What is an Armstrong number?

An Armstrong number (also called a narcissistic number) is a number that equals the sum of its own digits each raised to the power of the total digit count. For example, 153 is a 3-digit number and 1³ + 5³ + 3³ = 1 + 125 + 27 = 153.

Are single-digit numbers Armstrong numbers?

Yes. Every single-digit number (1–9) is trivially an Armstrong number because each equals itself raised to the first power (e.g., 7¹ = 7).

How many Armstrong numbers are there up to 10,000?

There are 16: the nine single-digit numbers (1–9) plus 153, 370, 371, 407, 1634, 8208, and 9474. Armstrong numbers become increasingly rare as the digit count grows.

Is 0 an Armstrong number?

Zero is sometimes included by convention (0¹ = 0), but this tool requires a positive integer, so the valid range starts at 1.

What is the largest known Armstrong number?

The largest known Armstrong number is a 39-digit number. There are exactly 88 Armstrong numbers in base 10, and no more exist beyond the 39-digit one.

Armstrong Number Checker

Name: Armstrong Number Checker
Availability: InStock
Author: Nham Vu

Enter a positive integer to see if it is an Armstrong number, with a full digit-by-digit breakdown and a reference list of all Armstrong numbers up to 10,000.

Check a Number

Enter a positive integer up to 15 digits.

Number

Calculation

Digit	Power (k)	Value
Sum

Try an example

Armstrong Numbers up to 10,000

All 16 Armstrong numbers in this range.

#	Number	Digits (k)	Verification

Summary

Enter a positive integer to see if it is an Armstrong number, with a full digit-by-digit breakdown and a reference list of all Armstrong numbers up to 10,000.

How it works

Enter a positive integer (up to 15 digits) in the input field.
The tool counts the digits (k) and raises each digit to the power k.
If the sum of all those powers equals the original number, it is an Armstrong number.
The breakdown panel shows each digit, its power, and the running total.
The reference table below lists every Armstrong number from 1 through 9,474.

Use cases

Verify whether a specific number satisfies the narcissistic property.
Study digit-power relationships for number theory coursework.
Find and confirm all small Armstrong numbers for a homework problem.
Demonstrate the concept of narcissistic numbers to students interactively.
Cross-check results from a manual or programmatic Armstrong-number algorithm.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu