Squares from 1 to 100: Complete List, Chart & Easy Tricks to Remember

Knowing the square of 1 to 50 by heart makes maths faster and far less stressful. It helps in arithmetic, algebra, geometry, mental maths, competitive exams, and everyday calculations like finding the area of a room. This guide gives you the full list and a quick-reference chart. It also teaches memory tricks that rely on patterns, not rote learning. Once you are comfortable here, you can move on to the Square of 1 to 100 using the same ideas.

☰ Table of Contents

What Is the Square of a Number?

The square of a number is the result of multiplying that number by itself.

The formula is:

n² = n × n

Read n² as “n squared.”

5² = 5 × 5 = 25
10² = 10 × 10 = 100
20² = 20 × 20 = 400

A perfect square is a whole number that is the square of another whole number. So 25 is a perfect square because 5 × 5 = 25, but 26 is not, because no whole number multiplied by itself gives 26.

The name comes from geometry. A square with sides of 5 units has an area of 5 × 5 = 25 square units.

Square of 1 to 50: Complete List

Number	Square	Number	Square
1	1	26	676
2	4	27	729
3	9	28	784
4	16	29	841
5	25	30	900
6	36	31	961
7	49	32	1024
8	64	33	1089
9	81	34	1156
10	100	35	1225
11	121	36	1296
12	144	37	1369
13	169	38	1444
14	196	39	1521
15	225	40	1600
16	256	41	1681
17	289	42	1764
18	324	43	1849
19	361	44	1936
20	400	45	2025
21	441	46	2116
22	484	47	2209
23	529	48	2304
24	576	49	2401
25	625	50	2500

Square of 1 to 50 Chart

Use this compact chart for quick revision, homework, and exam preparation.

1–10	11–20	21–30	31–40	41–50
1² = 1	11² = 121	21² = 441	31² = 961	41² = 1681
2² = 4	12² = 144	22² = 484	32² = 1024	42² = 1764
3² = 9	13² = 169	23² = 529	33² = 1089	43² = 1849
4² = 16	14² = 196	24² = 576	34² = 1156	44² = 1936
5² = 25	15² = 225	25² = 625	35² = 1225	45² = 2025
6² = 36	16² = 256	26² = 676	36² = 1296	46² = 2116
7² = 49	17² = 289	27² = 729	37² = 1369	47² = 2209
8² = 64	18² = 324	28² = 784	38² = 1444	48² = 2304
9² = 81	19² = 361	29² = 841	39² = 1521	49² = 2401
10² = 100	20² = 400	30² = 900	40² = 1600	50² = 2500

Easy Tricks to Remember Squares from 1 to 50

1. Master 1 to 10 first

Every larger square builds on these ten: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Practise them until they feel automatic. Most mistakes with bigger squares come from a shaky foundation here.

2. Use the difference between consecutive squares

Look at the first few squares: 1, 4, 9, 16, 25. The gaps between them are 3, 5, 7, 9. These are consecutive odd numbers. This happens because of the identity:

(n + 1)² = n² + 2n + 1

In simple words, to get the next square, add 2n + 1 to the current one. For example, to go from 7² to 8²: 49 + (2 × 7 + 1) = 49 + 15 = 64.

3. Squares of numbers ending in 5

Follow these steps:

Take the digit(s) before the 5. For 35, that is 3.
Multiply it by the next whole number. 3 × 4 = 12.
Write 25 after it. The answer is 1225.

Number	Multiply	Square
15	1 × 2 = 2	225
25	2 × 3 = 6	625
35	3 × 4 = 12	1225
45	4 × 5 = 20	2025

4. Use nearby round numbers

Round numbers are easy to square, so step off from them.

19² = (20 − 1)² = 400 − 40 + 1 = 361
31² = (30 + 1)² = 900 + 60 + 1 = 961
49² = (50 − 1)² = 2500 − 100 + 1 = 2401

5. Practise in groups of 10

Learn in chunks: 1–10, 11–20, 21–30, 31–40, 41–50. Short groups feel manageable, and you can revise one group a day. By the end of the week, you will know the whole list.

Easy Tricks to Remember Squares from 1 to 50

1. Master 1 to 10 first

Every larger square builds on these ten: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Practise them until they feel automatic. Most mistakes with bigger squares come from a shaky foundation here.

2. Use the difference between consecutive squares

Look at the first few squares: 1, 4, 9, 16, 25. The gaps between them are 3, 5, 7, 9. These are consecutive odd numbers. This happens because of the identity:

(n + 1)² = n² + 2n + 1

In simple words, to get the next square, add 2n + 1 to the current one. For example, to go from 7² to 8²: 49 + (2 × 7 + 1) = 49 + 15 = 64.

