Roman Numerals

One of the early systems of writing numerals is the system of Roman numerals. This system is still used in many places. For example,

• we can see Roman numerals in clocks
• they are used to number pages that come before the main pages of a book
• they are used to identify kings and queens (for example, Henry VIII of England)
• they are used to identify sporting events (like, The New York Giants won Super Bowl XLII).

They use the following seven letters of the alphabet to write all numbers.

I	V	X	L	C	D	M
1	5	10	50	100	500	1000

There is no zero (0) in the Roman system. The Roman system does not use place value concept. The Roman numerals I, II, III, IV, V, VI, VII, VIII, IX, X respectively denote 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This is followed by XI for 11, XII for 12, . . . , till XX for 20. The traditional Roman numeral system was only used for numbers up to 3,999 which is represented as MMMCMXCIX.

The rules for the system

(a) If a symbol is repeated, its value is added as many times as it occurs.

For example,

• II is equal 2
• XX is 20
• XXX is 30.

(b) A symbol is not repeated more than three times. But the symbols V, L and D are never repeated.

Hence, IIII, XXXXX are not valid. 

(c) If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol.

For example,

• VI = 5 + 1 = 6
• XII = 10 + 2 = 12
• XXVII = 10 + 10 + 5 + 1 + 1 = 27
• LXV = 50 + 10 + 5 = 65
• MDC = 1000 + 500 + 100 = 1600

(d) If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.

For example,

• IV = 5 – 1 = 4
• IX = 10 – 1 = 9
• XL= 50 – 10 = 40
• XC = 100 – 10 = 90

(e) The symbols V, L and D are never written to the left of a symbol of greater value. In other words, V, L and D are never subtracted.

(f) The symbol I can be subtracted from V and X only.

(g) The symbol X can be subtracted from L, M and C only.

Example. Write 69 in Roman Numerals.

Solution. We can write

69 = 60 + 9

= (50 + 10) + 9

= LX + IX

= LXIX

Example. Write 98 in Roman Numerals98.

Solution. We can write

98 = 90 + 8

= (100 – 10) + 8

= XC + VIII

= XCVIII

Example. Can we write 40 as XXXX?

Solution. No.

As we cannot repeat the symbol X for more than three times.

Example. How to write 800 in Roman numeral?

Solution. We can write, 800 = 500 + 100 + 100 + 100

We know that, 500 = D and 100 = C.

Therefore, 800 = DCCC.

Example. Write 3249 in the Roman number system.

Solution. We can write

3249

= 3000 + 200 + 40 + 9

= MMM + CC + XL + IX

= MMMCCXLIX

Example. Write MDCLXVII in the Hindu-Arabic system.

Solution. We can write

MDCLXVII

= M + DC + LX + VII

= 1000 + 600 + 60 + 7

= 1667

Below is the list of all Roman numerals up to 1000.

Roman Numerals 1 to 100

1	I	34	XXXIV	67	LXVII
2	II	35	XXXV	68	LXVIII
3	III	36	XXXVI	69	LXIX
4	IV	37	XXXVII	70	LXX
5	V	38	XXXVIII	71	LXXI
6	VI	39	XXXIX	72	LXXII
7	VII	40	XL	73	LXXIII
8	VIII	41	XLI	74	LXXIV
9	IX	42	XLII	75	LXXV
10	X	43	XLIII	76	LXXVI
11	XI	44	XLIV	77	LXXVII
12	XII	45	XLV	78	LXXVIII
13	XIII	46	XLVI	79	LXXIX
14	XIV	47	XLVII	80	LXXX
15	XV	48	XLVIII	81	LXXXI
16	XVI	49	XLIX	82	LXXXII
17	XVII	50	L	83	LXXXIII
18	XVIII	51	LI	84	LXXXIV
19	XIX	52	LII	85	LXXXV
20	XX	53	LIII	86	LXXXVI
21	XXI	54	LIV	87	LXXXVII
22	XXII	55	LV	88	LXXXVIII
23	XXIII	56	LVI	89	LXXXIX
24	XXIV	57	LVII	90	XC
25	XXV	58	LVIII	91	XCI
26	XXVI	59	LIX	92	XCII
27	XXVII	60	LX	93	XCIII
28	XXVIII	61	LXI	94	XCIV
29	XXIX	62	LXII	95	XCV
30	XXX	63	LXIII	96	XCVI
31	XXXI	64	LXIV	97	XCVII
32	XXXII	65	LXV	98	XCVIII
33	XXXIII	66	LXVI	99	XCIX
				100	C

