A 25x25 Magic Square

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for other topics including Irregular Squares, Algebraic Squares and more.
Other Magic Square Sizes: 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19 *
21 * 23 * 25 * 27 * 29 * 31 * 33 * 35 * 37 * 39 * 41 * 43 * 45 * 47 * 49 * 51 * 53 * 55 * 57 * 59 *
61 * 63 * 65 * 67 * 69 * 71 * 73 * 75 * 77 * 79 * 81 * 83 * 85 * 87 * 89 * 91 * 93 * 95 * 97 * 99 *
A 25x25 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (7825)

A Magic Square is a square of numbers in which every row, every column, and both diagonals add up to the same number. This number is often called the magic sum. The 25 by 25 magic square shown below has a magic sum equal to 7825.
Though magic squares can be made with non-consecutive and non-regular sequences, they are usually seen made up of consecutive numbers. To the best of my knowledge, the middle number in the sequence must be in the center square, and the magic sum will be equal to this middle number times the number of rows in the square. (In the case of 3x3 squares, I have proved that the middle number MUST be equal to one-third of the sum. See proof here.)
All odd-size Magic Squares can be made with the method shown below, which can be summarized as "start in the middle of the top and keep moving up and to the right except when you get blocked, in which case drop down and continue." The more detailed directions about creating these squares can be found further below. There are other methods for creating magic squares, but this is the easiest to learn. (There are basically only two methods of creating a 3x3 square but the larger squares have a large number of irregular variants, and probably other regular methods.)
Read more about Magic Squares
If you'd like to read more about magic squares, click one of these links to look for books about Magic Squares at Amazon.com, at Amazon.canada, and at Amazon.co.UK.

A 25-by-25 Magic Square

(Magic Sum = 7825)

Books about
Magic Squares
at Amazon.co.UK

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327	354	381	408	435	462	489	516	543	570	597	624	1	28	55	82	109	136	163	190	217	244	271	298	325
353	380	407	434	461	488	515	542	569	596	623	25	27	54	81	108	135	162	189	216	243	270	297	324	326
379	406	433	460	487	514	541	568	595	622	24	26	53	80	107	134	161	188	215	242	269	296	323	350	352
405	432	459	486	513	540	567	594	621	23	50	52	79	106	133	160	187	214	241	268	295	322	349	351	378
431	458	485	512	539	566	593	620	22	49	51	78	105	132	159	186	213	240	267	294	321	348	375	377	404
457	484	511	538	565	592	619	21	48	75	77	104	131	158	185	212	239	266	293	320	347	374	376	403	430
483	510	537	564	591	618	20	47	74	76	103	130	157	184	211	238	265	292	319	346	373	400	402	429	456
509	536	563	590	617	19	46	73	100	102	129	156	183	210	237	264	291	318	345	372	399	401	428	455	482
535	562	589	616	18	45	72	99	101	128	155	182	209	236	263	290	317	344	371	398	425	427	454	481	508
561	588	615	17	44	71	98	125	127	154	181	208	235	262	289	316	343	370	397	424	426	453	480	507	534
587	614	16	43	70	97	124	126	153	180	207	234	261	288	315	342	369	396	423	450	452	479	506	533	560
613	15	42	69	96	123	150	152	179	206	233	260	287	314	341	368	395	422	449	451	478	505	532	559	586
14	41	68	95	122	149	151	178	205	232	259	286	313	340	367	394	421	448	475	477	504	531	558	585	612
40	67	94	121	148	175	177	204	231	258	285	312	339	366	393	420	447	474	476	503	530	557	584	611	13
66	93	120	147	174	176	203	230	257	284	311	338	365	392	419	446	473	500	502	529	556	583	610	12	39
92	119	146	173	200	202	229	256	283	310	337	364	391	418	445	472	499	501	528	555	582	609	11	38	65
118	145	172	199	201	228	255	282	309	336	363	390	417	444	471	498	525	527	554	581	608	10	37	64	91
144	171	198	225	227	254	281	308	335	362	389	416	443	470	497	524	526	553	580	607	9	36	63	90	117
170	197	224	226	253	280	307	334	361	388	415	442	469	496	523	550	552	579	606	8	35	62	89	116	143
196	223	250	252	279	306	333	360	387	414	441	468	495	522	549	551	578	605	7	34	61	88	115	142	169
222	249	251	278	305	332	359	386	413	440	467	494	521	548	575	577	604	6	33	60	87	114	141	168	195
248	275	277	304	331	358	385	412	439	466	493	520	547	574	576	603	5	32	59	86	113	140	167	194	221
274	276	303	330	357	384	411	438	465	492	519	546	573	600	602	4	31	58	85	112	139	166	193	220	247
300	302	329	356	383	410	437	464	491	518	545	572	599	601	3	30	57	84	111	138	165	192	219	246	273
301	328	355	382	409	436	463	490	517	544	571	598	625	2	29	56	83	110	137	164	191	218	245	272	299