3. Squares of numbers ending in 5

Follow these steps:

Take the digit(s) before the 5. For 35, that is 3.
Multiply it by the next whole number. 3 × 4 = 12.
Write 25 after it. The answer is 1225.

Number	Multiply	Square
15	1 × 2 = 2	225
25	2 × 3 = 6	625
35	3 × 4 = 12	1225
45	4 × 5 = 20	2025

4. Use nearby round numbers

Round numbers are easy to square, so step off from them.

19² = (20 − 1)² = 400 − 40 + 1 = 361
31² = (30 + 1)² = 900 + 60 + 1 = 961
49² = (50 − 1)² = 2500 − 100 + 1 = 2401

5. Practise in groups of 10

Learn in chunks: 1–10, 11–20, 21–30, 31–40, 41–50. Short groups feel manageable, and you can revise one group a day. By the end of the week, you will know the whole list.

Important Patterns in Square Numbers

Squares of even numbers are even. Example: 6² = 36, 14² = 196.
Squares of odd numbers are odd. Example: 7² = 49, 13² = 169.
A perfect square never ends in 2, 3, 7, or 8. Squares end only in 0, 1, 4, 5, 6, or 9.
Consecutive squares differ by consecutive odd numbers. Example: 16 − 9 = 7 and 25 − 16 = 9.
Numbers ending in 5 always have squares ending in 25. Example: 15² = 225, 45² = 2025.

Here is the last-digit pattern in full:

Number ends in	Square ends in
1 or 9	1
2 or 8	4
3 or 7	9
4 or 6	6
5	5
0	0

This is a handy way to check your answers. If you get 23² = 528, the last digit is wrong, because a number ending in 3 must have a square ending in 9. The correct answer is 529.

Square 1 to 60

If you have mastered squares up to 50, extending to 60 is easy. The same patterns still work. Here are the next ten:

Number	Square
51	2601
52	2704
53	2809
54	2916
55	3025
56	3136
57	3249
58	3364
59	3481
60	3600

Notice that 55² = 3025 follows the “ending in 5” trick: 5 × 6 = 30, then 25.

Square 1 to 70

Squares up to 70 are useful in mental maths and competitive exams, where larger values appear often in aptitude sections.

Number	Square
61	3721
62	3844
63	3969
64	4096
65	4225
66	4356
67	4489
68	4624
69	4761
70	4900

Tip: 64² = 4096 is worth remembering because 64 is 2⁶ and 4096 is 2¹².

Square 1 to 100

A complete Square 1 to 100 chart is a strong reference for higher-level calculations and exams. You already have 1 to 70 above, so here is the rest.

Number	Square	Number	Square	Number	Square
71	5041	81	6561	91	8281
72	5184	82	6724	92	8464
73	5329	83	6889	93	8649
74	5476	84	7056	94	8836
75	5625	85	7225	95	9025
76	5776	86	7396	96	9216
77	5929	87	7569	97	9409
78	6084	88	7744	98	9604
79	6241	89	7921	99	9801
80	6400	90	8100	100	10000

The perfect squares from 1 to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Square 50 to 100

Here is a compact reference for Square 50 to 100, arranged for easy scanning.

Number	Square	Number	Square	Number	Square
50	2500	67	4489	84	7056
51	2601	68	4624	85	7225
52	2704	69	4761	86	7396
53	2809	70	4900	87	7569
54	2916	71	5041	88	7744
55	3025	72	5184	89	7921
56	3136	73	5329	90	8100
57	3249	74	5476	91	8281
58	3364	75	5625	92	8464
59	3481	76	5776	93	8649
60	3600	77	5929	94	8836
61	3721	78	6084	95	9025
62	3844	79	6241	96	9216
63	3969	80	6400	97	9409
64	4096	81	6561	98	9604
65	4225	82	6724	99	9801
66	4356	83	6889	100	10000

How to Calculate Squares Without Memorizing Them

If you forget a value, you can always work it out.

Method 1: Direct multiplication

Multiply the number by itself.

24² = 24 × 24 = 576

Method 2: Using (a + b)²

(a + b)² = a² + 2ab + b²

Split the number into a round number plus a small number.

32² = (30 + 2)²
= 900 + 120 + 4
= 1024

Method 3: Using (a − b)²

(a − b)² = a² − 2ab + b²

Use this when the number is just below a round number.