Roman Numerals 101 to 200

101	CI	134	CXXXIV	167	CLXVII
102	CII	135	CXXXV	168	CLXVIII
103	CIII	136	CXXXVI	169	CLXIX
104	CIV	137	CXXXVII	170	CLXX
105	CV	138	CXXXVIII	171	CLXXI
106	CVI	139	CXXXIX	172	CLXXII
107	CVII	140	CXL	173	CLXXIII
108	CVIII	141	CXLI	474	CLXXIV
109	CIX	142	CXLII	175	CLXXV
110	CX	143	CXLIII	176	CLXXVI
111	CXI	144	CXLIV	177	CLXXVII
112	CXII	145	CXLV	178	CLXXVIII
113	CXIII	146	CXLVI	179	CLXXIX
114	CXIV	147	CXLVII	180	CLXXX
115	CXV	148	CXLVIII	181	CLXXXI
116	CXVI	449	CXLIX	182	CLXXXII
117	CXVII	150	CL	183	CLXXXIII
118	CXVIII	151	CLI	184	CLXXXIV
119	CXIX	152	CLII	185	CLXXXV
120	CXX	153	CLIII	186	CLXXXVI
121	CXXI	154	CLIV	187	CLXXXII
122	CXXII	155	CLV	188	CLXXXVIII
123	CXXIII	156	CLVI	189	CLXXXIX
424	CXXIV	157	CLVII	190	CXC
125	CXXV	158	CLVIII	191	CXCI
126	CXXVI	159	CLIX	192	CXCII
127	CXXVII	160	CLX	193	CXCIII
128	CXXVIII	161	CLXI	194	CXCIV
129	CXXIX	162	CLXII	195	CXCV
130	CXXX	163	CLXIII	196	CXCVI
131	CXXXI	164	CLXIV	197	CXCVII
132	CXXXII	165	CLXV	198	CXCVIII
133	CXXXIII	166	CLXVI	499	CXCIX
				200	CC

Roman Numerals 201 to 300

201	CCI	234	CCXXXIV	267	CCLXVII
202	CCII	235	CCXXXV	268	CCLXVIII
203	CCIII	236	CCXXXVI	269	CCLXIX
204	CCIV	237	CCXXXVII	270	CCLXX
205	CCV	238	CCXXXVIII	271	CCLXXI
206	CCVI	239	CCXXXIX	272	CCLXXII
207	CCVII	240	CCXL	273	CCLXXIII
208	CCVIII	241	CCXLI	274	CCLXXIV
209	CCIX	242	CCXLII	275	CCLXXV
210	CCX	243	CCXLIII	276	CCLXXVI
211	CCXI	244	CCXLIV	277	CCLXXVII
212	CCXII	245	CCXLV	278	CLXXVIII
213	CCXIII	246	CCXLVI	279	CCLXXIX
214	CCXIV	247	CCXLVII	280	CCLXXX
215	CCXV	248	CCXLVIII	281	CCLXXXI
216	CCXVI	249	CCXLIX	282	CCLXXXII
217	CCXVII	250	CCL	283	CCLXXXIII
218	CCXVIII	251	CCLI	284	CCLXXXIV
219	CCXIX	252	CCLII	285	CCLXXXV
220	CCXX	253	CCLIII	286	CCLXXXVI
221	CCXXI	254	CCLIV	287	CCLXXXII
222	CCXXII	255	CCLV	288	CCLXXXVIII
223	CCXXIII	256	CCLVI	289	CCLXXXIX
224	CCXXIV	257	CCLVII	290	CCXC
225	CCXXV	258	CCLVIII	291	CCXCI
226	CCXXVI	259	CCLIX	292	CCXCII
227	CCXXVII	260	CCLX	293	CCXCIII
228	CCXXVIII	261	CCLXI	294	CCXCIV
229	CCXXIX	262	CCLXII	295	CCXCV
230	CCXXX	263	CCLXIII	296	CCXCVI
231	CCXXXI	264	CCLXIV	297	CCXCVII
232	CCXXXII	265	CCLXV	298	CCXCVIII
233	CCXXXIII	266	CCLXVI	299	CCXCIX
				300	CCC

