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Roman Numerals

Roman numerals, the numeric system in ancient Rome, use combinations of letters from the Latin alphabet to signify values.

Roman numerals have no concept of the number zero, nor do they have a rigid concept of place-value. Because of this, the character length of numerals increases and decreases raggedly as numbers increase.

Below are the numbers 1-500 displayed in Roman Numerals. You can read more about the format of the numbers here

1 I 2 II 3 III 4 IV 5 V 6 VI 7 VII 8 VIII 9 IX 10 X 11 XI 12 XII 13 XIII 14 XIV 15 XV 16 XVI 17 XVII 18 XVIII 19 XIX 20 XX 21 XXI 22 XXII 23 XXIII 24 XXIV 25 XXV 26 XXVI 27 XXVII 28 XXVIII 29 XXIX 30 XXX 31 XXXI 32 XXXII 33 XXXIII 34 XXXIV 35 XXXV 36 XXXVI 37 XXXVII 38 XXXVIII 39 XXXIX 40 XL 41 XLI 42 XLII 43 XLIII 44 XLIV 45 XLV 46 XLVI 47 XLVII 48 XLVIII 49 XLIX 50 L

51 LI 52 LII 53 LIII 54 LIV 55 LV 56 LVI 57 LVII 58 LVIII 59 LIX 60 LX 61 LXI 62 LXII 63 LXIII 64 LXIV 65 LXV 66 LXVI 67 LXVII 68 LXVIII 69 LXIX 70 LXX 71 LXXI 72 LXXII 73 LXXIII 74 LXXIV 75 LXXV 76 LXXVI 77 LXXVII 78 LXXVIII 79 LXXIX 80 LXXX 81 LXXXI 82 LXXXII 83 LXXXIII 84 LXXXIV 85 LXXXV 86 LXXXVI 87 LXXXVII 88 LXXXVIII 89 LXXXIX 90 XC 91 XCI 92 XCII 93 XCIII 94 XCIV 95 XCV 96 XCVI 97 XCVII 98 XCVIII 99 XCIX 100 C

101 CI 102 CII 103 CIII 104 CIV 105 CV 106 CVI 107 CVII 108 CVIII 109 CIX 110 CX 111 CXI 112 CXII 113 CXIII 114 CXIV 115 CXV 116 CXVI 117 CXVII 118 CXVIII 119 CXIX 120 CXX 121 CXXI 122 CXXII 123 CXXIII 124 CXXIV 125 CXXV 126 CXXVI 127 CXXVII 128 CXXVIII 129 CXXIX 130 CXXX 131 CXXXI 132 CXXXII 133 CXXXIII 134 CXXXIV 135 CXXXV 136 CXXXVI 137 CXXXVII 138 CXXXVIII 139 CXXXIX 140 CXL 141 CXLI 142 CXLII 143 CXLIII 144 CXLIV 145 CXLV 146 CXLVI 147 CXLVII 148 CXLVIII 149 CXLIX 150 CL

151 CLI 152 CLII 153 CLIII 154 CLIV 155 CLV 156 CLVI 157 CLVII 158 CLVIII 159 CLIX 160 CLX 161 CLXI 162 CLXII 163 CLXIII 164 CLXIV 165 CLXV 166 CLXVI 167 CLXVII 168 CLXVIII 169 CLXIX 170 CLXX 171 CLXXI 172 CLXXII 173 CLXXIII 174 CLXXIV 175 CLXXV 176 CLXXVI 177 CLXXVII 178 CLXXVIII 179 CLXXIX 180 CLXXX 181 CLXXXI 182 CLXXXII 183 CLXXXIII 184 CLXXXIV 185 CLXXXV 186 CLXXXVI 187 CLXXXVII 188 CLXXXVIII 189 CLXXXIX 190 CXC 191 CXCI 192 CXCII 193 CXCIII 194 CXCIV 195 CXCV 196 CXCVI 197 CXCVII 198 CXCVIII 199 CXCIX 200 CC

201 CCI 202 CCII 203 CCIII 204 CCIV 205 CCV 206 CCVI 207 CCVII 208 CCVIII 209 CCIX 210 CCX 211 CCXI 212 CCXII 213 CCXIII 214 CCXIV 215 CCXV 216 CCXVI 217 CCXVII 218 CCXVIII 219 CCXIX 220 CCXX 221 CCXXI 222 CCXXII 223 CCXXIII 224 CCXXIV 225 CCXXV 226 CCXXVI 227 CCXXVII 228 CCXXVIII 229 CCXXIX 230 CCXXX 231 CCXXXI 232 CCXXXII 233 CCXXXIII 234 CCXXXIV 235 CCXXXV 236 CCXXXVI 237 CCXXXVII 238 CCXXXVIII 239 CCXXXIX 240 CCXL 241 CCXLI 242 CCXLII 243 CCXLIII 244 CCXLIV 245 CCXLV 246 CCXLVI 247 CCXLVII 248 CCXLVIII 249 CCXLIX 250 CCL

Below is a plot showing how the lengths of these Roman numerals changes. As you can see it is very cyclic with the length growing as the digit I is added in stages, then dropping back as this passes a mutiple of five, being replaced by a higher value symbol.

The longest Roman Numeral under 250 is CLXXXVIII which is nine characters long, and represents the numer 188.

The first number to required ten digits is 288, and this is CCLXXXVIII

Multiplication table

Whilst of no practical use, here a heatmap showing the lengths of the product of two Roman Numerals. At the top left is I x I. The lighter color shorts the shorter strings, the darker colors the longer product strings.

Each square to the the right and down increases of number by one. For obvious reasons the chart is symmetric around the leading diagonal, but its interesting to make out the harmonics that make it look like there are rings in the plot. The graph plots products for 1-50 on each axis.

Uses

These days, Roman Numerals are used mainly for garnish, and add an air of sophistication whenever they are used.

They appear on watch and clock faces, in titles of Kings, Queens and Popes, Superbowl and Olympic Games' numbering, as numeric bullets in fancy documents, or as page numbers in book prefaces.

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