Armstrong Number Calculator

This calculator checks whether a whole number you enter is an Armstrong number, also known as a narcissistic or pluperfect digital invariant. A number qualifies when you raise each of its digits to the power of how many digits the number has, then add those results together, and the total equals the original number back. The classic example is 153, which has three digits, and 1 cubed plus 5 cubed plus 3 cubed comes to exactly 153. Type any whole number into the input box and the calculator instantly works out the digit count, raises each digit to that power, sums the results, and tells you whether the number is or is not an Armstrong number. Alongside the main verdict, it shows the sum of digits to the power and the number of digits used in the calculation, so you can see exactly how the result was reached rather than taking it on faith. It updates live as you type, so you can test as many numbers as you like without pressing a button. The tool uses the exact integer algorithm and groups larger results for readability. It is useful for students learning number theory, programmers practising loops and exponents, or anyone curious about how self-referential numbers like 153, 370, 371 and 407 work.

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Whole number

Sum of digits^k

Number of digits (k)

The formula

For a number with k digits, raise each digit to the power k and add them. If the total equals the original number, it is an Armstrong number. For 153 (k = 3): 1^3 + 5^3 + 3^3.

Worked example

153 has three digits, so 1 cubed plus 5 cubed plus 3 cubed = 1 + 125 + 27 = 153, which matches, so 153 is an Armstrong number. Enter 153 to confirm.

Frequently asked questions

What is an Armstrong number?

A number equal to the sum of its own digits each raised to the power of the digit count, such as 153 = 1 cubed + 5 cubed + 3 cubed.

Why is it called narcissistic?

Because the number is built from its own digits, in a sense admiring itself.

How many Armstrong numbers are there?

Only finitely many, since for enough digits the maximum possible sum falls short of the number. There are 88 in base ten.

Who this calculator is for

This calculator is for students, programmers and anyone exploring number theory.

What this calculator assumes

You enter a whole number within the stated range.
The exact integer algorithm is used.
Very large results are shown grouped for readability.

Formula and sources

Related calculators

Prime Factorization Calculator: break a number into prime factors.
LCM Calculator: lowest common multiple.
GCF Calculator: greatest common factor.

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