Roman Numerals 301 to 400

301	CCCI	334	CCCXXXIV	367	CCCLXVII
302	CCCII	335	CCCXXXV	368	CCCLXVIII
303	CCCIII	336	CCCXXXVI	369	CCCLXIX
304	CCCIV	337	CCCXXXVII	370	CCCLXX
305	CCCV	338	CCCXXXVIII	371	CCCLXXI
306	CCCVI	339	CCCXXXIX	372	CCCLXXII
307	CCCVII	340	CCCXL	373	CCCLXXIII
308	CCCVIII	341	CCCXLI	374	CCCLXXIV
309	CCCIX	342	CCCXLII	375	CCCLXXV
310	CCCX	343	CCCXLIII	376	CCCLXXVI
311	CCCXI	344	CCCXLIV	377	CCCLXXVII
312	CCCXII	345	CCCXLV	378	CCLXXVIII
313	CCCXIII	346	CCCXLVI	379	CCCLXXIX
314	CCCXIV	347	CCCXLVII	380	CCCLXXX
315	CCCXV	348	CCCXLVIII	381	CCCLXXXI
316	CCCXVI	349	CCCXLIX	382	CCCLXXXII
317	CCCXVII	350	CCCL	383	CCCLXXXIII
318	CCCXVIII	351	CCCLI	384	CCCLXXXIV
319	CCCXIX	352	CCCLII	385	CCCLXXXV
320	CCCXX	353	CCCLIII	386	CCCLXXXVI
321	CCCXXI	354	CCCLIV	387	CCCLXXXII
322	CCCXXII	355	CCCLV	388	CCCLXXXVIII
323	CCCXXIII	356	CCCLVI	389	CCCLXXXIX
324	CCCXXIV	357	CCCLVII	390	CCCXC
325	CCCXXV	358	CCCLVIII	391	CCCXCI
326	CCCXXVI	359	CCCLIX	392	CCCXCII
327	CCCXXVII	360	CCCLX	393	CCCXCIII
328	CCCXXVIII	361	CCCLXI	394	CCCXCIV
329	CCCXXIX	362	CCCLXII	395	CCCXCV
330	CCCXXX	363	CCCLXIII	396	CCCXCVI
331	CCCXXXI	364	CCCLXIV	397	CCCXCVII
332	CCCXXXII	365	CCCLXV	398	CCCXCVIII
333	CCCXXXIII	366	CCCLXVI	399	CCCXCIX
				400	CD

Roman Numerals 401 to 500

401	CDI	434	CDXXXIV	467	CDLXVII
402	CDII	435	CDXXXV	468	CDLXVIII
403	CDIII	436	CDXXXVI	469	CDLXIX
404	CDIV	437	CDXXXVII	470	CDLXX
405	CDV	438	CDXXXVIII	471	CDLXXI
406	CDVI	439	CDXXXIX	472	CDLXXII
407	CDVII	440	CDXL	473	CDLXXIII
408	CVIII	441	CXLI	474	CLXXIV
409	CDIX	442	CDXLII	475	CDLXXV
410	CDX	443	CDXLIII	476	CDLXXVI
411	CDXI	444	CDXLIV	477	CDLXXVII
412	CDXII	445	CDXLV	478	CDLXXVIII
413	CDXIII	446	CDXLVI	479	CDLXXIX
414	CDXIV	447	CDXLVII	480	CDLXXX
415	CDXV	448	CDXLVIII	481	CDLXXXI
416	CDXVI	449	CDXLIX	482	CDLXXXII
417	CDXVII	450	CDL	483	CDLXXXIII
418	CDXVIII	451	CDLI	484	CDLXXXIV
419	CDXIX	452	CDLII	485	CDLXXXV
420	CDXX	453	CDLIII	486	CDLXXXVI
421	CDXXI	454	CDLIV	487	CDLXXXII
422	CDXXII	455	CDLV	488	CDLXXXVIII
423	CDXXIII	456	CDLVI	489	CDLXXXIX
424	CDXXIV	457	CDLVII	490	CDXC
425	CDXXV	458	CDLVIII	491	CDXCI
426	CDXXVI	459	CDLIX	492	CDXCII
427	CDXXVII	460	CDLX	493	CDXCIII
428	CDXXVIII	461	CDLXI	494	CDXCIV
429	CDXXIX	462	CDLXII	495	CDXCV
430	CDXXX	463	CDLXIII	496	CDXCVI
431	CDXXXI	464	CDLXIV	497	CDXCVII
432	CDXXXII	465	CDLXV	498	CDXCVIII
433	CDXXXIII	466	CDLXVI	499	CDXCIX
				500	D

