Square Numbers List

Generate list of square numbers (perfect squares), find squares in a range, or check if a number is a perfect square. Interactive visualization with step-by-step calculations.

Square Numbers List

Square Numbers Generator

Generate perfect squares, explore patterns, and visualize mathematical relationships. Choose a mode below to get started.

Quick presets:

How many square numbers to generate?

Generate up to 1000 perfect squares with visualization and detailed breakdown.

Start Value

End Value

Find all perfect squares within your specified range.

Enter a number to check

Instantly verify if any number is a perfect square and find its root.

Embed Square Numbers List Widget

First 100 Square Numbers Generated

100 Perfect Squares

Range: 1² = 1 to 100² = 10,000

Count

100

First

Last

10,000

Sum

338,350

Visual Grid

n=1

1×1

n=2

2×2

n=3

3×3

n=4

4×4

n=5

5×5

n=6

6×6

n=7

7×7

n=8

8×8

n=9

9×9

n=10

100

10×10

n=11

121

11×11

n=12

144

12×12

n=13

169

13×13

n=14

196

14×14

n=15

225

15×15

n=16

256

16×16

n=17

289

17×17

n=18

324

18×18

n=19

361

19×19

n=20

400

20×20

n=21

441

21×21

n=22

484

22×22

n=23

529

23×23

n=24

576

24×24

n=25

625

25×25

n=26

676

26×26

n=27

729

27×27

n=28

784

28×28

n=29

841

29×29

n=30

900

30×30

n=31

961

31×31

n=32

1,024

32×32

n=33

1,089

33×33

n=34

1,156

34×34

n=35

1,225

35×35

n=36

1,296

36×36

n=37

1,369

37×37

n=38

1,444

38×38

n=39

1,521

39×39

n=40

1,600

40×40

n=41

1,681

41×41

n=42

1,764

42×42

n=43

1,849

43×43

n=44

1,936

44×44

n=45

2,025

45×45

n=46

2,116

46×46

n=47

2,209

47×47

n=48

2,304

48×48

n=49

2,401

49×49

n=50

2,500

50×50

n=51

2,601

51×51

n=52

2,704

52×52

n=53

2,809

53×53

n=54

2,916

54×54

n=55

3,025

55×55

n=56

3,136

56×56

n=57

3,249

57×57

n=58

3,364

58×58

n=59

3,481

59×59

n=60

3,600

60×60

n=61

3,721

61×61

n=62

3,844

62×62

n=63

3,969

63×63

n=64

4,096

64×64

n=65

4,225

65×65

n=66

4,356

66×66

n=67

4,489

67×67

n=68

4,624

68×68

n=69

4,761

69×69

n=70

4,900

70×70

n=71

5,041

71×71

n=72

5,184

72×72

n=73

5,329

73×73

n=74

5,476

74×74

n=75

5,625

75×75

n=76

5,776

76×76

n=77

5,929

77×77

n=78

6,084

78×78

n=79

6,241

79×79

n=80

6,400

80×80

n=81

6,561

81×81

n=82

6,724

82×82

n=83

6,889

83×83

n=84

7,056

84×84

n=85

7,225

85×85

n=86

7,396

86×86

n=87

7,569

87×87

n=88

7,744

88×88

n=89

7,921

89×89

n=90

8,100

90×90

n=91

8,281

91×91

n=92

8,464

92×92

n=93

8,649

93×93

n=94

8,836

94×94

n=95

9,025

95×95

n=96

9,216

96×96

n=97

9,409

