圓周率數字出現頻率統計表
分析前100億位圓周率中每個數字的出現次數，幫助數學愛好者和開發者了解 π 的數字分布規律
統計說明
本統計表展示了圓周率前100億位中 0-9 各數字的出現次數和頻率。透過直觀的數據分析，可以觀察 π 數字的分布情況，適合數學研究、演算法測試、隨機數分析及教學演示。
數據來源與精度
數據來源於高精度計算的圓周率前100億位小數，經過多重驗證，保證統計結果準確可靠。統計結果不包含 π 的整數部分“3”，僅針對小數部分進行分析。
如何使用
用戶可以通過本頁面查看各數字出現次數和百分比，也可以下載完整統計數據。數據可用於數學研究、算法測試、教學演示或趣味探索 π 的數字規律。
下載數據
提供 CSV 和 TXT 兩種格式下載。CSV 格式適合在 Excel 或數據分析軟體中打開，TXT 格式方便直接查看或程式處理。下載數據包含每個數字的出現次數和頻率百分比，方便二次分析。
適用場景
- 數學研究與統計分析
- 隨機數與概率實驗
- 演算法測試與程式驗證
- 教學示範與科普探索
溫馨提示
資料量較大，請在下載或處理時確保設備性能充足。統計結果僅供學習、科研和趣味探索使用，不用於商業用途。
0-9數字頻率統計表
下表展示了圓周率（PI）前100億位小數中數字 0-9 的出現次數及頻率分析。統計結果顯示，隨著圓周率位數樣本的增大，0-9 各數字的分布逐漸趨向均勻。
| 序號 | 總計 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 10 | 0 0.00% | 2 20.00% | 1 10.00% | 2 20.00% | 1 10.00% | 2 20.00% | 1 10.00% | 0 0.00% | 0 0.00% | 1 10.00% |
| 2 | 20 | 0 0.00% | 2 10.00% | 2 10.00% | 4 20.00% | 2 10.00% | 3 15.00% | 1 5.00% | 1 5.00% | 2 10.00% | 3 15.00% |
| 3 | 30 | 0 0.00% | 2 6.67% | 4 13.33% | 7 23.33% | 3 10.00% | 3 10.00% | 3 10.00% | 2 6.67% | 3 10.00% | 3 10.00% |
| 4 | 40 | 1 2.50% | 3 7.50% | 5 12.50% | 7 17.50% | 4 10.00% | 4 10.00% | 3 7.50% | 3 7.50% | 5 12.50% | 5 12.50% |
| 5 | 50 | 1 2.00% | 5 10.00% | 5 10.00% | 9 18.00% | 4 8.00% | 5 10.00% | 4 8.00% | 4 8.00% | 5 10.00% | 8 16.00% |
| 6 | 60 | 3 5.00% | 5 8.33% | 6 10.00% | 9 15.00% | 6 10.00% | 6 10.00% | 4 6.67% | 5 8.33% | 6 10.00% | 10 16.67% |
| 7 | 70 | 4 5.71% | 6 8.57% | 7 10.00% | 10 14.29% | 7 10.00% | 7 10.00% | 5 7.14% | 6 8.57% | 7 10.00% | 11 15.71% |
| 8 | 80 | 6 7.50% | 6 7.50% | 9 11.25% | 10 12.50% | 8 10.00% | 7 8.75% | 7 8.75% | 6 7.50% | 9 11.25% | 12 15.00% |
| 9 | 90 | 7 7.78% | 6 6.67% | 11 12.22% | 11 12.22% | 9 10.00% | 7 7.78% | 8 8.89% | 6 6.67% | 12 13.33% | 13 14.44% |
| 10 | 100 | 8 8.00% | 8 8.00% | 12 12.00% | 12 12.00% | 10 10.00% | 8 8.00% | 9 9.00% | 8 8.00% | 12 12.00% | 13 13.00% |
| 11 | 200 | 19 9.50% | 20 10.00% | 24 12.00% | 20 10.00% | 22 11.00% | 20 10.00% | 15 7.50% | 12 6.00% | 25 12.50% | 23 11.50% |
| 12 | 300 | 26 8.67% | 30 10.00% | 35 11.67% | 31 10.33% | 37 12.33% | 27 9.00% | 31 10.33% | 19 6.33% | 34 11.33% | 30 10.00% |
| 13 | 400 | 39 9.75% | 43 10.75% | 44 11.00% | 40 10.00% | 46 11.50% | 39 9.75% | 42 10.50% | 24 6.00% | 44 11.00% | 39 9.75% |
| 14 | 500 | 45 9.00% | 59 11.80% | 53 10.60% | 51 10.20% | 53 10.60% | 50 10.00% | 48 9.60% | 36 7.20% | 53 10.60% | 52 10.40% |
| 15 | 600 | 54 9.00% | 67 11.17% | 63 10.50% | 64 10.67% | 64 10.67% | 55 9.17% | 62 10.33% | 50 8.33% | 59 9.83% | 62 10.33% |
