is exponentiation, the sign follows the parity of the exponent: a negative base raised to an even exponent yields a positive integer ((-3)² = 9), while an odd exponent keeps the negative sign ((-3)³ = -27). The modulo operation returns the remainder after division, preserving the sign of the dividend.
Why Use an Online Integers Calculator?
Manual integer arithmetic is straightforward but error-prone when multiple negatives or large numbers are involved. This tool eliminates sign mistakes and gives instant verification. Common use cases include:
- Education – checking algebra assignments, practicing integer operations
- Programming – testing boundary values, modulo logic, or index calculations
- Finance – reconciling debits and credits without decimal rounding
- Everyday math – temperature differences, scorekeeping, or inventory counts
The calculator also respects order of operations, handling each pair of inputs independently. For longer expressions, simply chain results by using the output as the next input.
This calculator provides results for educational and general purposes. Always verify critical calculations manually or with a dedicated system.