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How to Make Your Own Odd-Size Magic Square

Draw a square with any odd number of rows and columns.
Put your first number in the MIDDLE square of the TOP row.
Move UP and to the RIGHT to find the position for your next number, but ...
- if the next "position" is ABOVE a column, go to BOTTOM of that column (you can see a sample of this movement by looking at how we moved from 1 to 2 in the square above).
- if the next "position" is to the RIGHT of a row, go to LEFT of that row (you can see this movement between (13) and (14) above).
- if the next cell is already filled in, drop down to the cell below the number you just filled in for the next number (you can see this when you look at how we moved from 25 to the next number above).
- if the next cell is both ABOVE and to the RIGHT of the entire square, drop down to the cell below the number you just filled in for your next number (you can see this if you look at (325) and the next number).
Print your NEXT number into the new square you just moved to.
Repeat steps 3-4 until the entire square is full.
You can see how it works by printing this page and drawing arrows to see how it worked when I created this magic square

This Magic Square was created by John Knoderer, a webmaster and computer programmer who is available to telecommute to your location.

If you found this page useful, and especially if you printed this page to distribute to students, we invite you to send a suitable donation to John (address below) or PayPal your donation to Donations (at) Mazes.com.

You can find more of John's puzzling materials at www.MAZES.com and at www.GodLovesEveryone.org. You can reach John at Webmaster (at) Mazes.com.

Fine Print: If you print and duplicate these magic squares for classroom use or other multiple copy use, please send a payment of $(however much you think this is worth) to the author. John puts a GREAT DEAL of time into creating and posting materials to the internet for you to use (and enjoy). Your donations will help pay bills and keep new materials coming your way.

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E-mail the webmaster: webmaster (at) mazes.com