| 16 | 700 | 64 9.14% | 76 10.86% | 75 10.71% | 72 10.29% | 73 10.43% | 66 9.43% | 70 10.00% | 65 9.29% | 68 9.71% | 71 10.14% |
| 17 | 800 | 74 9.25% | 92 11.50% | 83 10.38% | 80 10.00% | 80 10.00% | 73 9.13% | 77 9.63% | 75 9.38% | 76 9.50% | 90 11.25% |
| 18 | 900 | 86 9.56% | 103 11.44% | 93 10.33% | 94 10.44% | 89 9.89% | 84 9.33% | 85 9.44% | 83 9.22% | 88 9.78% | 95 10.56% |
| 19 | 1,000 | 93 9.30% | 116 11.60% | 103 10.30% | 103 10.30% | 93 9.30% | 97 9.70% | 94 9.40% | 95 9.50% | 101 10.10% | 105 10.50% |
| 20 | 2,000 | 182 9.10% | 212 10.60% | 207 10.35% | 189 9.45% | 195 9.75% | 205 10.25% | 200 10.00% | 197 9.85% | 202 10.10% | 211 10.55% |
| 21 | 3,000 | 259 8.63% | 308 10.27% | 303 10.10% | 266 8.87% | 318 10.60% | 315 10.50% | 302 10.07% | 287 9.57% | 310 10.33% | 332 11.07% |
| 22 | 4,000 | 362 9.05% | 429 10.73% | 408 10.20% | 369 9.23% | 405 10.13% | 417 10.43% | 397 9.93% | 377 9.43% | 405 10.13% | 431 10.78% |
| 23 | 5,000 | 466 9.32% | 531 10.62% | 496 9.92% | 460 9.20% | 508 10.16% | 525 10.50% | 513 10.26% | 488 9.76% | 492 9.84% | 521 10.42% |
| 24 | 6,000 | 556 9.27% | 626 10.43% | 594 9.90% | 573 9.55% | 613 10.22% | 622 10.37% | 619 10.32% | 606 10.10% | 582 9.70% | 609 10.15% |
| 25 | 7,000 | 657 9.39% | 733 10.47% | 692 9.89% | 687 9.81% | 702 10.03% | 730 10.43% | 708 10.11% | 693 9.90% | 680 9.71% | 718 10.26% |
| 26 | 8,000 | 754 9.43% | 833 10.41% | 811 10.14% | 782 9.78% | 809 10.11% | 834 10.43% | 816 10.20% | 785 9.81% | 764 9.55% | 812 10.15% |
| 27 | 9,000 | 855 9.50% | 936 10.40% | 911 10.12% | 885 9.83% | 910 10.11% | 932 10.36% | 914 10.16% | 883 9.81% | 854 9.49% | 920 10.22% |
| 28 | 10,000 | 968 9.68% | 1026 10.26% | 1021 10.21% | 975 9.75% | 1012 10.12% | 1046 10.46% | 1021 10.21% | 970 9.70% | 947 9.47% | 1014 10.14% |
| 29 | 20,000 | 1954 9.77% | 1997 9.99% | 1986 9.93% | 1987 9.94% | 2043 10.22% | 2082 10.41% | 2017 10.09% | 1953 9.77% | 1961 9.81% | 2020 10.10% |
| 30 | 30,000 | 2998 9.99% | 3048 10.16% | 2897 9.66% | 2979 9.93% | 3057 10.19% | 3049 10.16% | 3012 10.04% | 2974 9.91% | 2972 9.91% | 3014 10.05% |
| 31 | 40,000 | 3989 9.97% | 4060 10.15% | 3892 9.73% | 3972 9.93% | 4014 10.04% | 4040 10.10% | 4026 10.07% | 3977 9.94% | 4032 10.08% | 3998 10.00% |
| 32 | 50,000 | 5033 10.07% | 5054 10.11% | 4867 9.73% | 4948 9.90% | 5011 10.02% | 5052 10.10% | 5018 10.04% | 4977 9.95% | 5030 10.06% | 5010 10.02% |
