Integer Calculator – Guide & Formulas
Perform integer arithmetic with addition, subtraction, multiplication, division, and modulus. Calculate with whole numbers and see exact integer results without decimals.
Perform integer arithmetic with whole numbers. Enter two integers to add, subtract, multiply, divide, or find the modulus — get exact integer results without any decimals.
Key Takeaway
Use the free Integer Calculator to perform integer arithmetic with addition, subtraction, multiplication, division, and modulus. calculate with whole numbers and see exact integer results without decimals. Get instant results with step-by-step explanations.
How to Use the Integer Calculator
- Enter the first integer (positive or negative).
- Select the operation: +, -, ×, ÷, or % (modulus).
- Enter the second integer.
- Review the integer result and step-by-step breakdown.
- Check the quotient and remainder for division operations.
The Formula
Variable Definitions
- a: The first integer operand
- b: The second integer operand
- q: The integer quotient (result of floor division)
- r: The remainder (modulus): a = b × q + r
- %: The modulus operator — returns the remainder of division
Integer Division and Modulus of 17 by 5
Compute the integer quotient and remainder of 17 ÷ 5.
- Step 1: Identify inputs: a = 17, b = 5.
- Step 2: Perform integer division: 17 ÷ 5 = 3 (remainder 2).
- Step 3: Integer quotient q = 3.
- Step 4: Compute modulus: 17 % 5 = 17 - (5 × 3) = 17 - 15 = 2.
- Step 5: Verify: 5 × 3 + 2 = 15 + 2 = 17. ✓
- Step 6: The integer result is 3 with remainder 2.
Frequently Asked Questions
What is an integer?
An integer is any whole number (positive, negative, or zero) without a fractional or decimal part. The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...}. Examples: -5, 0, 42, -1000. Non-examples: 3.14, -2.5, 1/2, √2.
What is integer division?
Integer division divides two integers and returns only the whole number quotient (discarding any remainder). In most languages, 17 / 5 = 3 (not 3.4). The discarded part is the remainder, obtained with the modulus operator: 17 % 5 = 2.
What is the modulus operator?
The modulus operator % returns the remainder after integer division. For a % b: it computes a - b × ⌊a/b⌋. For example, 17 % 5 = 2 because 17 = 5 × 3 + 2. The result always has the same sign as the divisor in floor division.
How do negative integers work in arithmetic?
Negative integers follow standard arithmetic rules: (-3) + (-5) = -8, (-3) - (-5) = 2, (-3) × 5 = -15. For division: (-7) / 3 = -2 (integer) with remainder -1. Signs: same signs give positive product, different signs give negative.
What is the difference between / and // in programming?
/ is true division (returns decimal): 7 / 2 = 3.5. // is floor division (returns integer): 7 // 2 = 3. In Python, // always rounds toward negative infinity. In some other languages, / with integers automatically truncates.
How do I perform integer arithmetic with very large numbers?
Most programming languages handle arbitrary-precision integers (Python, Java BigInteger). The mathematical operations are the same, but very large numbers may be slower to compute. For truly enormous numbers, specialized algorithms (Karatsuba multiplication) are used.
Can I use this calculator for negative moduli?
Yes. The modulus operation works with negative divisors. For example, 7 % (-3) = 1 (since 7 = (-3)(-2) + 1). The remainder always has the same sign as the divisor in floor division.
What are common uses of integer arithmetic?
Integer arithmetic is used in: (1) Array indexing, (2) Time/date calculations, (3) Currency (cents), (4) Cryptography (modular arithmetic), (5) Hash functions, (6) Computer graphics (pixel coordinates), (7) Number theory and algorithms.
How do I convert between integer and floating-point?
Integer to float: automatic in most languages (int → float). Float to int: explicit cast needed, which truncates toward zero in most languages. For true floor behavior, use floor() function. Example: (int)3.7 = 3, (int)-3.7 = -3 (truncation), floor(-3.7) = -4 (floor).