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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:

Generate up to 1000 perfect squares with visualization and detailed breakdown.
Find all perfect squares within your specified range.
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
1
Last
10,000
Sum
338,350

Visual Grid

n=1
1
1×1
n=2
4
2×2
n=3
9
3×3
n=4
16
4×4
n=5
25
5×5
n=6
36
6×6
n=7
49
7×7
n=8
64
8×8
n=9
81
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

nn²Calculation
111 × 1
242 × 2
393 × 3
4164 × 4
5255 × 5
6366 × 6
7497 × 7
8648 × 8
9819 × 9
1010010 × 10
1112111 × 11
1214412 × 12
1316913 × 13
1419614 × 14
1522515 × 15
1625616 × 16
1728917 × 17
1832418 × 18
1936119 × 19
2040020 × 20

Properties of Square Numbers

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

  1. First N Squares: Enter how many square numbers you want (1-1000) and click Generate
  2. Range of Squares: Enter start and end values to find all squares in that range
  3. 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

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