Happy Number Checker Calculator

Work out happy number checker instantly with clear inputs, formula shown and shareable results.

About Happy Number Checker Calculator

Repeatedly replace a number by the sum of the squares of its digits. If you reach 1 the number is happy; otherwise you always fall into the single cycle 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4.

Formula

Happy step

v → Σ d² over the digits of v

Worked example

With the default values below, Happy Number Checker Calculator returns Result of Happy number, it reaches 1. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number to testminimum 1: 23
Maximum steps to followaccepts 1–200: 50

Results

Result: Happy number, it reaches 1
Steps to reach 1: 3
Sequence followed: 23 → 13 → 10 → 1
Value where it settled: 1

Step by step

1Values used
2Happy step
3Result= Happy number, it reaches 1
4Steps to reach 1= 3
5Sequence followed= 23 → 13 → 10 → 1
6Value where it settled= 1

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is 23 happy?

Yes: 4 + 9 = 13, then 1 + 9 = 10, then 1 + 0 = 1, in three steps.

Why is there only one bad cycle?

For numbers below 1000 the map always drops below 244, and exhaustive checking of that small range finds just the one cycle.