Reproduction: These tables can be regenerated
or extended by running scripts/generate_math_tables.py.
The script uses only the Python standard library.
1. COMMON LOGARITHMS (BASE
10)
Four-figure logarithms for values 1.0 to 9.9. To find
log₁₀(N):
- Write N in scientific notation: N = M × 10^p where 1 ≤ M <
10
- Look up log₁₀(M) in the table below
- log₁₀(N) = log₁₀(M) + p
Example: log₁₀(4370) = log₁₀(4.37 × 10³) = 0.6405 + 3 =
3.6405
| N |
.00 |
.01 |
.02 |
.03 |
.04 |
.05 |
.06 |
.07 |
.08 |
.09 |
| 1.0 |
0.0000 |
0.0043 |
0.0086 |
0.0128 |
0.0170 |
0.0212 |
0.0253 |
0.0294 |
0.0334 |
0.0374 |
| 1.1 |
0.0414 |
0.0453 |
0.0492 |
0.0531 |
0.0569 |
0.0607 |
0.0645 |
0.0682 |
0.0719 |
0.0755 |
| 1.2 |
0.0792 |
0.0828 |
0.0864 |
0.0899 |
0.0934 |
0.0969 |
0.1004 |
0.1038 |
0.1072 |
0.1106 |
| 1.3 |
0.1139 |
0.1173 |
0.1206 |
0.1239 |
0.1271 |
0.1303 |
0.1335 |
0.1367 |
0.1399 |
0.1430 |
| 1.4 |
0.1461 |
0.1492 |
0.1523 |
0.1553 |
0.1584 |
0.1614 |
0.1644 |
0.1673 |
0.1703 |
0.1732 |
| 1.5 |
0.1761 |
0.1790 |
0.1818 |
0.1847 |
0.1875 |
0.1903 |
0.1931 |
0.1959 |
0.1987 |
0.2014 |
| 1.6 |
0.2041 |
0.2068 |
0.2095 |
0.2122 |
0.2148 |
0.2175 |
0.2201 |
0.2227 |
0.2253 |
0.2279 |
| 1.7 |
0.2304 |
0.2330 |
0.2355 |
0.2380 |
0.2405 |
0.2430 |
0.2455 |
0.2480 |
0.2504 |
0.2529 |
| 1.8 |
0.2553 |
0.2577 |
0.2601 |
0.2625 |
0.2648 |
0.2672 |
0.2695 |
0.2718 |
0.2742 |
0.2765 |
| 1.9 |
0.2788 |
0.2810 |
0.2833 |
0.2856 |
0.2878 |
0.2900 |
0.2923 |
0.2945 |
0.2967 |
0.2989 |
| 2.0 |
0.3010 |
0.3032 |
0.3054 |
0.3075 |
0.3096 |
0.3118 |
0.3139 |
0.3160 |
0.3181 |
0.3201 |
| 2.1 |
0.3222 |
0.3243 |
0.3263 |
0.3284 |
0.3304 |
0.3324 |
0.3345 |
0.3365 |
0.3385 |
0.3404 |
| 2.2 |
0.3424 |
0.3444 |
0.3464 |
0.3483 |
0.3502 |
0.3522 |
0.3541 |
0.3560 |
0.3579 |
0.3598 |
| 2.3 |
0.3617 |
0.3636 |
0.3655 |
0.3674 |
0.3692 |
0.3711 |
0.3729 |
0.3747 |
0.3766 |
0.3784 |
| 2.4 |
0.3802 |
0.3820 |
0.3838 |
0.3856 |
0.3874 |
0.3892 |
0.3909 |
0.3927 |
0.3945 |
0.3962 |
| 2.5 |
0.3979 |
0.3997 |
0.4014 |
0.4031 |
0.4048 |
0.4065 |
0.4082 |
0.4099 |
0.4116 |
0.4133 |
| 2.6 |
0.4150 |
0.4166 |
0.4183 |
0.4200 |
0.4216 |
0.4232 |
0.4249 |
0.4265 |
0.4281 |
0.4298 |
| 2.7 |