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327	354	381	408	435	462	489	516	543	570	597	624	1	28	55	82	109	136	163	190	217	244	271	298	325
353	380	407	434	461	488	515	542	569	596	623	25	27	54	81	108	135	162	189	216	243	270	297	324	326
379	406	433	460	487	514	541	568	595	622	24	26	53	80	107	134	161	188	215	242	269	296	323	350	352
405	432	459	486	513	540	567	594	621	23	50	52	79	106	133	160	187	214	241	268	295	322	349	351	378
431	458	485	512	539	566	593	620	22	49	51	78	105	132	159	186	213	240	267	294	321	348	375	377	404
457	484	511	538	565	592	619	21	48	75	77	104	131	158	185	212	239	266	293	320	347	374	376	403	430
483	510	537	564	591	618	20	47	74	76	103	130	157	184	211	238	265	292	319	346	373	400	402	429	456
509	536	563	590	617	19	46	73	100	102	129	156	183	210	237	264	291	318	345	372	399	401	428	455	482
535	562	589	616	18	45	72	99	101	128	155	182	209	236	263	290	317	344	371	398	425	427	454	481	508
561	588	615	17	44	71	98	125	127	154	181	208	235	262	289	316	343	370	397	424	426	453	480	507	534
587	614	16	43	70	97	124	126	153	180	207	234	261	288	315	342	369	396	423	450	452	479	506	533	560
613	15	42	69	96	123	150	152	179	206	233	260	287	314	341	368	395	422	449	451	478	505	532	559	586
14	41	68	95	122	149	151	178	205	232	259	286	313	340	367	394	421	448	475	477	504	531	558	585	612
40	67	94	121	148	175	177	204	231	258	285	312	339	366	393	420	447	474	476	503	530	557	584	611	13
66	93	120	147	174	176	203	230	257	284	311	338	365	392	419	446	473	500	502	529	556	583	610	12	39
92	119	146	173	200	202	229	256	283	310	337	364	391	418	445	472	499	501	528	555	582	609	11	38	65
118	145	172	199	201	228	255	282	309	336	363	390	417	444	471	498	525	527	554	581	608	10	37	64	91
144	171	198	225	227	254	281	308	335	362	389	416	443	470	497	524	526	553	580	607	9	36	63	90	117
170	197	224	226	253	280	307	334	361	388	415	442	469	496	523	550	552	579	606	8	35	62	89	116	143
196	223	250	252	279	306	333	360	387	414	441	468	495	522	549	551	578	605	7	34	61	88	115	142	169
222	249	251	278	305	332	359	386	413	440	467	494	521	548	575	577	604	6	33	60	87	114	141	168	195
248	275	277	304	331	358	385	412	439	466	493	520	547	574	576	603	5	32	59	86	113	140	167	194	221
274	276	303	330	357	384	411	438	465	492	519	546	573	600	602	4	31	58	85	112	139	166	193	220	247
300	302	329	356	383	410	437	464	491	518	545	572	599	601	3	30	57	84	111	138	165	192	219	246	273
301	328	355	382	409	436	463	490	517	544	571	598	625	2	29	56	83	110	137	164	191	218	245	272	299

327	354	381	408	435	462	489	516	543	570	597	624	1	28	55	82	109	136	163	190	217	244	271	298	325
353	380	407	434	461	488	515	542	569	596	623	25	27	54	81	108	135	162	189	216	243	270	297	324	326
379	406	433	460	487	514	541	568	595	622	24	26	53	80	107	134	161	188	215	242	269	296	323	350	352
405	432	459	486	513	540	567	594	621	23	50	52	79	106	133	160	187	214	241	268	295	322	349	351	378
431	458	485	512	539	566	593	620	22	49	51	78	105	132	159	186	213	240	267	294	321	348	375	377	404
457	484	511	538	565	592	619	21	48	75	77	104	131	158	185	212	239	266	293	320	347	374	376	403	430
483	510	537	564	591	618	20	47	74	76	103	130	157	184	211	238	265	292	319	346	373	400	402	429	456
509	536	563	590	617	19	46	73	100	102	129	156	183	210	237	264	291	318	345	372	399	401	428	455	482
535	562	589	616	18	45	72	99	101	128	155	182	209	236	263	290	317	344	371	398	425	427	454	481	508
561	588	615	17	44	71	98	125	127	154	181	208	235	262	289	316	343	370	397	424	426	453	480	507	534
587	614	16	43	70	97	124	126	153	180	207	234	261	288	315	342	369	396	423	450	452	479	506	533	560
613	15	42	69	96	123	150	152	179	206	233	260	287	314	341	368	395	422	449	451	478	505	532	559	586
14	41	68	95	122	149	151	178	205	232	259	286	313	340	367	394	421	448	475	477	504	531	558	585	612
40	67	94	121	148	175	177	204	231	258	285	312	339	366	393	420	447	474	476	503	530	557	584	611	13
66	93	120	147	174	176	203	230	257	284	311	338	365	392	419	446	473	500	502	529	556	583	610	12	39
92	119	146	173	200	202	229	256	283	310	337	364	391	418	445	472	499	501	528	555	582	609	11	38	65
118	145	172	199	201	228	255	282	309	336	363	390	417	444	471	498	525	527	554	581	608	10	37	64	91
144	171	198	225	227	254	281	308	335	362	389	416	443	470	497	524	526	553	580	607	9	36	63	90	117
170	197	224	226	253	280	307	334	361	388	415	442	469	496	523	550	552	579	606	8	35	62	89	116	143
196	223	250	252	279	306	333	360	387	414	441	468	495	522	549	551	578	605	7	34	61	88	115	142	169
222	249	251	278	305	332	359	386	413	440	467	494	521	548	575	577	604	6	33	60	87	114	141	168	195
248	275	277	304	331	358	385	412	439	466	493	520	547	574	576	603	5	32	59	86	113	140	167	194	221
274	276	303	330	357	384	411	438	465	492	519	546	573	600	602	4	31	58	85	112	139	166	193	220	247
300	302	329	356	383	410	437	464	491	518	545	572	599	601	3	30	57	84	111	138	165	192	219	246	273
301	328	355	382	409	436	463	490	517	544	571	598	625	2	29	56	83	110	137	164	191	218	245	272	299

