★ MATH · EXPONENTS · CONVERTERS
2^64 = 18446744073709551616 — all 20 digits, exact. Enter a base and an exponent up to 1000 and this calculator gives the exact integer power — no rounding, no scientific notation — plus the digit count, and exact reciprocals for negative exponents.
Ordinary calculators give up at about 15 digits: type 2^64 into one and you get 1.8446744073709552 × 10^19, with the last five digits rounded away. This calculator uses BigInt — exact integer arithmetic with no size limit — so 2^64 comes back as 18446744073709551616, all 20 digits, exact. Negative integer exponents give the exact reciprocal, and decimal bases use ordinary floating-point math and are labelled approximate.
An exponent says how many times to multiply the base by itself: 2^64 is 2 multiplied by itself 64 times. Ordinary computer arithmetic stores numbers in 64-bit floating point, which holds about 15 to 16 significant digits — so 2^64 comes back as 1.8446744073709552 × 10^19, and the last five digits are gone. BigInt is a different kind of number: it stores integers exactly, digit by digit, with no size limit, so 2^64 comes back as 18446744073709551616 — all 20 digits, every one of them right. The same holds for 3^40, which is 12157665459056928801, and for 10^100, a googol, which is 1 followed by 100 zeros and has 101 digits. The calculator caps the exponent at 1000 and the base at 1000, because beyond that the answers run to thousands of digits and stop being useful on a page.
2^64 is the number that shows up everywhere in computing: it is the number of values a 64-bit unsigned integer can hold, from 0 to 18,446,744,073,709,551,615. It is the size of the IPv6 address space in its early form, the number of distinct values in a 64-bit register, and the reason your phone's processor is called 64-bit. The chessboard legend uses it too: put 1 grain of rice on the first square, 2 on the second, 4 on the third, doubling each time, and the 64th square alone holds 2^63 grains — 9,223,372,036,854,775,808 — while the whole board holds 2^64 minus 1. Knowing the exact digits matters when you are checking code, verifying a hash boundary, or settling an argument about how big 2^64 really is: the rounded version ends in ...55152, and the exact version ends in ...551616.
A negative exponent flips the power into a fraction: 2^-10 is 1 divided by 2^10, which is 1/1024, or 0.0009765625. The calculator shows both forms — the exact fraction 1/1024 and the decimal — because the fraction is exact and the decimal is exact too for powers of two, but for other bases the decimal may repeat: 3^-2 is 1/9, which is 0.111... forever, so the fraction is the honest answer and the decimal is a rounded display. The same rule gives 10^-3 as 1/1000, or 0.001, and 5^-3 as 1/125, or 0.008. Zero to a negative power is undefined — you cannot divide by zero — so the calculator shows an error for 0^-1, and 0^0 is undefined too, so that shows an error as well.
Whole-number bases give exact BigInt results, but decimal bases cannot: 1.5 is not an integer, so the calculator falls back to ordinary floating-point math and labels the result approximate. 1.5^20 comes back as 3325.256730079651, which is the floating-point value — correct to about 15 significant digits, with the last digit or two possibly rounded. The same applies to any decimal base: 2.5^10, 0.5^8, and 9.99^3 all come back approximate, and the page says so on the result. If you need an exact answer for a decimal base, scale it to an integer first: 1.5^20 is 3^20 divided by 2^20, and both of those are exact BigInt powers — 3,486,784,401 divided by 1,048,576 — which is 3325.25673007965087890625 exactly.
Rounding convention, stated plainly: there is no rounding in the exact path — BigInt results are the full integer, every digit, and the digit count is the count of those digits. The approximate path rounds to the floating-point value, about 15 significant digits, and the page labels it approximate. Reciprocals show the exact fraction first and the decimal second, so the exact answer is never hidden behind a rounded display.
| Power | Value | Digits |
|---|---|---|
| 2^10 | 1,024 | 4 |
| 2^20 | 1,048,576 | 7 |
| 2^32 | 4,294,967,296 | 10 |
| 2^64 | 18,446,744,073,709,551,616 | 20 |
| 3^40 | 12,157,665,459,056,928,801 | 20 |
| 5^25 | 298,023,223,876,953,125 | 18 |
| 10^100 | 1 followed by 100 zeros (a googol) | 101 |
| Output | Formula | What it means |
|---|---|---|
| Exact power | Base multiplied by itself exponent times (BigInt) | 2^64 = 18446744073709551616. |
| Digit count | Number of digits in the result | 20 digits for 2^64. |
| Negative exponent | 1 ÷ base^|exponent| | 2^-10 = 1/1024 = 0.0009765625. |
| Decimal base | Math.pow, floating point | 1.5^20 = 3325.256730079651, approximate. |
| 3^40 | 3 multiplied by itself 40 times | 12157665459056928801, 20 digits. |
| 10^100 | 1 followed by 100 zeros | A googol, 101 digits. |
| Exponent over 1000 | Limit check | Error — the exponent must be from −1000 to 1000. |
| Non-integer exponent | Whole-number check | Error — exact integer powers need whole-number exponents. |
Whole-number bases with whole-number exponents are exact: the BigInt path computes the full integer, every digit, with no rounding and no size limit inside the caps — base from −1000 to 1000, exponent from −1000 to 1000. Negative integer exponents give the exact reciprocal as a fraction plus its decimal value, which may be rounded for display when it repeats. Decimal bases use floating-point math and are approximate to about 15 significant digits, and the page labels them approximate. Non-integer exponents are refused with an error, because this tool gives exact integer powers — 2^0.5 is the square root of 2, about 1.4142135623730951, and belongs in a scientific calculator, not here. 0^0 and 0 to a negative power are undefined and show errors. Results over the caps are refused rather than computed, because a 3000-digit answer is not useful on a page.
Bright Side Kit. "Large Exponent Calculator: Exact Powers with BigInt" https://brightoolbox.com/large-exponent-calculator/ Accessed October 24, 2026.18446744073709551616 — all 20 digits, exact. It is the number of values a 64-bit unsigned integer can hold, and an ordinary calculator rounds it to 1.8446744073709552 × 10^19.
12157665459056928801 — 20 digits, exact. Enter base 3 and exponent 40 to see it, or check the powers table on this page.
A googol: 1 followed by 100 zeros, 101 digits in total. Enter base 10 and exponent 100 to see the full number.
1/1024, or 0.0009765625. A negative exponent gives the exact reciprocal: 2^-10 is 1 divided by 2^10, and this calculator shows both the fraction and the decimal.
Because it rounds. Ordinary calculators store numbers in floating point with about 15 significant digits, so 2^64 comes back as 1.8446744073709552 × 10^19 with the last five digits rounded away. This calculator uses BigInt — exact integer arithmetic — so every digit is right.
Yes, but the result is approximate. 1.5^20 is 3325.256730079651 by floating-point math, correct to about 15 significant digits, and the page labels it approximate. Whole-number bases give exact results.
No — this calculator gives exact integer powers and needs a whole-number exponent, so it shows an error for 2.5 or 0.5. 2^0.5 is the square root of 2, about 1.4142135623730951, and belongs in a scientific calculator.
1000, and the base must be from −1000 to 1000. An exponent of 1001 shows an error, because beyond that the answers run to thousands of digits and stop being useful on a page.