0.4314 |
0.4330 |
0.4346 |
0.4362 |
0.4378 |
0.4393 |
0.4409 |
0.4425 |
0.4440 |
0.4456 |
| 2.8 |
0.4472 |
0.4487 |
0.4502 |
0.4518 |
0.4533 |
0.4548 |
0.4564 |
0.4579 |
0.4594 |
0.4609 |
| 2.9 |
0.4624 |
0.4639 |
0.4654 |
0.4669 |
0.4683 |
0.4698 |
0.4713 |
0.4728 |
0.4742 |
0.4757 |
| 3.0 |
0.4771 |
0.4786 |
0.4800 |
0.4814 |
0.4829 |
0.4843 |
0.4857 |
0.4871 |
0.4886 |
0.4900 |
| 3.1 |
0.4914 |
0.4928 |
0.4942 |
0.4955 |
0.4969 |
0.4983 |
0.4997 |
0.5011 |
0.5024 |
0.5038 |
| 3.2 |
0.5051 |
0.5065 |
0.5079 |
0.5092 |
0.5105 |
0.5119 |
0.5132 |
0.5145 |
0.5159 |
0.5172 |
| 3.3 |
0.5185 |
0.5198 |
0.5211 |
0.5224 |
0.5237 |
0.5250 |
0.5263 |
0.5276 |
0.5289 |
0.5302 |
| 3.4 |
0.5315 |
0.5328 |
0.5340 |
0.5353 |
0.5366 |
0.5378 |
0.5391 |
0.5403 |
0.5416 |
0.5428 |
| 3.5 |
0.5441 |
0.5453 |
0.5465 |
0.5478 |
0.5490 |
0.5502 |
0.5514 |
0.5527 |
0.5539 |
0.5551 |
| 3.6 |
0.5563 |
0.5575 |
0.5587 |
0.5599 |
0.5611 |
0.5623 |
0.5635 |
0.5647 |
0.5658 |
0.5670 |
| 3.7 |
0.5682 |
0.5694 |
0.5705 |
0.5717 |
0.5729 |
0.5740 |
0.5752 |
0.5763 |
0.5775 |
0.5786 |
| 3.8 |
0.5798 |
0.5809 |
0.5821 |
0.5832 |
0.5843 |
0.5855 |
0.5866 |
0.5877 |
0.5888 |
0.5899 |
| 3.9 |
0.5911 |
0.5922 |
0.5933 |
0.5944 |
0.5955 |
0.5966 |
0.5977 |
0.5988 |
0.5999 |
0.6010 |
| 4.0 |
0.6021 |
0.6031 |
0.6042 |
0.6053 |
0.6064 |
0.6075 |
0.6085 |
0.6096 |
0.6107 |
0.6117 |
| 4.1 |
0.6128 |
0.6138 |
0.6149 |
0.6160 |
0.6170 |
0.6180 |
0.6191 |
0.6201 |
0.6212 |
0.6222 |
| 4.2 |
0.6232 |
0.6243 |
0.6253 |
0.6263 |
0.6274 |
0.6284 |
0.6294 |
0.6304 |
0.6314 |
0.6325 |
| 4.3 |
0.6335 |
0.6345 |
0.6355 |
0.6365 |
0.6375 |
0.6385 |
0.6395 |
0.6405 |
0.6415 |
0.6425 |
| 4.4 |
0.6435 |
0.6444 |
0.6454 |
0.6464 |
0.6474 |
0.6484 |
0.6493 |
0.6503 |
0.6513 |
0.6522 |
| 4.5 |
0.6532 |
0.6542 |
0.6551 |
0.6561 |
0.6571 |
0.6580 |
0.6590 |
0.6599 |
0.6609 |
0.6618 |
| 4.6 |
0.6628 |
0.6637 |
0.6646 |
0.6656 |
0.6665 |
0.6675 |
0.6684 |
0.6693 |
0.6702 |
0.6712 |
| 4.7 |
0.6721 |
0.6730 |
0.6739 |
0.6749 |
0.6758 |
0.6767 |
0.6776 |
0.6785 |
0.6794 |
0.6803 |
| 4.8 |
0.6812 |
0.6821 |
0.6830 |
0.6839 |
0.6848 |
0.6857 |
0.6866 |
0.6875 |
0.6884 |
0.6893 |
| 4.9 |
0.6902 |
0.6911 |