| 33 | 60,000 | 6009 10.02% | 6071 10.12% | 5894 9.82% | 5976 9.96% | 5983 9.97% | 6086 10.14% | 5980 9.97% | 5995 9.99% | 6015 10.03% | 5991 9.99% |
| 34 | 70,000 | 6992 9.99% | 7106 10.15% | 6892 9.85% | 7018 10.03% | 6948 9.93% | 7033 10.05% | 6966 9.95% | 7047 10.07% | 7013 10.02% | 6985 9.98% |
| 35 | 80,000 | 7972 9.97% | 8141 10.18% | 7920 9.90% | 7976 9.97% | 7957 9.95% | 8044 10.06% | 8025 10.03% | 8031 10.04% | 7953 9.94% | 7981 9.98% |
| 36 | 90,000 | 8990 9.99% | 9193 10.21% | 8887 9.87% | 9020 10.02% | 8957 9.95% | 9026 10.03% | 8992 9.99% | 9028 10.03% | 8953 9.95% | 8954 9.95% |
| 37 | 100,000 | 9999 10.00% | 10137 10.14% | 9908 9.91% | 10026 10.03% | 9971 9.97% | 10026 10.03% | 10028 10.03% | 10025 10.03% | 9978 9.98% | 9902 9.90% |
| 38 | 200,000 | 20104 10.05% | 20063 10.03% | 19892 9.95% | 20011 10.01% | 19874 9.94% | 20199 10.10% | 19898 9.95% | 20163 10.08% | 19955 9.98% | 19841 9.92% |
| 39 | 300,000 | 30001 10.00% | 30034 10.01% | 29879 9.96% | 30139 10.05% | 29844 9.95% | 30272 10.09% | 29890 9.96% | 30226 10.08% | 29926 9.98% | 29789 9.93% |
| 40 | 400,000 | 40013 10.00% | 40069 10.02% | 39813 9.95% | 40098 10.02% | 40093 10.02% | 40261 10.07% | 39859 9.96% | 40278 10.07% | 39814 9.95% | 39702 9.93% |
| 41 | 500,000 | 49915 9.98% | 49984 10.00% | 49752 9.95% | 50001 10.00% | 50357 10.07% | 50235 10.05% | 49824 9.96% | 50230 10.05% | 49911 9.98% | 49791 9.96% |
| 42 | 600,000 | 60019 10.00% | 59874 9.98% | 59627 9.94% | 60051 10.01% | 60475 10.08% | 60177 10.03% | 59761 9.96% | 60145 10.02% | 60015 10.00% | 59856 9.98% |
| 43 | 700,000 | 70037 10.01% | 69839 9.98% | 69796 9.97% | 69994 10.00% | 70601 10.09% | 70180 10.03% | 69577 9.94% | 69976 10.00% | 70138 10.02% | 69862 9.98% |
| 44 | 800,000 | 79949 9.99% | 79851 9.98% | 79872 9.98% | 79963 10.00% | 80447 10.06% | 80298 10.04% | 79650 9.96% | 79883 9.99% | 80167 10.02% | 79920 9.99% |
| 45 | 900,000 | 89995 10.00% | 89778 9.98% | 89912 9.99% | 90070 10.01% | 90330 10.04% | 90180 10.02% | 89574 9.95% | 89865 9.99% | 90214 10.02% | 90082 10.01% |
| 46 | 1,000,000 | 99959 10.00% | 99757 9.98% | 100026 10.00% | 100230 10.02% | 100230 10.02% | 100359 10.04% | 99548 9.95% | 99800 9.98% | 99985 10.00% | 100106 10.01% |
| 47 | 2,000,000 | 199792 9.99% | 199535 9.98% | 200077 10.00% | 200142 10.01% | 200083 10.00% | 200521 10.03% | 199403 9.97% | 200310 10.02% | 199447 9.97% | 200690 10.03% |
| 48 | 3,000,000 | 299451 9.98% | 299640 9.99% | 299867 10.00% | 300311 10.01% | 300234 10.01% | 300342 10.01% | 299461 9.98% | 300655 10.02% | 299440 9.98% | 300599 10.02% |