Roman Numerals 501 to 600

501	DI	534	DXXXIV	567	DLXVII
502	DII	535	DXXXV	568	DLXVIII
503	DIII	536	DXXXVI	569	DLXIX
504	DIV	537	DXXXVII	570	DLXX
505	DV	538	DXXXVIII	571	DLXXI
506	DVI	539	DXXXIX	572	DLXXII
507	DVII	540	DXL	573	DLXXIII
508	DVIII	541	DXLI	574	DLXXIV
509	DIX	542	DXLII	575	DLXXV
510	DX	543	DXLIII	576	DLXXVI
511	DXI	544	DXLIV	577	DLXXVII
512	DXII	545	DXLV	578	DLXXVIII
513	DXIII	546	DXLVI	579	DLXXIX
514	DXIV	547	DXLVII	580	DLXXX
515	DXV	548	DXLVIII	581	DLXXXI
516	DXVI	549	DXLIX	582	DLXXXII
517	DXVII	550	DL	583	DLXXXIII
518	DXVIII	551	DLI	584	DLXXXIV
519	DXIX	552	DLII	585	DLXXXV
520	DXX	553	DLIII	586	DLXXXVI
521	DXXI	554	DLIV	587	DLXXXII
522	DXXII	555	DLV	588	DLXXXVIII
523	DXXIII	556	DLVI	589	DLXXXIX
524	DXXIV	557	DLVII	590	DXC
525	DXXV	558	DLVIII	591	DXCI
526	DXXVI	559	DLIX	592	DXCII
527	DXXVII	560	DLX	593	DXCIII
528	DXXVIII	561	DLXI	594	DXCIV
529	DXXIX	562	DLXII	595	DXCV
530	DXXX	563	DLXIII	596	DXCVI
31	DXXXI	564	DLXIV	597	DXCVII
532	DXXXII	565	DLXV	598	DXCVIII
533	DXXXIII	566	DLXVI	599	DXCIX
				600	DC

Roman Numerals 601 to 700

601	DCI	634	DCXXXIV	667	DCLXVII
602	DCII	635	DCXXXV	668	DCLXVIII
603	DCIII	636	DCXXXVI	669	DCLXIX
604	DCIV	637	DCXXXVII	670	DCLXX
605	DCV	638	DCXXXVIII	671	DCLXXI
606	DCVI	639	DCXXXIX	672	DCLXXII
607	DCVII	640	DCXL	673	DCLXXIII
608	DCVIII	641	DCXLI	674	DCLXXIV
609	DCIX	642	DCXLII	675	DCLXXV
610	DCX	643	DCXLIII	676	DCLXXVI
611	DCXI	644	DCXLIV	677	DCLXXVII
612	DCXII	645	DCXLV	678	DCLXXVIII
613	DCXIII	646	DCXLVI	679	DCLXXIX
614	DCXIV	647	DCXLVII	680	DCLXXX
615	DCXV	648	DCXLVIII	681	DCLXXXI
616	DCXVI	649	DCXLIX	682	DCLXXXII
617	DCXVII	650	DCL	683	DCLXXXIII
618	DCXVIII	651	DCLI	684	DCLXXXIV
619	DCXIX	652	DCLII	685	DCLXXXV
620	DCXX	653	DCLIII	686	DCLXXXVI
621	DCXXI	654	DCLIV	687	DCLXXXII
622	DCXXII	655	DCLV	688	DCLXXXVIII
623	DCXXIII	656	DCLVI	689	DCLXXXIX
624	DCXXIV	657	DCLVII	690	DCXC
625	DCXXV	658	DCLVIII	691	DCXCI
626	DCXXVI	659	DCLIX	692	DCXCII
627	DCXXVII	660	DCLX	693	DCXCIII
628	DCXXVIII	661	DCLXI	694	DCXCIV
629	DCXXIX	662	DCLXII	695	DCXCV
630	DCXXX	663	DCLXIII	696	DCXCVI
631	DCXXXI	664	DCLXIV	697	DCXCVII
632	DCXXXII	665	DCLXV	698	DCXCVIII
633	DCXXXIII	666	DCLXVI	699	DCXCIX
				700	DCC