0.6920 |
0.6928 |
0.6937 |
0.6946 |
0.6955 |
0.6964 |
0.6972 |
0.6981 |
| 5.0 |
0.6990 |
0.6998 |
0.7007 |
0.7016 |
0.7024 |
0.7033 |
0.7042 |
0.7050 |
0.7059 |
0.7067 |
| 5.1 |
0.7076 |
0.7084 |
0.7093 |
0.7101 |
0.7110 |
0.7118 |
0.7126 |
0.7135 |
0.7143 |
0.7152 |
| 5.2 |
0.7160 |
0.7168 |
0.7177 |
0.7185 |
0.7193 |
0.7202 |
0.7210 |
0.7218 |
0.7226 |
0.7235 |
| 5.3 |
0.7243 |
0.7251 |
0.7259 |
0.7267 |
0.7275 |
0.7284 |
0.7292 |
0.7300 |
0.7308 |
0.7316 |
| 5.4 |
0.7324 |
0.7332 |
0.7340 |
0.7348 |
0.7356 |
0.7364 |
0.7372 |
0.7380 |
0.7388 |
0.7396 |
| 5.5 |
0.7404 |
0.7412 |
0.7419 |
0.7427 |
0.7435 |
0.7443 |
0.7451 |
0.7459 |
0.7466 |
0.7474 |
| 5.6 |
0.7482 |
0.7490 |
0.7497 |
0.7505 |
0.7513 |
0.7520 |
0.7528 |
0.7536 |
0.7543 |
0.7551 |
| 5.7 |
0.7559 |
0.7566 |
0.7574 |
0.7582 |
0.7589 |
0.7597 |
0.7604 |
0.7612 |
0.7619 |
0.7627 |
| 5.8 |
0.7634 |
0.7642 |
0.7649 |
0.7657 |
0.7664 |
0.7672 |
0.7679 |
0.7686 |
0.7694 |
0.7701 |
| 5.9 |
0.7709 |
0.7716 |
0.7723 |
0.7731 |
0.7738 |
0.7745 |
0.7752 |
0.7760 |
0.7767 |
0.7774 |
| 6.0 |
0.7782 |
0.7789 |
0.7796 |
0.7803 |
0.7810 |
0.7818 |
0.7825 |
0.7832 |
0.7839 |
0.7846 |
| 6.1 |
0.7853 |
0.7860 |
0.7868 |
0.7875 |
0.7882 |
0.7889 |
0.7896 |
0.7903 |
0.7910 |
0.7917 |
| 6.2 |
0.7924 |
0.7931 |
0.7938 |
0.7945 |
0.7952 |
0.7959 |
0.7966 |
0.7973 |
0.7980 |
0.7987 |
| 6.3 |
0.7993 |
0.8000 |
0.8007 |
0.8014 |
0.8021 |
0.8028 |
0.8035 |
0.8041 |
0.8048 |
0.8055 |
| 6.4 |
0.8062 |
0.8069 |
0.8075 |
0.8082 |
0.8089 |
0.8096 |
0.8102 |
0.8109 |
0.8116 |
0.8122 |
| 6.5 |
0.8129 |
0.8136 |
0.8142 |
0.8149 |
0.8156 |
0.8162 |
0.8169 |
0.8176 |
0.8182 |
0.8189 |
| 6.6 |
0.8195 |
0.8202 |
0.8209 |
0.8215 |
0.8222 |
0.8228 |
0.8235 |
0.8241 |
0.8248 |
0.8254 |
| 6.7 |
0.8261 |
0.8267 |
0.8274 |
0.8280 |
0.8287 |
0.8293 |
0.8299 |
0.8306 |
0.8312 |
0.8319 |
| 6.8 |
0.8325 |
0.8331 |
0.8338 |
0.8344 |
0.8351 |
0.8357 |
0.8363 |
0.8370 |
0.8376 |
0.8382 |
| 6.9 |
0.8388 |
0.8395 |
0.8401 |
0.8407 |
0.8414 |
0.8420 |
0.8426 |
0.8432 |
0.8439 |
0.8445 |
| 7.0 |
0.8451 |
0.8457 |
0.8463 |
0.8470 |
0.8476 |
0.8482 |
0.8488 |
0.8494 |
0.8500 |
0.8506 |
| 7.1 |
0.8513 |
0.8519 |
0.8525 |
0.8531 |
