Digits are added exactly, carrying across every place, within the input and workload limits. For example, 999999999999999999 + 1 = 1000000000000000000.
Useful for totalling large counts, checking ledger sums or verifying programming results.
Subtraction handles signs automatically, so a larger second number simply produces a negative result. 1000000000000000000 − 1 = 999999999999999999, and 5 − 12 = −7.
Handy for finding exact differences between big identifiers, timestamps or balances.
This calculator retains the full integer product: 999999999999999999 × 999999999999999999 = 999999999999999998000000000000000001.
Use exact products to check integer arithmetic and combinatorial calculations.
For whole-number inputs, division returns the integer quotient (rounded toward zero), the remainder, and the reduced fraction. A decimal view is also available, clearly marked as rounded to your chosen number of places. For 100000000000000000000 ÷ 7 the quotient is 14285714285714285714 with remainder 2.
Use it to split large quantities or confirm divisibility.
Raise an integer or decimal base to a non-negative whole-number power, such as 2^100 = 1267650600228229401496703205376. To keep your browser responsive, results estimated to exceed two million digits are refused with an explanation.
Useful for growth calculations, binary sizes and number-theory exercises.
Modulo gives the remainder after division. 123456789012345678901234567890 mod 97 = 52. With negative numbers the remainder takes the sign of the first number (truncated division), so −7 mod 3 = −1.
Common in checksums, hashing and clock-style arithmetic.
The factorial n! multiplies every whole number from 1 to n. 25! = 15511210043330985984000000, and by definition 0! = 1. Negative inputs are rejected, and n is capped at 50,000 as a workload safeguard. Calculation time depends on the input and device.
Factorials appear whenever you count arrangements or permutations.
For nonzero inputs, the GCD is the largest positive integer dividing both values, and the LCM is their smallest positive common multiple. Signs are ignored; this calculator returns GCD(0, 0) = 0 and LCM(a, 0) = 0. gcd(1071, 462) = 21 and lcm(4, 6) = 12.
Use GCD to simplify fractions and LCM to find common denominators or repeating cycles.
Square multiplies a number by itself: 123456789² = 15241578750190521. Square root returns the exact integer square root (rounded down): ⌊√10^40⌋ = 10^20, and ⌊√99⌋ = 9.
Useful for geometry, perfect-square checks and number theory.
Bitwise operations work on the binary form of whole numbers within the input and workload limits. 0xFF AND 0x0F = 15, 12 OR 3 = 15, 12 XOR 10 = 6, 1 << 100 = 2^100 and 1024 >> 3 = 128. Negative numbers follow unbounded two's-complement rules, rather than a fixed-width mask.
Use these operations to inspect masks, flags, and integer bit patterns. Switch the result to Hex or Binary view to see the bits.
Enter values like 3.5e19 or 0.000125. Add, subtract, multiply, divide, power and square keep decimals exact using fractions, then show the exact decimal, or a rounded decimal to your chosen precision when it repeats forever (like 1 ÷ 3).
No floating-point rounding: 0.1 + 0.2 = 0.3 exactly.
nCr counts ways to choose r items from n when order doesn't matter; nPr counts ordered arrangements. C(52, 5) = 2598960 poker hands, and P(10, 3) = 720.
These formulas count selections of distinct items without replacement.