Arbitrary Precision Calculator

Q: What functions does this calculator support?

The calculator supports these functions: sqrt , abs , sign , floor , ceil , round , inverse , factorial , exp , log (natural), log10 , log2 , sin , cos , tan , gcd , lcm , prime , and random .

Q: What is the difference between Arbitrary and Fixed precision mode?

In Arbitrary mode, the calculator uses a default precision of 100 digits and keeps exact fractions when possible. In Fixed mode, you choose exactly how many significant digits (1 to 2,000) the calculator uses during computation. Fixed mode gives you more control but may run slower at high digit counts.

Q: What does the three dots (…) at the end of a result mean?

The three dots mean the number has been truncated or is an approximation. The full result has more digits than what is shown. You can increase the precision or display digits settings to see more of the answer.

Q: How do variables work?

The workspace gives you ten variables named p through z . Type an expression next to any letter, then press the arrow button or Tab to evaluate it. You can use one variable inside another. For example, set p = 2^100 and then set q = p + 1 . When you change p, q updates automatically.

Arbitrary Precision Calculator

Updated Jul 14, 2026 By Jehan Wadia

Introduction

This arbitrary precision calculator lets you work with numbers of any size — no rounding, no limits. Most calculators stop at 15 or 16 digits. This one can handle hundreds or even thousands of digits with exact results. You can add, subtract, multiply, divide, raise numbers to large powers, compute factorials, find square roots, and much more.

Type an expression like 2^1000 or 100! into the quick input box and press Calculate to see the full result. Use variables p through z in the workspace below to store values and build on them. The calculator supports functions such as sqrt, gcd, log, sin, cos, and factorial, along with constants like pi, e, and phi. You can choose how results display — as fractions, decimals, scientific notation, or even hexadecimal — and adjust precision up to 2,000 significant digits.

Whether you need to check a big exponent, verify a prime number, or simply do math beyond what a standard calculator allows, this tool gives you the exact answer fast, right in your browser.

How to Use Our Arbitrary Precision Calculator

This calculator lets you type math expressions with very large or very small numbers and get exact results. You enter expressions, pick how precise and how formatted you want the output, and the calculator returns your answer instantly.

Precision Mode: Choose "Arbitrary" for automatic precision or "Fixed" to set an exact number of digits. Arbitrary mode works well for most tasks. Use Fixed mode when you need to control how deep the calculation goes.

Significant Digits: This box appears when you pick Fixed mode. Type a number from 1 to 2000 to set how many digits the calculator keeps during its work. A lower number runs faster. A higher number gives more detail.

Output Display Format: Pick how your answer looks. "Fixed Decimal" shows a normal number. "Rational" shows a fraction. "Scientific" uses powers of ten. "Floating" shows a short decimal. "Magnitude" shows the rough size. "Hexadecimal" shows base-16.

Display Digits: Set how many digits show up in Scientific and Floating formats. You can pick from 1 to 200.

Show Primality (P?): Click this button to turn on a tag that tells you if a whole-number result is a prime number or not.

Group Digits: Click this button to add thin spaces every three digits in your results. This makes big numbers easier to read.

Quick Expression: Type any one-off math expression here, like 2^1000 or 100!, and press Enter or click "Calculate" to get your answer right away. You can also click any example chip below the box to load a sample expression.

Variable Workspace (p–z): Use these ten rows to store and chain expressions. Type a formula next to any letter, then press the arrow button or Tab to evaluate it. Variables can reference each other by letter — for example, set p = 2^100 and then set q = p + 1. All dependent results update automatically when you change a value.

Evaluate All / Reset: Click "Evaluate All" to recalculate every variable and the quick expression at once. Click "Reset" to restore all fields back to the default sample values.

What Is Arbitrary Precision Arithmetic?

Most calculators and computers have a limit on how many digits they can handle. Once a number gets too big or has too many decimal places, they round it off or give a wrong answer. Arbitrary precision arithmetic removes that limit. It lets you work with numbers that have hundreds, thousands, or even millions of digits and still get an exact result.

Why Does Precision Matter?

Regular calculators use a fixed amount of memory to store numbers. This means they can only hold about 15 to 17 digits. That works fine for everyday math, but it falls apart with very large or very small numbers. For example, 2 raised to the power of 1000 creates a number with over 300 digits. A normal calculator cannot show the full answer. An arbitrary precision calculator can.

How This Calculator Works

This tool uses rational arithmetic to keep results exact whenever possible. A rational number is simply a fraction, like 1/7 or 355/113. Instead of turning fractions into rounded decimals right away, the calculator stores the top number (numerator) and bottom number (denominator) separately. This means no precision is lost during addition, subtraction, multiplication, or division.

For operations like square roots, logarithms, and trigonometric functions, exact fractions are not possible. In those cases, the calculator uses scaled integer math to compute results to as many decimal places as you choose — up to 2,000 significant digits.

Common Uses

Arbitrary precision calculators are useful in number theory, cryptography, and scientific research where rounding errors can cause real problems. Students use them to explore large factorials, check if huge numbers are prime, or see hundreds of digits of pi. Programmers use them to verify algorithms that deal with big integers.

Key Features

Big number support — handle numbers with thousands of digits without overflow.
Exact fractions — results stay as ratios (like 1/3) instead of rounded decimals (like 0.333).
Variable workspace — store results in variables (p through z) and reference them in other expressions.
Built-in functions — factorial, square root, GCD, LCM, logarithms, trig functions, and more.
Multiple output formats — view results as fractions, decimals, scientific notation, or hexadecimal.
Primality testing — quickly check whether a large integer is a prime number.