0.8537 |
0.8543 |
0.8549 |
0.8555 |
0.8561 |
0.8567 |
| 7.2 |
0.8573 |
0.8579 |
0.8585 |
0.8591 |
0.8597 |
0.8603 |
0.8609 |
0.8615 |
0.8621 |
0.8627 |
| 7.3 |
0.8633 |
0.8639 |
0.8645 |
0.8651 |
0.8657 |
0.8663 |
0.8669 |
0.8675 |
0.8681 |
0.8686 |
| 7.4 |
0.8692 |
0.8698 |
0.8704 |
0.8710 |
0.8716 |
0.8722 |
0.8727 |
0.8733 |
0.8739 |
0.8745 |
| 7.5 |
0.8751 |
0.8756 |
0.8762 |
0.8768 |
0.8774 |
0.8779 |
0.8785 |
0.8791 |
0.8797 |
0.8802 |
| 7.6 |
0.8808 |
0.8814 |
0.8820 |
0.8825 |
0.8831 |
0.8837 |
0.8842 |
0.8848 |
0.8854 |
0.8859 |
| 7.7 |
0.8865 |
0.8871 |
0.8876 |
0.8882 |
0.8887 |
0.8893 |
0.8899 |
0.8904 |
0.8910 |
0.8915 |
| 7.8 |
0.8921 |
0.8927 |
0.8932 |
0.8938 |
0.8943 |
0.8949 |
0.8954 |
0.8960 |
0.8965 |
0.8971 |
| 7.9 |
0.8976 |
0.8982 |
0.8987 |
0.8993 |
0.8998 |
0.9004 |
0.9009 |
0.9015 |
0.9020 |
0.9025 |
| 8.0 |
0.9031 |
0.9036 |
0.9042 |
0.9047 |
0.9053 |
0.9058 |
0.9063 |
0.9069 |
0.9074 |
0.9079 |
| 8.1 |
0.9085 |
0.9090 |
0.9096 |
0.9101 |
0.9106 |
0.9112 |
0.9117 |
0.9122 |
0.9128 |
0.9133 |
| 8.2 |
0.9138 |
0.9143 |
0.9149 |
0.9154 |
0.9159 |
0.9165 |
0.9170 |
0.9175 |
0.9180 |
0.9186 |
| 8.3 |
0.9191 |
0.9196 |
0.9201 |
0.9206 |
0.9212 |
0.9217 |
0.9222 |
0.9227 |
0.9232 |
0.9238 |
| 8.4 |
0.9243 |
0.9248 |
0.9253 |
0.9258 |
0.9263 |
0.9269 |
0.9274 |
0.9279 |
0.9284 |
0.9289 |
| 8.5 |
0.9294 |
0.9299 |
0.9304 |
0.9309 |
0.9315 |
0.9320 |
0.9325 |
0.9330 |
0.9335 |
0.9340 |
| 8.6 |
0.9345 |
0.9350 |
0.9355 |
0.9360 |
0.9365 |
0.9370 |
0.9375 |
0.9380 |
0.9385 |
0.9390 |
| 8.7 |
0.9395 |
0.9400 |
0.9405 |
0.9410 |
0.9415 |
0.9420 |
0.9425 |
0.9430 |
0.9435 |
0.9440 |
| 8.8 |
0.9445 |
0.9450 |
0.9455 |
0.9460 |
0.9465 |
0.9469 |
0.9474 |
0.9479 |
0.9484 |
0.9489 |
| 8.9 |
0.9494 |
0.9499 |
0.9504 |
0.9509 |
0.9513 |
0.9518 |
0.9523 |
0.9528 |
0.9533 |
0.9538 |
| 9.0 |
0.9542 |
0.9547 |
0.9552 |
0.9557 |
0.9562 |
0.9566 |
0.9571 |
0.9576 |
0.9581 |
0.9586 |
| 9.1 |
0.9590 |
0.9595 |
0.9600 |
0.9605 |
0.9609 |
0.9614 |
0.9619 |
0.9624 |
0.9628 |
0.9633 |
| 9.2 |
0.9638 |
0.9643 |
0.9647 |
0.9652 |
0.9657 |
0.9661 |
0.9666 |
0.9671 |
0.9675 |
0.9680 |
| 9.3 |
0.9685 |
0.9689 |
0.9694 |
0.9699 |
0.9703 |
0.9708 |