Roman Numerals 701 to 800

701	DCCI	734	DCCXXXIV	767	DCCLXVII
702	DCCII	735	DCCXXXV	768	DCCLXVIII
703	DCCIII	736	DCCXXXVI	769	DCCLXIX
704	DCCIV	737	DCCXXXVII	770	DCCLXX
705	DCCV	738	DCCXXXVIII	771	DCCLXXI
706	DCCVI	739	DCCXXXIX	772	DCCLXXII
707	DCCVII	740	DCCXL	773	DCCLXXIII
708	DCCVIII	741	DCCXLI	774	DCCLXXIV
709	DCCIX	742	DCCXLII	775	DCCLXXV
710	DCCX	743	DCCXLIII	776	DCCLXXVI
711	DCCXI	744	DCCXLIV	777	DCCLXXVII
712	DCCXII	745	DCCXLV	778	DCCLXXVIII
713	DCCXIII	746	DCCXLVI	779	DCCLXXIX
714	DCCXIV	747	DCCXLVII	780	DCCLXXX
715	DCCXV	748	DCCXLVIII	781	DCCLXXXI
716	DCCXVI	749	DCCXLIX	782	DCCLXXXII
717	DCCXVII	750	DCCL	783	DCCLXXXIII
718	DCCXVIII	751	DCCLI	784	DCCLXXXIV
719	DCCXIX	752	DCCLII	785	DCCLXXXV
720	DCCXX	753	DCCLIII	786	DCCLXXXVI
721	DCCXXI	754	DCCLIV	787	DCCLXXXII
722	DCCXXII	755	DCCLV	788	DCCLXXXVIII
723	DCCXXIII	756	DCCLVI	789	DCCLXXXIX
724	DCCXXIV	757	DCCLVII	790	DCCXC
725	DCCXXV	758	DCCLVIII	791	DCCXCI
726	DCCXXVI	759	DCCLIX	792	DCCXCII
727	DCCXXVII	760	DCCLX	793	DCCXCIII
728	DCCXXVIII	761	DCCLXI	794	DCCXCIV
729	DCCXXIX	762	DCCLXII	795	DCCXCV
730	DCCXXX	763	DCCLXIII	796	DCCXCVI
731	DCCXXXI	764	DCCLXIV	797	DCCXCVII
732	DCCXXXII	765	DCCLXV	798	DCCXCVIII
733	DCCXXXIII	766	DCCLXVI	799	DCCXCIX
				800	DCCC

