Calculators
Sum of Fourth Powers Calculator
Calculate the exact sum of fourth powers from 1 through n using browser-only integer arithmetic.
Sum 1⁴ + 2⁴ + … + n⁴ exactly. Enter a non-negative upper limit with up to 100 digits. Zero returns zero. Results stay in your browser.
Sum consecutive integer fourth powers exactly.
The sum 1⁴ + 2⁴ + … + n⁴ equals n(n + 1)(2n + 1)(3n² + 3n − 1)/30. For n = 3, the sum is 1 + 16 + 81 = 98. For n = 10, the sum is 25333. The zero upper limit gives the empty sum of zero. This sums the fourth powers of consecutive positive integers, rather than taking the fourth power of their sum. Enter a non-negative whole number using up to 100 digits. Leading zeros and surrounding whitespace are accepted; signs, decimals, separators and scientific notation are rejected. A direct formula avoids looping over the terms, and BigInt arithmetic preserves every digit even beyond the safe integer range. The result includes its decimal digit count; zero has one digit. All calculations run locally without uploading or storing inputs.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What formula does this calculator use?
It uses n(n + 1)(2n + 1)(3n² + 3n − 1)/30 to sum the fourth powers of integers from 1 through n. For n = 3 the result is 98.
What happens when n is zero?
The sum has no terms and equals zero. Zero is shown with a digit count of one.
Can large results lose precision?
No. BigInt integer arithmetic preserves every digit for upper limits of up to 100 digits. Inputs must be non-negative integers without separators or scientific notation, and remain in your browser.