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Math powerhouse

Big Number Calculator

The calculator below can compute very large numbers. Acceptable formats include: integers, decimal, or the E-notation form of scientific notation, i.e. 23E18, 3.5e19, etc. The world's best big number calculator with arbitrary precision.

Calculate Big Numbers

digits after the decimal place in the result

Click the buttons below to calculate:

Powers of 10 Name

Powers of 10Name
10^9Billion
10^12Trillion
10^15Quadrillion
10^18Quintillion
10^21Sextillion
10^24Septillion
10^27Octillion
10^30Nonillion
10^33Decillion
10^36Undecillion
10^39Duodecillion
10^42Tredecillion
10^45Quattuordecillion
10^48Quindecillion
10^51Sexdecillion
10^54Septendecillion
10^57Octodecillion
10^60Novemdecillion
10^63Vigintillion
10^100Googol
10^303Centillion
10^googolGoogolplex

Why Big Number Calculators?

Standard calculators typically support numbers up to approximately 10 decimal places. However, many fields of study require calculations involving much larger numbers. Big number calculators are essential tools for:

  • Cosmology and Astronomy: Calculating distances, masses, and timescales of celestial objects
  • Mathematics: Working with extremely large integers, factorials, and mathematical constants
  • Cryptography: Handling large prime numbers and encryption keys
  • Statistical Mechanics: Computing probabilities and partition functions
  • Computer Science: Analyzing algorithms and data structures with large inputs

Examples of Big Numbers

Here are some real-world examples of very large numbers:

Bits on a computer's hard disk: Modern hard drives can store trillions of bits (terabytes to petabytes)

Cells in the human body: Approximately 37.2 trillion (3.72 × 10¹³) cells

Neurons in the human brain: Approximately 86 billion (8.6 × 10¹⁰) neurons

Avogadro's constant: 6.022 × 10²³ (number of atoms in one mole of a substance)

Estimated atoms in the observable universe: Approximately 10⁸⁰ atoms

Advanced Notations for Extremely Large Numbers

For numbers beyond standard scientific notation, mathematicians have developed several advanced notation systems:

Knuth's Up-Arrow Notation

Uses up-arrows (↑) to represent repeated exponentiation. For example, 3↑↑3 represents 3^(3^3) = 3^27.

3↑↑3 = 3^(3^3) = 7,625,597,484,987

Conway Chained Arrow Notation

A notation system that can express extremely large numbers using chains of arrows.

a → b → c represents a^(b^c) in a more compact form

Steinhaus-Moser Notation

Uses geometric shapes (triangle, square, pentagon) to represent recursive operations.

Triangle(n) = n^n, Square(n) = Triangle(Triangle(...Triangle(n)...))

Scientific and Entertainment Value

Big number calculators serve both scientific and educational purposes. They allow researchers to perform precise calculations with numbers that would be impossible to handle manually or with standard calculators.

Additionally, they provide entertainment value by allowing users to explore extremely large numbers. For example, calculating 10,000 factorial (10,000!) results in a number with over 35,000 digits, demonstrating the vastness of mathematical possibilities.

Fun Fact: The factorial of 100 (100!) is approximately 9.33 × 10¹⁵⁷, which is larger than the estimated number of atoms in the observable universe!

Understanding E-notation

E-notation (also called scientific notation) is a way to represent very large or very small numbers compactly:

Format: aEb or aeb represents a × 10^b

Examples:

23E18 = 23 × 10¹⁸ = 23,000,000,000,000,000,000

3.5e19 = 3.5 × 10¹⁹ = 35,000,000,000,000,000,000

1.5E-5 = 1.5 × 10⁻⁵ = 0.000015