0.9713 |
0.9717 |
0.9722 |
0.9727 |
| 9.4 |
0.9731 |
0.9736 |
0.9741 |
0.9745 |
0.9750 |
0.9754 |
0.9759 |
0.9763 |
0.9768 |
0.9773 |
| 9.5 |
0.9777 |
0.9782 |
0.9786 |
0.9791 |
0.9795 |
0.9800 |
0.9805 |
0.9809 |
0.9814 |
0.9818 |
| 9.6 |
0.9823 |
0.9827 |
0.9832 |
0.9836 |
0.9841 |
0.9845 |
0.9850 |
0.9854 |
0.9859 |
0.9863 |
| 9.7 |
0.9868 |
0.9872 |
0.9877 |
0.9881 |
0.9886 |
0.9890 |
0.9894 |
0.9899 |
0.9903 |
0.9908 |
| 9.8 |
0.9912 |
0.9917 |
0.9921 |
0.9926 |
0.9930 |
0.9934 |
0.9939 |
0.9943 |
0.9948 |
0.9952 |
| 9.9 |
0.9956 |
0.9961 |
0.9965 |
0.9969 |
0.9974 |
0.9978 |
0.9983 |
0.9987 |
0.9991 |
0.9996 |
2. TRIGONOMETRIC FUNCTIONS
Values of sin, cos, and tan at 1-degree intervals. For
interpolation between degrees, use: sin(A + δ) ≈ sin(A) + δ·cos(A)
where δ is in radians (multiply degrees by π/180 = 0.01745).
| Deg |
sin |
cos |
tan |
Deg |
sin |
cos |
tan |
| 0° |
0.00000 |
1.00000 |
0.00000 |
90° |
1.00000 |
0.00000 |
∞ |
| 1° |
0.01745 |
0.99985 |
0.01746 |
89° |
0.99985 |
0.01745 |
57.28996 |
| 2° |
0.03490 |
0.99939 |
0.03492 |
88° |
0.99939 |
0.03490 |
28.63625 |
| 3° |
0.05234 |
0.99863 |
0.05241 |
87° |
0.99863 |
0.05234 |
19.08114 |
| 4° |
0.06976 |
0.99756 |
0.06993 |
86° |
0.99756 |
0.06976 |
14.30067 |
| 5° |
0.08716 |
0.99619 |
0.08749 |
85° |
0.99619 |
0.08716 |
11.43005 |
| 6° |
0.10453 |
0.99452 |
0.10510 |
84° |
0.99452 |
0.10453 |
9.51436 |
| 7° |
0.12187 |
0.99255 |
0.12278 |
83° |
0.99255 |
0.12187 |
8.14435 |
| 8° |
0.13917 |
0.99027 |
0.14054 |
82° |
0.99027 |
0.13917 |
7.11537 |
| 9° |
0.15643 |
0.98769 |
0.15838 |
81° |
0.98769 |
0.15643 |
6.31375 |
| 10° |
0.17365 |
0.98481 |
0.17633 |
80° |
0.98481 |
0.17365 |
5.67128 |
| 11° |
0.19081 |
0.98163 |
0.19438 |
79° |
0.98163 |
0.19081 |
5.14455 |
| 12° |
0.20791 |
0.97815 |
0.21256 |
78° |
0.97815 |
0.20791 |
4.70463 |
| 13° |
0.22495 |
0.97437 |
0.23087 |
77° |
0.97437 |
0.22495 |
4.33148 |
| 14° |
0.24192 |
0.97030 |
0.24933 |
76° |
0.97030 |
0.24192 |
4.01078 |
| 15° |
0.25882 |
0.96593 |
0.26795 |
75° |
0.96593 |
0.25882 |
3.73205 |
| 16° |
0.27564 |
0.96126 |
0.28675 |
74° |
0.96126 |
0.27564 |
3.48741 |
| 17° |
0.29237 |
0.95630 |
0.30573 |
73° |
