Happy Number Calculator

The Happy Number Calculator is a free online tool used to check if the number is a happy number or an unhappy number.

Happy Number Calculator

Eg, Is 145 a happy number? Enter 145 into the input box and click Calculate button.

Calculate Reset

What is a happy number?

A happy number is a number that reaches 1 when the number is replaced by the sum of squares of each digit. If the answer doesn’t reach one and it starts looping with the same numbers, then the number is not a happy number. It is called a sad or unhappy number.

The sum of squares of all unhappy numbers will eventually enter a loop of 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4.

To calculate a happy number, start by calculating the sum of squares of each digit of the number. This process is repeated until the result is 1. The algorithm will determine if the number is a happy number when the sum of squares of each digit results in 1. If it never reaches 1 or loops between numbers that have already appeared, then it is not a happy number.

For example, Is 5555 a happy number?

5555 -> 5² + 5² + 5² + 5² = 25 + 25 + 25 + 25 = 100

100 -> 1² + 0² + 0² = 1 + 0 + 0 = 1

So, 5555 is a happy number.

First 100 happy numbers

1	7	10	13	19	23	28	31	32	44
49	68	70	79	82	86	91	94	97	100
103	109	129	130	133	139	167	176	188	190
192	193	203	208	219	226	230	236	239	262
263	280	291	293	301	302	310	313	319	320
326	329	331	338	356	362	365	367	368	376
379	383	386	391	392	397	404	409	440	446
464	469	478	487	490	496	536	556	563	565
566	608	617	622	623	632	635	637	638	644
649	653	655	656	665	671	673	680	683	694

How to use the happy number calculator

The procedure to use the happy number calculator is as follows:

1Enter the positive number.
2Click Calculate button to verify whether the input number is a happy number or an unhappy number.
3Click the Reset button to start a new verification.

Solved examples using the happy number calculator

Example 1: Is 478 a happy number?

Enter 478 into the input box and click Calculate button, as shown in the figure, 478 is a happy number.

478 -> 4² + 7² + 8² = 16 + 49 + 64 = 129

129 -> 1² + 2² + 9² = 1 + 4 + 81 = 86

86 -> 8² + 6² = 64 + 36 = 100

100 -> 1² + 0² + 0² = 1 + 0 + 0 = 1

Example 2: Is 2023 a happy number?

Enter 2023 into the input box and click Calculate button, as shown in the figure, 2023 is an unhappy number.

2023 -> 2² + 0² + 2² + 3² = 4 + 0 + 4 + 9 = 17

17 -> 1² + 7² = 1 + 49 = 50

50 -> 5² + 0² = 25 + 0 = 25

25 -> 2² + 5² = 4 + 25 = 29

29 -> 2² + 9² = 4 + 81 = 85

85 -> 8² + 5² = 64 + 25 = 89

89 enters the cycle of unhappy numbers. So, 2023 is an unhappy number.

Happy Number Calculator