Integer Geometry Suitegcd(a, b, c) = 1

Pythagorean Triples Validator & Generator

Verify whether any three positive integers form a valid right-angled triangle and check whether the triple is primitive (gcd = 1) or a scaled multiple. For triangles with irrational radical sides or missing angles, switch to the main Pythagoras equation solver.

Strict Positive Integer VerificationEuclid’s Formula Interactive SlidersSearchable Primitive Triples Catalog

Pythagorean Triples Explorer & Generator

Check Any 3 Numbers

Enter positive integers a, b, and c to verify if they form a right-angled triple.

Leg a

Leg b

Hypotenuse c

Is a valid Pythagorean Triple! (3, 4, 5)

★ Primitive (gcd = 1) • Area (A): 6, Perimeter (P): 12

Euclid's Formula Generator: a = m² - n², b = 2mn, c = m² + n²

Generate primitive triples using two integers m and n (where m > n > 0).

Parameter m = 3Must be > n

Parameter n = 2Must be > 0

Resulting TriplePrimitive

(5, 12, 13)

a = 3² - 2² = 5 | b = 2·3·2 = 12 | c = 3² + 2² = 13

Catalog of 50 Primitive Pythagorean Triples

Verify integer triples, generate new triples with Euclid's formula, or explore the catalog.

#	Leg a	Leg b	Hypotenuse c	Perimeter (P)	Area (A)
1	3	4	5	12	6
2	5	12	13	30	30
3	8	15	17	40	60
4	7	24	25	56	84
5	20	21	29	70	210
6	12	35	37	84	210
7	9	40	41	90	180
8	28	45	53	126	630
9	11	60	61	132	330
10	33	56	65	154	924
11	16	63	65	144	504
12	48	55	73	176	1,320
13	13	84	85	182	546
14	36	77	85	198	1,386
15	39	80	89	208	1,560
16	65	72	97	234	2,340
17	20	99	101	220	990
18	60	91	109	260	2,730
19	15	112	113	240	840
20	44	117	125	286	2,574
21	88	105	137	330	4,620
22	17	144	145	306	1,224
23	24	143	145	312	1,716
24	51	140	149	340	3,570
25	85	132	157	374	5,610
26	119	120	169	408	7,140
27	52	165	173	390	4,290
28	19	180	181	380	1,710
29	57	176	185	418	5,016
30	104	153	185	442	7,956
31	95	168	193	456	7,980
32	28	195	197	420	2,730