# Big Number Calculator

> Add, subtract, multiply, divide, raise to powers and take remainders of numbers with thousands of digits, exactly and without rounding errors.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/big-number-calculator

Ordinary calculators keep about 15 to 16 significant digits. This one works on every digit you enter, so 2¹⁰⁰ or a 50-digit product comes out exactly.

Also called: Large number calculator, Arbitrary-precision calculator.

## Inputs
- X (default 2)
- Operation (options: X + Y, X − Y, X × Y, X ÷ Y, X to the power Y, X mod Y (remainder); default pow)
- Y (default 100)
- Decimal places for division (default 20; optional)

## Results
- Result
- Precision
- Digits before the decimal point
- Approximately

## Formula

```
Each number is held as an integer of any length with a decimal scale: X = m ÷ 10ˢ. Addition, subtraction, multiplication and whole powers are exact; division rounds half up at the chosen decimal place
```

Where:
- m: all the digits as one integer
- s: the number of decimal places

## Worked example
1. 2¹⁰ = 1024, so 2¹⁰⁰ = 1024¹⁰, about 1.27 × 10³⁰.
2. Multiplying out with every digit kept gives 1,267,650,600,228,229,401,496,703,205,376.
3. That is 31 digits; ordinary double-precision arithmetic keeps only the first 16 or so (1.267650600228229 × 10³⁰).

**Result:** 2¹⁰⁰ = 1267650600228229401496703205376 exactly.

## What the result means

Use this when the last digits matter: checking cryptography or number-theory examples, exact factorial-sized products, or showing that 0.1 + 0.2 is exactly 0.3 in decimal.

## Assumptions and limits
- Mod uses truncated division, so the remainder has the sign of X (as in most programming languages).
- Results are limited to about 200,000 digits.
- Powers must be whole numbers; roots and logarithms are not supported.

## Questions

### Why does my phone show 0.30000000000000004 for 0.1 + 0.2?

Most software stores numbers in binary floating point, where 0.1 has no exact representation. This calculator stores decimal digits exactly.

### How precise is division?

Division gives as many decimal places as you ask for, up to 1,000, rounded half up; the result is marked exact when the division terminates.

## Related calculators
- [Scientific Notation Calculator](https://calculators.geekmidst.com/calculators/scientific-notation-calculator)
- [Rounding Calculator](https://calculators.geekmidst.com/calculators/rounding-calculator)
- [Long Division Calculator](https://calculators.geekmidst.com/calculators/long-division-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/big-number-calculator