Happy Number Checker

How it is calculated

A happy number is one that ends at 1 when you repeat a simple step: replace the number with the sum of the squares of its digits. The tool does exactly this loop, n → Σ dᵢ², counting each step, and stops when it reaches 1 or when a value repeats, which means it is stuck in a cycle. If 1 is reached the number is called happy and the step count is shown; otherwise it is not happy and the steps show a dash. Whole numbers from 1 to 1,000,000,000 are accepted, and decimals are cut to the integer part. Every unhappy number eventually falls into the same cycle that contains 4.

Common mistakes

• Squaring the whole number instead of each digit. For 19 you add 1² and 9², not 19².
• Forgetting zero digits. They add nothing, but they must not be skipped when you are counting the digits by hand.
• Counting the starting number as a step. The tool counts only the replacements, so 19 takes 4 steps and not 5.
• Expecting a result for 0 or negative numbers. The tool accepts positive whole numbers only, up to 1,000,000,000.
• Assuming the sequence for an unhappy number can run forever. It always lands in the same loop, so the check always ends.