Big Number Calculator
Exact arithmetic on whole numbers of up to 79 digits: add, subtract, multiply, divide, raise to a power or take the remainder, with every digit kept.
Result
Result: 1.219326311 × 10^59
Exact: no digit is rounded, except in the scientific form and a cut-off decimal.
- Every digit
- 121932631137021795226185032733622923332237463801111263526900
- Digits in the result
- 60
- In scientific notation
- 1.219326311 × 10^59
https://calcgallery.com/algebra-numbers/big-number-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Big Number Calculator
- Type two whole numbers of up to 79 digits each, with a minus sign if negative. Leave out commas and spaces.
- Choose add, subtract, multiply, divide, power or mod.
- Read the exact answer. Past 50 digits the headline is in scientific notation and every digit is listed below.
Exact whole numbers
The page reads each number as a string of digits and does the arithmetic on the whole string, the way long multiplication and long division work on paper. There is no rounding at any step, so the last digit of a 60-digit product is as reliable as the first.
a + b, a − b, a × b, a^b exacta ÷ b decimal, cut off at 40 places if it repeatsa = b × q + r whole-number division, 0 ≤ r < |b|Reading a long answer
A result longer than 50 digits is headlined in scientific notation, rounded to ten significant figures from its own digits, so the size is clear at a glance, and the full number is given below it with a count of its digits. To write a number in scientific notation or to convert it back, use the scientific notation calculator.
Not covered
Decimals and fractions as inputs, and roots. For the prime factors of a number, use the prime number calculator; for exact factorials of up to 1,000, the factorial calculator.
With your numbers
- Every digit is computed exactly, with no rounding.
Quick reference
Exact: no digit is rounded, except in the scientific form and a cut-off decimal.
| Example | Result |
|---|---|
| 30 digits × 30 digits | 1.219326311 × 10^59 |
| 2 to the 100 | 1267650600228229401496703205376 |
| 3 to the 200 | 2.656139889 × 10^95 |
| 100 ÷ 7 | 14.2857142857142857142857142857142857142857… |
| 10^40 + 1 − 10^40 | 1 |
| −7 mod 3 | 2 |
Common questions about the Big Number Calculator
- Why does my ordinary calculator get big numbers wrong?
- Most calculators and spreadsheets store numbers as 64-bit floating point, which keeps only about 15 to 17 significant digits. 123456789012345678901234567890 × 987654321098765432109876543210 has 60 digits; floating point keeps the first 15 or so and silently drops the rest. This page works on whole numbers exactly, digit by digit, so nothing is lost.
- How does division work here?
- It gives two answers. The first is the quotient as a decimal, exact when it ends and cut off after 40 decimal places, marked with …, when it repeats forever, as 100 ÷ 7 does. The second is whole-number division: 100 = 7 × 14 + 2, a quotient of 14 and a remainder of 2.
- What does mod mean for negative numbers?
- Conventions differ. This page uses the Euclidean one, where the remainder is always between 0 and one less than |b|: −7 mod 3 is 2, because −7 = 3 × (−3) + 2. Many programming languages give −1 instead. The modulo calculator shows all three conventions side by side.
- How large a power can it compute?
- Any whole-number power whose answer has at most 3,000 digits: 2⁹⁹⁰⁰, with 2,981 digits, is shown in full, while 2¹⁰⁰⁰⁰, with 3,011, is too long. A negative power is a fraction rather than a whole number, so it is left out; the exponent calculator handles those.