Roman Numerals 801 to 900

801	DCCCI	834	DCCCXXXIV	867	DCCCLXVII
802	DCCCII	835	DCCCXXXV	868	DCCCLXVIII
803	DCCCIII	836	DCCCXXXVI	869	DCCCLXIX
804	DCCCIV	837	DCCCXXXVII	870	DCCCLXX
805	DCCCV	838	DCCCXXXVIII	871	DCCCLXXI
806	DCCCVI	839	DCCCXXXIX	872	DCCCLXXII
807	DCCCVII	840	DCCCXL	873	DCCCLXXIII
808	DCCCVIII	841	DCCCXLI	874	DCCCLXXIV
809	DCCCIX	842	DCCCXLII	875	DCCCLXXV
810	DCCCX	843	DCCCXLIII	876	DCCCLXXVI
811	DCCCXI	844	DCCCXLIV	877	DCCCLXXVII
812	DCCCXII	845	DCCCXLV	878	DCCCLXXVIII
813	DCCCXIII	846	DCCCXLVI	879	DCCCLXXIX
814	DCCCXIV	847	DCCCXLVII	880	DCCCLXXX
815	DCCCXV	848	DCCCXLVIII	881	DCCCLXXXI
816	DCCCXVI	849	DCCCXLIX	882	DCCCLXXXII
817	DCCCXVII	850	DCCCL	883	DCCCLXXXIII
818	DCCCXVIII	851	DCCCLI	884	DCCCLXXXIV
819	DCCCXIX	852	DCCCLII	885	DCCCLXXXV
820	DCCCXX	853	DCCCLIII	886	DCCCLXXXVI
821	DCCCXXI	854	DCCCLIV	887	DCCCLXXXII
822	DCCCXXII	855	DCCCLV	888	DCCCLXXXVIII
823	DCCCXXIII	856	DCCCLVI	889	DCCCLXXXIX
824	DCCCXXIV	857	DCCCLVII	890	DCCCXC
825	DCCCXXV	858	DCCCLVIII	891	DCCCXCI
826	DCCCXXVI	859	DCCCLIX	892	DCCCXCII
827	DCCCXXVII	860	DCCCLX	893	DCCCXCIII
828	DCCCXXVIII	861	DCCCLXI	894	DCCCXCIV
829	DCCCXXIX	862	DCCCLXII	895	DCCCXCV
830	DCCCXXX	863	DCCCLXIII	896	DCCCXCVI
831	DCCCXXXI	864	DCCCLXIV	897	DCCCXCVII
832	DCCCXXXII	865	DCCCLXV	898	DCCCXCVIII
833	DCCCXXXIII	866	DCCCLXVI	899	DCCCXCIX
				900	CM

Roman Numerals 901 to 1000

901	CMI	934	CMXXXIV	967	CMLXVII
902	CMII	935	CMXXXV	968	CMLXVIII
903	CMIII	936	CMXXXVI	969	CMLXIX
904	CMIV	937	CMXXXVII	970	CMLXX
905	CMV	938	CMXXXVIII	971	CMLXXI
906	CMVI	939	CMXXXIX	972	CMLXXII
907	CMVII	940	CMXL	973	CMLXXIII
908	CMVIII	941	CMXLI	974	CMLXXIV
909	CMIX	942	CMXLII	975	CMLXXV
910	CMX	943	CMXLIII	976	CMLXXVI
911	CMXI	944	CMXLIV	977	CMLXXVII
912	CMXII	945	CMXLV	978	CMLXXVIII
913	CMXIII	946	CMXLVI	979	CMLXXIX
914	CMXIV	947	CMXLVII	980	CMLXXX
915	CMXV	948	CMXLVIII	981	CMLXXXI
916	CMXVI	949	CMXLIX	982	CMLXXXII
917	CMXVII	950	CML	983	CMLXXXIII
918	CMXVIII	951	CMLI	984	CMLXXXIV
919	CMXIX	952	CMLII	985	CMLXXXV
920	CMXX	953	CMLIII	986	CMLXXXVI
921	CMXXI	954	CMLIV	987	CMLXXXII
922	CMXXII	955	CMLV	988	CMLXXXVIII
923	CMXXIII	956	CMLVI	989	CMLXXXIX
924	CMXXIV	957	CMLVII	990	CMXC
925	CMXXV	958	CMLVIII	991	CMXCI
926	CMXXVI	959	CMLIX	992	CMXCII
927	CMXXVII	960	CMLX	993	CMXCIII
928	CMXXVIII	961	CMLXI	994	CMXCIV
929	CMXXIX	962	CMLXII	995	CMXCV
930	CMXXX	963	CMLXIII	996	CMXCVI
931	CMXXXI	964	CMLXIV	997	CMXCVII
932	CMXXXII	965	CMLXV	998	CMXCVIII
933	CMXXXIII	966	CMLXVI	999	CMXCIX
				1000	M