Big Number Calculator

What this calculator does

The Big Number Calculator performs arithmetic on values that are too large for an ordinary handheld calculator. It supports addition, subtraction, multiplication, division, powers, square roots, squares, factorials, remainders, greatest common divisors, and least common multiples.

Big-number arithmetic matters in cryptography, astronomy, combinatorics, statistical mechanics, and any field where values exceed the roughly 15-digit precision of standard floating-point numbers. The calculator keeps integer results exact and rounds division and square roots to the precision you request.

How to use this calculator

1. Choose an operation.
2. Enter X. Enter Y when the operation uses two values.
3. Set the precision, which controls the number of digits after the decimal point in the result.
4. Click Calculate.

The default example adds X = 12,345,678,901,234,567,890 and Y = 98,765,432,109,876,543,210. The exact result is 111,111,111,011,111,111,100.

Operations

X + Y        addition
X − Y        subtraction
X × Y        multiplication
X ÷ Y        division
X^Y          power
√X           square root
X²           square
X!           factorial
X MOD Y      remainder
GCD(X, Y)    greatest common divisor
LCM(X, Y)    least common multiple

Addition, subtraction, multiplication, powers with whole-number exponents, squares, factorials, remainders, GCD, and LCM are computed with exact integer arithmetic when both inputs are whole numbers. Division and square roots use decimal arithmetic and are rounded to the requested precision.

What the results mean

The result panel shows X, Y when the operation uses it, the full result, the number of digits in the result, and a scientific-notation summary. The primary result is the exact integer or the rounded decimal answer.

For example, 2¹⁰⁰ is exactly 1,267,650,600,228,229,401,496,703,205,376. That value has 31 digits, and its scientific notation is approximately 1.2676506002e+30.

Assumptions and limitations

• Each input may contain up to 10,000 characters.
• Precision must be between 0 and 1,000 digits after the decimal point.
• Factorial input must be a non-negative whole number up to 5,000.
• A power exponent must be zero or greater and is limited to 10,000 when exact integer exponentiation is used.
• GCD, LCM, and MOD require whole numbers.
• Division by zero is rejected.
• Results longer than 200,000 characters are rejected to keep the page responsive.
• The calculator does not support complex numbers or symbolic expressions.

Frequently asked questions

Why use a big-number calculator instead of a normal calculator?

Most calculators store numbers in floating-point format, which has about 15 to 17 significant digits. A big-number calculator keeps every digit of an integer, so it can compute exact values for large factorials, powers, and cryptographic-sized numbers.

Is the division result exact?

Division can produce a repeating decimal, so the result is rounded to the precision you select. The underlying integer operations remain exact.

What is the largest factorial I can calculate?

The calculator allows factorial inputs up to 5,000. The result is exact, but it can be tens of thousands of digits long, so the page limits the display length.

Why does GCD require whole numbers?

The greatest common divisor is defined for integers. If you enter a decimal, the calculator cannot return a meaningful integer divisor and asks for whole numbers instead.

Reference table

Powers of 10 and names

The short scale is used here: one billion is 10⁹. The long scale used in some countries calls 10⁹ a thousand million and reserves "billion" for 10¹².

Source

Reference: Calculator.net — Big Number Calculator.