Formulas used

Pi (Machin's formula)

\pi = 16\arctan\!\left(\frac{1}{5}\right) - 4\arctan\!\left(\frac{1}{239}\right)

Exponential (Taylor series with argument reduction)

e^{x} = \sum_{k=0}^{\infty} \frac{x^{k}}{k!}

Natural logarithm (series)

\ln v = 2\sum_{k=0}^{\infty} \frac{1}{2k+1}\left(\frac{v-1}{v+1}\right)^{2k+1}

Sine (Taylor series)

\sin x = \sum_{k=0}^{\infty} \frac{(-1)^{k}\, x^{2k+1}}{(2k+1)!}

Cosine (Taylor series)

\cos x = \sum_{k=0}^{\infty} \frac{(-1)^{k}\, x^{2k}}{(2k)!}

General real power

a^{b} = e^{\,b \ln a}

Square root (Newton's method)

x_{n+1} = \frac{1}{2}\left(x_n + \frac{N}{x_n}\right)

Golden ratio

\phi = \frac{1 + \sqrt{5}}{2}

Frequently asked questions

What does arbitrary precision mean?

Arbitrary precision means the calculator can work with numbers of any size. Most calculators stop at about 15 digits. This one can handle hundreds or thousands of digits and still give you the exact answer.

What operators and symbols can I use?

You can use + for addition, - for subtraction, * for multiplication, / for division, % or mod for remainder, ^ for powers, and ! for factorial. You can also use parentheses ( ) to group parts of an expression.

What functions does this calculator support?

The calculator supports these functions: sqrt, abs, sign, floor, ceil, round, inverse, factorial, exp, log (natural), log10, log2, sin, cos, tan, gcd, lcm, prime, and random.

What constants are available?

You can use three built-in constants: pi (3.14159…), e (2.71828…), and phi (the golden ratio, 1.61803…). Just type the name in your expression.

How do I enter hexadecimal numbers?

Start the number with 0x followed by hex digits. For example, type 0xFF for 255 or 0x1A3 for 419. You can also set the output format to Hexadecimal to see results in base-16.

What is the difference between Arbitrary and Fixed precision mode?

In Arbitrary mode, the calculator uses a default precision of 100 digits and keeps exact fractions when possible. In Fixed mode, you choose exactly how many significant digits (1 to 2,000) the calculator uses during computation. Fixed mode gives you more control but may run slower at high digit counts.

Why is my calculation slow?

Large precision values and complex expressions take more time. If you set significant digits above 600, the calculator shows a warning. Try lowering the precision, simplifying your expression, or breaking it into smaller steps using the variable workspace.

What does the three dots (…) at the end of a result mean?

The three dots mean the number has been truncated or is an approximation. The full result has more digits than what is shown. You can increase the precision or display digits settings to see more of the answer.

How do variables work?

The workspace gives you ten variables named p through z. Type an expression next to any letter, then press the arrow button or Tab to evaluate it. You can use one variable inside another. For example, set p = 2^100 and then set q = p + 1. When you change p, q updates automatically.

Can I use variables in the Quick Expression box?

Yes. The Quick Expression box can reference any variable from the workspace. If you set p = 2^100 in the workspace, you can type p * 3 in the quick box and it will use that value.

What happens if two variables depend on each other?

The calculator detects circular dependencies and shows an error. For example, if p uses q and q uses p, neither can be solved. Change one of them so the loop is broken.

How does the primality test work?

Click the Show Primality (P?) button in Global Configuration. Each whole-number result will then show a tag that says Prime or Composite. The test uses the Miller-Rabin algorithm with multiple witnesses, which is very accurate even for large numbers.

Can this calculator handle negative exponents?

Yes. A negative exponent gives you a fraction. For example, 2^-3 returns 1/8. You can see this as a fraction by setting the output format to Rational.

Can I use decimal exponents like 2^0.5?

Yes. Decimal exponents work for positive bases. Typing 2^0.5 gives you the square root of 2. The result will be an approximation since it is an irrational number.

What is the largest number this calculator can handle?

There is no hard limit on number size. The calculator runs in your browser and uses its memory. In practice, numbers with tens of thousands of digits work fine. Extremely large computations may slow down or run out of memory depending on your device.

Does this calculator work offline?

All calculations run directly in your browser using JavaScript. Once the page loads, no internet connection is needed to perform computations. However, you do need to load the page first.

How do I copy a result?

Click the Copy button next to any result. The raw, unformatted value is copied to your clipboard. This gives you the full number without digit grouping spaces.

What does the chart at the bottom show?

The bar chart shows the size of each result measured in number of digits. This helps you quickly compare how large your computed values are across all variables.

How do I calculate a factorial?

You can use either the ! symbol or the factorial() function. For example, 100! and factorial(100) both give you 100 factorial. The input must be a non-negative whole number.

Why does 1/3 show as a fraction instead of 0.333…?

The calculator keeps exact fractions when possible. In Rational output format, 1/3 stays as 1/3. Switch the output format to Fixed Decimal to see it as 0.333… with as many digits as your precision allows.

What does the Display Digits setting do?

Display Digits controls how many digits appear in Scientific and Floating output formats. It does not affect the actual precision of the calculation — only how much of the result you see on screen. You can set it from 1 to 200.

Rate this calculator