Integer Calculator & Negative Number Calculator
Welcome to CalcuGo's integer calculator, where you can perform all core arithmetic operations on whole numbers — including negative integers. Whether you need to add, subtract, multiply, perform integer division, compute exponents and roots, or find a logarithm, this tool handles it all. Select a unit system (metric or US imperial) or a world currency to put your integers in real-world context.
What Is an Integer in Math? — Integer Definition
An integer is any whole number — positive, negative, or zero — that contains no fractional or decimal part. Formally:
An integer is any real number that can be written without a fractional component.
Examples of integers: …, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, …
The set of all integers is denoted ℤ (from the German word Zahlen, meaning "numbers").
- Positive integers (natural numbers): 1, 2, 3, … — all whole numbers greater than zero.
- Zero: neither positive nor negative, but still an integer.
- Negative integers: −1, −2, −3, … — whole numbers less than zero.
Note: 4/2 = 2 is an integer (the result is whole), while 5/2 = 2.5 is not an integer.
The Positive and Negative Number Line
The number line is a straight horizontal line where every integer occupies an equally spaced position:
←────────────────────────────────────────────────────────────→
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 …
↑
Zero
- Moving right on the number line increases the value (positive direction).
- Moving left decreases the value (negative direction).
- Absolute value |n| is the distance from zero, always non-negative: |−5| = 5, |5| = 5.
Adding and Subtracting Integers
The rules for adding and subtracting integers depend on the signs of the numbers involved:
| Operation | Rule | Example |
|---|---|---|
| ( + ) + ( + ) | Add, keep positive sign | 4 + 3 = 7 |
| ( − ) + ( − ) | Add, keep negative sign | −4 + (−3) = −7 |
| ( + ) + ( − ) | Subtract, take sign of larger absolute value | 4 + (−6) = −2 |
| ( − ) + ( + ) | Subtract, take sign of larger absolute value | −4 + 6 = 2 |
| a − b | Same as a + (−b) | 7 − 10 = 7 + (−10) = −3 |
Multiplying Integers and Integer Division
The sign rules for multiplication and division are straightforward:
| Signs | Result Sign | Example |
|---|---|---|
| ( + ) × ( + ) | Positive | 3 × 4 = 12 |
| ( − ) × ( − ) | Positive | (−3) × (−4) = 12 |
| ( + ) × ( − ) | Negative | 3 × (−4) = −12 |
| ( − ) × ( + ) | Negative | (−3) × 4 = −12 |
Integer division (also called Euclidean division) expresses the division of integer a by integer b as:
a = q × b + r, where 0 ≤ |r| < |b|
- q = integer quotient (whole part of the division)
- r = remainder
- Example: 17 ÷ 5 → quotient = 3, remainder = 2, because 17 = 3 × 5 + 2
- Example: −17 ÷ 5 → quotient = −3, remainder = −2, because −17 = (−3) × 5 + (−2)
Exponents, Roots, and Logarithms
Exponents (Powers)
The expression Aᴮ means multiplying A by itself B times:
- 2³ = 2 × 2 × 2 = 8
- (−2)³ = (−2) × (−2) × (−2) = −8
- (−2)⁴ = (−2) × (−2) × (−2) × (−2) = 16 (even power of negative = positive)
- 2⁻³ = 1 / 2³ = 1/8 = 0.125 (negative exponent = reciprocal)
- What is a negative number squared? (−n)² = n² — always positive!
Roots
The nth root of A is the number that, raised to the power n, gives A: ⁿ√A
- √9 = 3 (square root, n = 2)
- ∛27 = 3 (cube root, n = 3)
- ∛(−8) = −2 (odd root of negative number — valid!)
- √(−4) = undefined in real numbers (even root of negative)
Logarithms
The logarithm logB(A) answers: "B raised to what power gives A?"
- log10(100) = 2, because 10² = 100
- log2(8) = 3, because 2³ = 8
- The logarithm of a negative number is undefined in real numbers.
- The logarithm base 1 is undefined (no power of 1 can produce a different number).
Change-of-base formula: logB(A) = ln(A) / ln(B)
Using the Integer Calculator
- Enter Number A — any integer (positive, negative, or zero).
- Select the operation — choose from Add (+), Subtract (−), Multiply (×), Divide (÷), Power (Aᴮ), Root (ᴮ√A), or Logarithm (logB A).
- Enter Number B — the second operand, exponent, root index, or logarithm base.
- Optional: choose a unit or currency — display results in dollars ($), rubles (₽), euros (€), meters (m), feet (ft), and many more.
- Click Calculate — see the result, formula, and number classification instantly.
FAQs
Is zero an integer?
Yes. Zero is an integer — it is a whole number with no fractional part, neither positive nor negative.
What is a negative number squared?
(−n)² = n². Squaring any real number always yields a non-negative result. For example, (−5)² = 25.
What is the log of a negative number?
In real-number arithmetic, the logarithm of a negative number is undefined. Logarithms only apply to positive arguments. (In complex analysis, log of negatives exists but goes beyond this tool.)
What is the difference between integer division and regular division?
Regular division gives an exact decimal result (e.g., 7 ÷ 2 = 3.5). Integer division gives only the whole-number quotient and a remainder (7 ÷ 2 = quotient 3, remainder 1).
Can I use this as a negative number calculator?
Absolutely. All seven operations support negative integers. The number classification table in the results tells you whether each number is positive, negative, or zero.