A 25x25 Magic Square

Scroll down to see a magic squarein which all rows, columns, and both diagonalsadd up to the same magic sum (7825)

Read more about Magic Squares

A 25-by-25 Magic Square

How to Make Your Own Odd-Size Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (7825)

327	354	381	408	435	462	489	516	543	570	597	624	1	28	55	82	109	136	163	190	217	244	271	298	325
353	380	407	434	461	488	515	542	569	596	623	25	27	54	81	108	135	162	189	216	243	270	297	324	326
379	406	433	460	487	514	541	568	595	622	24	26	53	80	107	134	161	188	215	242	269	296	323	350	352
405	432	459	486	513	540	567	594	621	23	50	52	79	106	133	160	187	214	241	268	295	322	349	351	378
431	458	485	512	539	566	593	620	22	49	51	78	105	132	159	186	213	240	267	294	321	348	375	377	404
457	484	511	538	565	592	619	21	48	75	77	104	131	158	185	212	239	266	293	320	347	374	376	403	430
483	510	537	564	591	618	20	47	74	76	103	130	157	184	211	238	265	292	319	346	373	400	402	429	456
509	536	563	590	617	19	46	73	100	102	129	156	183	210	237	264	291	318	345	372	399	401	428	455	482
535	562	589	616	18	45	72	99	101	128	155	182	209	236	263	290	317	344	371	398	425	427	454	481	508
561	588	615	17	44	71	98	125	127	154	181	208	235	262	289	316	343	370	397	424	426	453	480	507	534
587	614	16	43	70	97	124	126	153	180	207	234	261	288	315	342	369	396	423	450	452	479	506	533	560
613	15	42	69	96	123	150	152	179	206	233	260	287	314	341	368	395	422	449	451	478	505	532	559	586
14	41	68	95	122	149	151	178	205	232	259	286	313	340	367	394	421	448	475	477	504	531	558	585	612
40	67	94	121	148	175	177	204	231	258	285	312	339	366	393	420	447	474	476	503	530	557	584	611	13
66	93	120	147	174	176	203	230	257	284	311	338	365	392	419	446	473	500	502	529	556	583	610	12	39
92	119	146	173	200	202	229	256	283	310	337	364	391	418	445	472	499	501	528	555	582	609	11	38	65
118	145	172	199	201	228	255	282	309	336	363	390	417	444	471	498	525	527	554	581	608	10	37	64	91
144	171	198	225	227	254	281	308	335	362	389	416	443	470	497	524	526	553	580	607	9	36	63	90	117
170	197	224	226	253	280	307	334	361	388	415	442	469	496	523	550	552	579	606	8	35	62	89	116	143
196	223	250	252	279	306	333	360	387	414	441	468	495	522	549	551	578	605	7	34	61	88	115	142	169
222	249	251	278	305	332	359	386	413	440	467	494	521	548	575	577	604	6	33	60	87	114	141	168	195
248	275	277	304	331	358	385	412	439	466	493	520	547	574	576	603	5	32	59	86	113	140	167	194	221
274	276	303	330	357	384	411	438	465	492	519	546	573	600	602	4	31	58	85	112	139	166	193	220	247
300	302	329	356	383	410	437	464	491	518	545	572	599	601	3	30	57	84	111	138	165	192	219	246	273
301	328	355	382	409	436	463	490	517	544	571	598	625	2	29	56	83	110	137	164	191	218	245	272	299