97×97

n=98

9,604

98×98

n=99

9,801

99×99

n=100

10,000

100×100

Complete List

n	n² (Square)	Calculation
1	1	= 1 × 1
2	4	= 2 × 2
3	9	= 3 × 3
4	16	= 4 × 4
5	25	= 5 × 5
6	36	= 6 × 6
7	49	= 7 × 7
8	64	= 8 × 8
9	81	= 9 × 9
10	100	= 10 × 10
11	121	= 11 × 11
12	144	= 12 × 12
13	169	= 13 × 13
14	196	= 14 × 14
15	225	= 15 × 15
16	256	= 16 × 16
17	289	= 17 × 17
18	324	= 18 × 18
19	361	= 19 × 19
20	400	= 20 × 20
21	441	= 21 × 21
22	484	= 22 × 22
23	529	= 23 × 23
24	576	= 24 × 24
25	625	= 25 × 25
26	676	= 26 × 26
27	729	= 27 × 27
28	784	= 28 × 28
29	841	= 29 × 29
30	900	= 30 × 30
31	961	= 31 × 31
32	1,024	= 32 × 32
33	1,089	= 33 × 33
34	1,156	= 34 × 34
35	1,225	= 35 × 35
36	1,296	= 36 × 36
37	1,369	= 37 × 37
38	1,444	= 38 × 38
39	1,521	= 39 × 39
40	1,600	= 40 × 40
41	1,681	= 41 × 41
42	1,764	= 42 × 42
43	1,849	= 43 × 43
44	1,936	= 44 × 44
45	2,025	= 45 × 45
46	2,116	= 46 × 46
47	2,209	= 47 × 47
48	2,304	= 48 × 48
49	2,401	= 49 × 49
50	2,500	= 50 × 50
51	2,601	= 51 × 51
52	2,704	= 52 × 52
53	2,809	= 53 × 53
54	2,916	= 54 × 54
55	3,025	= 55 × 55
56	3,136	= 56 × 56
57	3,249	= 57 × 57
58	3,364	= 58 × 58
59	3,481	= 59 × 59
60	3,600	= 60 × 60
61	3,721	= 61 × 61
62	3,844	= 62 × 62
63	3,969	= 63 × 63
64	4,096	= 64 × 64
65	4,225	= 65 × 65
66	4,356	= 66 × 66
67	4,489	= 67 × 67
68	4,624	= 68 × 68
69	4,761	= 69 × 69
70	4,900	= 70 × 70
71	5,041	= 71 × 71
72	5,184	= 72 × 72
73	5,329	= 73 × 73
74	5,476	= 74 × 74
75	5,625	= 75 × 75
76	5,776	= 76 × 76
77	5,929	= 77 × 77
78	6,084	= 78 × 78
79	6,241	= 79 × 79
80	6,400	= 80 × 80
81	6,561	= 81 × 81
82	6,724	= 82 × 82
83	6,889	= 83 × 83
84	7,056	= 84 × 84
85	7,225	= 85 × 85
86	7,396	= 86 × 86
87	7,569	= 87 × 87
88	7,744	= 88 × 88
89	7,921	= 89 × 89
90	8,100	= 90 × 90
91	8,281	= 91 × 91
92	8,464	= 92 × 92
93	8,649	= 93 × 93
94	8,836	= 94 × 94
95	9,025	= 95 × 95
96	9,216	= 96 × 96
97	9,409	= 97 × 97
98	9,604	= 98 × 98
99	9,801	= 99 × 99
100	10,000	= 100 × 100

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1,024, 1,089, 1,156, 1,225, 1,296, 1,369, 1,444, 1,521, 1,600, 1,681, 1,764, 1,849, 1,936, 2,025, 2,116, 2,209, 2,304, 2,401, 2,500, 2,601, 2,704, 2,809, 2,916, 3,025, 3,136, 3,249, 3,364, 3,481, 3,600, 3,721, 3,844, 3,969, 4,096, 4,225, 4,356, 4,489, 4,624, 4,761, 4,900, 5,041, 5,184, 5,329, 5,476, 5,625, 5,776, 5,929, 6,084, 6,241, 6,400, 6,561, 6,724, 6,889, 7,056, 7,225, 7,396, 7,569, 7,744, 7,921, 8,100, 8,281, 8,464, 8,649, 8,836, 9,025, 9,216, 9,409, 9,604, 9,801, 10,000

Interesting Patterns

Odd Number Sum

The sum of the first n odd numbers equals n². For example: 1+3+5+7 = 16 = 4²

Last Digit Pattern

Square numbers can only end in: 0, 1, 4, 5, 6, or 9. Never 2, 3, 7, or 8!