49² = (50 − 1)²
= 2500 − 100 + 1
= 2401

Why Should Students Learn Squares from 1 to 50?

Faster mental calculation: quick recall saves time in exams.
Easier algebra: expressions like x² and identities like (a + b)² become less intimidating.
Square roots: if you know 36 = 6², you instantly know √36 = 6.
Geometry: area of squares and many formulas use squares.
Pythagorean theorem: a² + b² = c² relies on squares. For example, 3² + 4² = 9 + 16 = 25 = 5².
Competitive exams and aptitude tests: squares appear constantly in number series and data questions.
Better number sense: you start to see how numbers relate to each other.

Common Mistakes While Learning Square Numbers

Confusing square with double. 8² is 64, not 16. Squaring means multiplying by itself, not by 2.
Writing 12² as 12 × 2. The correct working is 12 × 12 = 144.
Mixing up nearby values. Students often swap 17² = 289 and 19² = 361. Use the last-digit pattern to check.
Memorizing without understanding. Pure rote learning fades quickly. Learn one pattern for each group.
Calculation slips with larger numbers. Use the (a ± b)² method and double-check the last digit.

Practice Questions on Squares from 1 to 50

What is 14²?
Find the square of 27.
What is 35²?
Which number has a square of 1600?
Calculate 49² without direct multiplication.
What is 18²?
Find 41².
What is 23²?
Find the number whose square is 2025.
Calculate 29² using a nearby round number.
What is 48²?
What is the difference between 30² and 29²?
Is 1000 a perfect square? Between which two squares does it lie?

Answers

196
729
1225
40
(50 − 1)² = 2500 − 100 + 1 = 2401
324
1681
529
45
(30 − 1)² = 900 − 60 + 1 = 841
2304
900 − 841 = 59, which equals 2 × 29 + 1
No. It lies between 31² = 961 and 32² = 1024.

Conclusion

Learning the square of 1 to 50 is one of the most useful habits in school maths. Start with 1 to 10, study in groups, and lean on the patterns: odd gaps, endings in 5, and round-number shortcuts. When you understand why a square works, you will remember it far longer than if you only memorize the table. Revise a group each day, test yourself with the practice questions, and you will be ready to extend to 100.

Frequently Asked Questions

What is the square of 1 to 50?

It is the list of squares from 1² = 1 up to 50² = 2500, shown in the table above.

What is the easiest way to memorize squares from 1 to 50?

Learn 1 to 10 first, then study in groups of 10. Use patterns like the “ending in 5” trick and the (a ± b)² method.

What is the square of 50?

50² = 50 × 50 = 2500.

What is the formula for finding the square of a number?

n² = n × n.

How can I learn squares from 1 to 100 quickly?

First master 1 to 50, then add 51 to 100 in groups of 10. Use round-number shortcuts, such as 98² = (100 − 2)² = 9604.

What are the perfect squares between 1 and 100?

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

What is the difference between a square and a square root?

Squaring multiplies a number by itself (6² = 36). A square root reverses this (√36 = 6).

Why should students memorize square numbers?

They speed up mental calculation and support algebra, geometry, and exam problem solving.

Which square numbers should students learn first?

Start with 1² to 10², then 11² to 20², since these are used most often.

How can I calculate large squares mentally?

Split the number around a round number and apply (a + b)² or (a − b)². For example, 47² = (50 − 3)² = 2500 − 300 + 9 = 2209.

Squares from 1 to 100: Complete List, Chart & Easy Tricks to Remember

What Is the Square of a Number?

Square of 1 to 50: Complete List

Square of 1 to 50 Chart

Easy Tricks to Remember Squares from 1 to 50

1. Master 1 to 10 first

2. Use the difference between consecutive squares

3. Squares of numbers ending in 5

4. Use nearby round numbers

5. Practise in groups of 10

Easy Tricks to Remember Squares from 1 to 50

1. Master 1 to 10 first

2. Use the difference between consecutive squares

3. Squares of numbers ending in 5

4. Use nearby round numbers

5. Practise in groups of 10

Important Patterns in Square Numbers

Square 1 to 60

Square 1 to 70

Square 1 to 100

Square 50 to 100

How to Calculate Squares Without Memorizing Them

Method 1: Direct multiplication

Method 2: Using (a + b)²

Method 3: Using (a − b)²

Why Should Students Learn Squares from 1 to 50?

Common Mistakes While Learning Square Numbers

Practice Questions on Squares from 1 to 50

Answers

Conclusion

Frequently Asked Questions

Start Your Child's Learning Journey

Thank You! 🎉

Book Your Free Demo