Square numbers from 1 to 100

A square number is a whole number multiplied by itself: 7² = 7 × 7 = 49. Here is every square from 1² to 100², the perfect squares up to 1,000, and the patterns that let you work them out without the list.

Drill two-digit squares

Squares from 1² to 100²

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

Perfect squares up to 100 and 1,000

The perfect squares up to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 — ten of them. Up to 1,000 there are 31, the last being 31² = 961; 32² is already 1,024.

Patterns worth knowing

The gaps are the odd numbers

1, 4, 9, 16, 25 … the differences are 3, 5, 7, 9 … So from any square you know, the next is one addition away. The gap between two neighbouring squares is the sum of the two numbers: 12² = 144, so 13² = 144 + 12 + 13 = 169.

A square never ends in 2, 3, 7 or 8

Every perfect square ends in 0, 1, 4, 5, 6 or 9. That's an instant check: 7,283 can't be a perfect square, whatever its size — useful when you're estimating square roots.

Numbers ending in 5

Take the digits in front of the 5, multiply by the next number up, and write 25 after it. 35²: 3 × 4 = 12, so 1,225. 85²: 8 × 9 = 72, so 7,225.

Any two-digit square, without the list

Round the number to the nearest ten, move the same distance the other way, multiply those two, and add the distance squared: 47² = 50 × 44 + 3² = 2,200 + 9 = 2,209. The full method, with shortcuts near 50 and 100, is in how to square numbers in your head.

R3CK0N's Secret mode drills both. n² asks two-digit squares — 10 to 30 on Easy, up to 99 on Hard — and n² (…5) asks numbers ending in 5. Every run is timed, and every answer's time is shown afterwards, so you can see which squares you know and which you're still working out.

Frequently asked questions

How many square numbers are there from 1 to 100?

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

Is 0 a square number?

Yes — 0 × 0 = 0, so 0 is a perfect square. Lists that start at 1, like this one, usually leave it out.

What is 100 squared?

100² = 10,000.

Practise squares ending in 5