Consecutive Difference

The difference between consecutive squares is always odd: (n+1)² - n² = 2n + 1

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About Square Numbers List

Welcome to the Square Numbers List Generator, a comprehensive tool for generating, exploring, and understanding perfect squares. Generate the first N square numbers, find squares within any range, or check if a number is a perfect square. With interactive visualization, step-by-step formulas, and pattern exploration, this calculator makes learning about square numbers engaging and intuitive.

What is a Square Number?

A square number (also called a perfect square) is an integer that results from multiplying an integer by itself. In mathematical notation, if n is an integer, then n² = n × n is a square number. For example, 49 is a perfect square because 49 = 7 × 7.

Square Number Formula

$$n^2 = n \times n$$

The first ten square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

First 20 Square Numbers

n	n²	Calculation
1	1	1 × 1
2	4	2 × 2
3	9	3 × 3
4	16	4 × 4
5	25	5 × 5
6	36	6 × 6
7	49	7 × 7
8	64	8 × 8
9	81	9 × 9
10	100	10 × 10
11	121	11 × 11
12	144	12 × 12
13	169	13 × 13
14	196	14 × 14
15	225	15 × 15
16	256	16 × 16
17	289	17 × 17
18	324	18 × 18
19	361	19 × 19
20	400	20 × 20

Properties of Square Numbers

Last digits: Square numbers can only end in 0, 1, 4, 5, 6, or 9 (never 2, 3, 7, or 8)
Odd number sum: The sum of the first n odd numbers equals n² (e.g., 1+3+5+7 = 16 = 4²)
Consecutive difference: The difference between consecutive squares is always an odd number: (n+1)² - n² = 2n + 1
Divisors: Perfect squares have an odd number of divisors
Digital roots: The digital root of a square number is always 1, 4, 7, or 9

Sum of Square Numbers

The sum of the first n square numbers can be calculated using the formula:

Sum of First n Squares

$$\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}$$

How to Use This Calculator

First N Squares: Enter how many square numbers you want (1-1000) and click Generate
Range of Squares: Enter start and end values to find all squares in that range
Check Number: Enter any number to verify if it is a perfect square

Frequently Asked Questions

What is a square number (perfect square)?

A square number (or perfect square) is an integer that can be expressed as the product of an integer multiplied by itself. For example, 25 is a square number because 25 = 5 × 5. The first ten square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

How do I generate a list of square numbers?

To generate the first N square numbers, simply input how many square numbers you want (e.g., 10) and click Generate. The calculator will compute n² for each value from 1 to N. For example, for N=5, you get: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25.

What are the properties of square numbers?

Square numbers have interesting properties: (1) They always end in 0, 1, 4, 5, 6, or 9; (2) The difference between consecutive squares follows the pattern 2n+1 (odd numbers); (3) The sum of the first n odd numbers equals n²; (4) Square numbers have an odd number of divisors; (5) The digital root of a square is always 1, 4, 7, or 9.

How can I check if a number is a perfect square?

A number is a perfect square if its square root is an integer. For example, √144 = 12 (integer), so 144 is a perfect square. You can also use the Check Number mode in this calculator, which instantly verifies any number.

What is the formula for the nth square number?

The formula for the nth square number is simply n². For example, the 7th square number is 7² = 49. Additionally, the sum of the first n square numbers can be calculated using the formula: n(n+1)(2n+1)/6.

Reference this content, page, or tool as:

"Square Numbers List" at https://MiniWebtool.com/square-numbers-list/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 18, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Square Numbers List

Square Numbers Generator

Visual Grid

Complete List

Interesting Patterns

Odd Number Sum

Last Digit Pattern

Consecutive Difference

Related MiniWebtools:

About Square Numbers List

What is a Square Number?

First 20 Square Numbers

Properties of Square Numbers

Sum of Square Numbers

How to Use This Calculator

Frequently Asked Questions

What is a square number (perfect square)?

How do I generate a list of square numbers?

What are the properties of square numbers?

How can I check if a number is a perfect square?

What is the formula for the nth square number?

Sequence Tools:

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