| 49 | 4,000,000 | 399418 9.99% | 399463 9.99% | 399822 10.00% | 399914 10.00% | 400792 10.02% | 400032 10.00% | 399032 9.98% | 400650 10.02% | 400183 10.00% | 400694 10.02% |
| 50 | 5,000,000 | 499620 9.99% | 499898 10.00% | 499508 9.99% | 499934 10.00% | 500544 10.01% | 500024 10.00% | 498758 9.98% | 500880 10.02% | 499880 10.00% | 500954 10.02% |
| 51 | 6,000,000 | 599476 9.99% | 600346 10.01% | 599682 9.99% | 599977 10.00% | 600357 10.01% | 599769 10.00% | 598438 9.97% | 600779 10.01% | 600255 10.00% | 600921 10.02% |
| 52 | 7,000,000 | 699323 9.99% | 700456 10.01% | 699948 10.00% | 700330 10.00% | 700266 10.00% | 699837 10.00% | 698428 9.98% | 700410 10.01% | 700551 10.01% | 700451 10.01% |
| 53 | 8,000,000 | 799111 9.99% | 800110 10.00% | 799788 10.00% | 800235 10.00% | 800201 10.00% | 800154 10.00% | 798885 9.99% | 800560 10.01% | 800638 10.01% | 800318 10.00% |
| 54 | 9,000,000 | 898824 9.99% | 899910 10.00% | 899961 10.00% | 899822 10.00% | 900949 10.01% | 900632 10.01% | 899243 9.99% | 900445 10.00% | 900209 10.00% | 900005 10.00% |
| 55 | 10,000,000 | 999440 9.99% | 999333 9.99% | 1000306 10.00% | 999965 10.00% | 1001093 10.01% | 1000466 10.00% | 999337 9.99% | 1000206 10.00% | 999814 10.00% | 1000040 10.00% |
| 56 | 20,000,000 | 2001162 10.01% | 1999832 10.00% | 2001409 10.01% | 1999344 10.00% | 2001105 10.01% | 2000125 10.00% | 1999269 10.00% | 1998404 9.99% | 1999720 10.00% | 1999630 10.00% |
| 57 | 30,000,000 | 2999157 10.00% | 3000553 10.00% | 3000969 10.00% | 2999223 10.00% | 3002593 10.01% | 2999997 10.00% | 2999548 10.00% | 2998175 9.99% | 2999592 10.00% | 3000193 10.00% |
| 58 | 40,000,000 | 3998620 10.00% | 4000689 10.00% | 4001754 10.00% | 3999046 10.00% | 4002297 10.01% | 4000678 10.00% | 3998804 10.00% | 3998685 10.00% | 3998711 10.00% | 4000716 10.00% |
| 59 | 50,000,000 | 4999632 10.00% | 5002220 10.00% | 5000573 10.00% | 4998631 10.00% | 5004008 10.01% | 4999797 10.00% | 4998017 10.00% | 4998895 10.00% | 4998494 10.00% | 4999733 10.00% |
| 60 | 60,000,000 | 6000989 10.00% | 6002957 10.00% | 6000496 10.00% | 5998066 10.00% | 6003573 10.01% | 5998454 10.00% | 5997776 10.00% | 5998499 10.00% | 5999666 10.00% | 5999524 10.00% |
| 61 | 70,000,000 | 6998752 10.00% | 7004229 10.01% | 7000755 10.00% | 6999582 10.00% | 7002962 10.00% | 6996862 10.00% | 6997933 10.00% | 6998514 10.00% | 7000965 10.00% | 6999446 10.00% |