0.95630 |
0.29237 |
3.27085 |
| 18° |
0.30902 |
0.95106 |
0.32492 |
72° |
0.95106 |
0.30902 |
3.07768 |
| 19° |
0.32557 |
0.94552 |
0.34433 |
71° |
0.94552 |
0.32557 |
2.90421 |
| 20° |
0.34202 |
0.93969 |
0.36397 |
70° |
0.93969 |
0.34202 |
2.74748 |
| 21° |
0.35837 |
0.93358 |
0.38386 |
69° |
0.93358 |
0.35837 |
2.60509 |
| 22° |
0.37461 |
0.92718 |
0.40403 |
68° |
0.92718 |
0.37461 |
2.47509 |
| 23° |
0.39073 |
0.92050 |
0.42447 |
67° |
0.92050 |
0.39073 |
2.35585 |
| 24° |
0.40674 |
0.91355 |
0.44523 |
66° |
0.91355 |
0.40674 |
2.24604 |
| 25° |
0.42262 |
0.90631 |
0.46631 |
65° |
0.90631 |
0.42262 |
2.14451 |
| 26° |
0.43837 |
0.89879 |
0.48773 |
64° |
0.89879 |
0.43837 |
2.05030 |
| 27° |
0.45399 |
0.89101 |
0.50953 |
63° |
0.89101 |
0.45399 |
1.96261 |
| 28° |
0.46947 |
0.88295 |
0.53171 |
62° |
0.88295 |
0.46947 |
1.88073 |
| 29° |
0.48481 |
0.87462 |
0.55431 |
61° |
0.87462 |
0.48481 |
1.80405 |
| 30° |
0.50000 |
0.86603 |
0.57735 |
60° |
0.86603 |
0.50000 |
1.73205 |
| 31° |
0.51504 |
0.85717 |
0.60086 |
59° |
0.85717 |
0.51504 |
1.66428 |
| 32° |
0.52992 |
0.84805 |
0.62487 |
58° |
0.84805 |
0.52992 |
1.60033 |
| 33° |
0.54464 |
0.83867 |
0.64941 |
57° |
0.83867 |
0.54464 |
1.53986 |
| 34° |
0.55919 |
0.82904 |
0.67451 |
56° |
0.82904 |
0.55919 |
1.48256 |
| 35° |
0.57358 |
0.81915 |
0.70021 |
55° |
0.81915 |
0.57358 |
1.42815 |
| 36° |
0.58779 |
0.80902 |
0.72654 |
54° |
0.80902 |
0.58779 |
1.37638 |
| 37° |
0.60182 |
0.79864 |
0.75355 |
53° |
0.79864 |
0.60182 |
1.32704 |
| 38° |
0.61566 |
0.78801 |
0.78129 |
52° |
0.78801 |
0.61566 |
1.27994 |
| 39° |
0.62932 |
0.77715 |
0.80978 |
51° |
0.77715 |
0.62932 |
1.23490 |
| 40° |
0.64279 |
0.76604 |
0.83910 |
50° |
0.76604 |
0.64279 |
1.19175 |
| 41° |
0.65606 |
0.75471 |
0.86929 |
49° |
0.75471 |
0.65606 |
1.15037 |
| 42° |
0.66913 |
0.74314 |
0.90040 |
48° |
0.74314 |
0.66913 |
1.11061 |
| 43° |
0.68200 |
0.73135 |
0.93252 |
47° |
0.73135 |
0.68200 |
1.07237 |
| 44° |
0.69466 |
0.71934 |
0.96569 |
46° |
0.71934 |
0.69466 |
1.03553 |
| 45° |
0.70711 |
0.70711 |
1.00000 |
45° |
0.70711 |
0.70711 |
1.00000 |
3. NATURAL LOGARITHMS (BASE
e)
ln(N) for N = 1.0 to 10.0. Relationship: ln(N) = log₁₀(N) ×