| 62 | 80,000,000 | 7998807 10.00% | 8002788 10.00% | 8001827 10.00% | 7997657 10.00% | 8003525 10.00% | 7996500 10.00% | 7998165 10.00% | 7999389 10.00% | 8000308 10.00% | 8001034 10.00% |
| 63 | 90,000,000 | 8999061 10.00% | 9002299 10.00% | 9001832 10.00% | 8999115 10.00% | 9004437 10.00% | 8994836 9.99% | 8998902 10.00% | 8998963 10.00% | 9000947 10.00% | 8999608 10.00% |
| 64 | 100,000,000 | 9999922 10.00% | 10002475 10.00% | 10001091 10.00% | 9998443 10.00% | 10003863 10.00% | 9993478 9.99% | 9999417 10.00% | 9999610 10.00% | 10002180 10.00% | 9999521 10.00% |
| 65 | 200,000,000 | 19997437 10.00% | 20003774 10.00% | 20002185 10.00% | 20001411 10.00% | 19999846 10.00% | 19993031 10.00% | 19999161 10.00% | 20000287 10.00% | 20002307 10.00% | 20000561 10.00% |
| 66 | 300,000,000 | 29998356 10.00% | 30000582 10.00% | 30006337 10.00% | 29999868 10.00% | 29999810 10.00% | 29993099 10.00% | 29998913 10.00% | 29999071 10.00% | 30003682 10.00% | 30000282 10.00% |
| 67 | 400,000,000 | 39996048 10.00% | 39997375 10.00% | 40011791 10.00% | 39995030 10.00% | 40001014 10.00% | 39992123 10.00% | 40001899 10.00% | 40000314 10.00% | 40005735 10.00% | 39998671 10.00% |
| 68 | 500,000,000 | 49995279 10.00% | 50000437 10.00% | 50011436 10.00% | 49992410 10.00% | 50005121 10.00% | 49990678 10.00% | 49998820 10.00% | 50000319 10.00% | 50006632 10.00% | 49998868 10.00% |
| 69 | 600,000,000 | 59991725 10.00% | 59997597 10.00% | 60008591 10.00% | 59992559 10.00% | 60007990 10.00% | 59990211 10.00% | 60003895 10.00% | 59998772 10.00% | 60010958 10.00% | 59997702 10.00% |
| 70 | 700,000,000 | 69989891 10.00% | 69997755 10.00% | 70006497 10.00% | 69994029 10.00% | 70009581 10.00% | 69994536 10.00% | 70003795 10.00% | 69997014 10.00% | 70005161 10.00% | 70001741 10.00% |
| 71 | 800,000,000 | 79991897 10.00% | 79997003 10.00% | 80003316 10.00% | 79989652 10.00% | 80016073 10.00% | 79996120 10.00% | 80004148 10.00% | 79995109 10.00% | 80002932 10.00% | 80003750 10.00% |
| 72 | 900,000,000 | 89991208 10.00% | 89998381 10.00% | 90000968 10.00% | 89990084 10.00% | 90013132 10.00% | 89996086 10.00% | 90006412 10.00% | 89995658 10.00% | 90001979 10.00% | 90006092 10.00% |
| 73 | 1,000,000,000 | 99993942 10.00% | 99997334 10.00% | 100002410 10.00% | 99986912 10.00% | 100011958 10.00% | 99998885 10.00% | 100010387 10.00% | 99996061 10.00% | 100001839 10.00% | 100000272 10.00% |
| 74 | 2,000,000,000 | 199994316 10.00% | 199995284 10.00% | 199992575 10.00% | 199999471 10.00% | 200014368 10.00% | 199989852 10.00% | 200004785 10.00% | 199979293 10.00% | 200017844 10.00% | 200012212 10.00% |
| 75 | 3,000,000,000 | 299999143 10.00% | 299995932 10.00% | 299989126 10.00% | 299992291 10.00% | 300002257 10.00% | 299979016 10.00% | 300025447 10.00% | 299975510 10.00% | 300016549 10.00% | 300024729 10.00% |
| 76 | 4,000,000,000 | 400001233 10.00% | 400002285 10.00% | 399965405 10.00% | 399984470 10.00% | 400006936 10.00% | 399989052 10.00% | 400033034 10.00% | 399996122 10.00% | 400004741 10.00% | 400016722 10.00% |
| 77 | 5,000,000,000 | 499989001 10.00% | 500034127 10.00% | 499984949 10.00% | 499990322 10.00% | 499978284 10.00% | 499995352 10.00% | 500019818 10.00% | 500001702 10.00% | 499990522 10.00% | 500015923 10.00% |
| 78 | 6,000,000,000 | 599963005 10.00% | 600033260 10.00% | 599999169 10.00% | 600000244 10.00% | 599957439 10.00% | 600017176 10.00% | 600016588 10.00% | 600009043 10.00% | 599987038 10.00% | 600017038 10.00% |
| 79 | 7,000,000,000 | 699971579 10.00% | 700032287 10.00% | 700014462 10.00% | 699990865 10.00% | 699956491 10.00% | 700007095 10.00% | 700001460 10.00% | 700007943 10.00% | 699991522 10.00% | 700026296 10.00% |
| 80 | 8,000,000,000 | 799959839 10.00% | 800031172 10.00% | 800016834 10.00% | 799985887 10.00% | 799942991 10.00% | 799995302 10.00% | 800003383 10.00% | 800012745 10.00% | 800011229 10.00% | 800040618 10.00% |
| 81 | 9,000,000,000 | 899957813 10.00% | 900030375 10.00% | 900016141 10.00% | 899992753 10.00% | 899941810 10.00% | 899997750 10.00% | 900002183 10.00% | 900023381 10.00% | 899991718 10.00% | 900046076 10.00% |
| 82 | 10,000,000,000 | 999967994 10.00% | 1000037790 10.00% | 1000017271 10.00% | 999976484 10.00% | 999937688 10.00% | 1000007928 10.00% | 999985731 10.00% | 1000041330 10.00% | 999991772 10.00% | 1000036012 10.00% |
常見問題
關於圓周率數字頻率統計的常見疑問解答
1. 什麼是圓周率數字頻率統計？
圓周率數字頻率統計是指計算 π 的小數部分中每個數字（0-9）出現的次數，並分析其分佈規律，以研究圓周率數字的隨機性和均勻性。
2. 數據統計的範圍有多大？
本統計表分析了圓周率前 100 億位小數（不含整數部分“3”），覆蓋足夠大範圍來觀察數字分布趨勢。
3. 數字 0-9 出現的次數是否相等？
由於 π 是一個無限不循環小數，每個數字出現次數會非常接近，但不完全相等。統計結果顯示整體趨勢趨向均勻分佈。
4. 數字出現頻率有明顯偏差嗎？
在前 100 億位小數中，各數字出現頻率差異很小，整體來看分佈接近 10% 的均勻水平。
5. 統計結果是否包含整數部分“3”？
統計僅針對 π 的小數部分，不包含整數部分“3”，以便更準確地分析 0-9 數字的分佈情況。
6. 為什麼數字分布會趨於均勻？
π 的小數是無限且不循環的，這意味著在大樣本下每個數字出現的概率趨於相等，因此長期來看 0-9 分布接近均勻。
7. 資料可以下載嗎？
使用者可以下載完整統計資料（CSV / TXT 格式），方便進一步分析或用於科研、教學。
8. 統計可以用於科研或教學嗎？
是的，這些統計數據可用於數學研究、機率實驗、算法測試和課堂演示，幫助理解 π 的數字規律。
9. 是否可以統計更多位數的圓周率？
我們的資料庫目前提供前 100 億位小數的統計，如果需要更多位數的頻率分析，請聯繫我們了解定制方案。
10. 總結結論是什麼？
根據統計分析，圓周率前 100 億位小數中數字 0-9 的出現次數總體接近均勻分布，每個數字出現頻率約為 10%。