2.302585
| N |
.0 |
.1 |
.2 |
.3 |
.4 |
.5 |
.6 |
.7 |
.8 |
.9 |
| 1 |
0.0000 |
0.0953 |
0.1823 |
0.2624 |
0.3365 |
0.4055 |
0.4700 |
0.5306 |
0.5878 |
0.6419 |
| 2 |
0.6931 |
0.7419 |
0.7885 |
0.8329 |
0.8755 |
0.9163 |
0.9555 |
0.9933 |
1.0296 |
1.0647 |
| 3 |
1.0986 |
1.1314 |
1.1632 |
1.1939 |
1.2238 |
1.2528 |
1.2809 |
1.3083 |
1.3350 |
1.3610 |
| 4 |
1.3863 |
1.4110 |
1.4351 |
1.4586 |
1.4816 |
1.5041 |
1.5261 |
1.5476 |
1.5686 |
1.5892 |
| 5 |
1.6094 |
1.6292 |
1.6487 |
1.6677 |
1.6864 |
1.7047 |
1.7228 |
1.7405 |
1.7579 |
1.7750 |
| 6 |
1.7918 |
1.8083 |
1.8245 |
1.8405 |
1.8563 |
1.8718 |
1.8871 |
1.9021 |
1.9169 |
1.9315 |
| 7 |
1.9459 |
1.9601 |
1.9741 |
1.9879 |
2.0015 |
2.0149 |
2.0281 |
2.0412 |
2.0541 |
2.0669 |
| 8 |
2.0794 |
2.0919 |
2.1041 |
2.1163 |
2.1282 |
2.1401 |
2.1518 |
2.1633 |
2.1748 |
2.1861 |
| 9 |
2.1972 |
2.2083 |
2.2192 |
2.2300 |
2.2407 |
2.2513 |
2.2618 |
2.2721 |
2.2824 |
2.2925 |
| 10 |
2.3026 |
2.3125 |
2.3224 |
2.3321 |
2.3418 |
2.3514 |
2.3609 |
2.3702 |
2.3795 |
2.3888 |
4. SQUARE ROOTS
√N for N = 1 to 100.
| N |
√N |
N |
√N |
N |
√N |
N |
√N |
N |
√N |
| 1 |
1.0000 |
21 |
4.5826 |
41 |
6.4031 |
61 |
7.8102 |
81 |
9.0000 |
| 2 |
1.4142 |
22 |
4.6904 |
42 |
6.4807 |
62 |
7.8740 |
82 |
9.0554 |
| 3 |
1.7321 |
23 |
4.7958 |
43 |
6.5574 |
63 |
7.9373 |
83 |
9.1104 |
| 4 |
2.0000 |
24 |
4.8990 |
44 |
6.6332 |
64 |
8.0000 |
84 |
9.1652 |
| 5 |
2.2361 |
25 |
5.0000 |
45 |
6.7082 |
65 |
8.0623 |
85 |
9.2195 |
| 6 |
2.4495 |
26 |
5.0990 |
46 |
6.7823 |
66 |
8.1240 |
86 |
9.2736 |
| 7 |
2.6458 |
27 |
5.1962 |
47 |
6.8557 |
67 |
8.1854 |
87 |
9.3274 |
| 8 |
2.8284 |
28 |
5.2915 |
48 |
6.9282 |
68 |
8.2462 |
88 |
9.3808 |
| 9 |
3.0000 |
29 |
5.3852 |
49 |
7.0000 |
69 |
8.3066 |
89 |
9.4340 |
| 10 |
3.1623 |
30 |
5.4772 |
50 |
7.0711 |
70 |
8.3666 |
90 |
9.4868 |
| 11 |
3.3166 |
31 |
5.5678 |
51 |
7.1414 |
71 |
8.4261 |
91 |
9.5394 |
| 12 |
3.4641 |
32 |
5.6569 |
52 |
7.2111 |
72 |
8.4853 |
92 |
9.5917 |
| 13 |
3.6056 |
33 |
5.7446 |
53 |
7.2801 |
73 |
8.5440 |
93 |
9.6437 |
| 14 |
3.7417 |
34 |
5.8310 |
54 |
7.3485 |
74 |
8.6023 |
94 |
9.6954 |
| 15 |
3.8730 |
35 |
5.9161 |
55 |
7.4162 |
75 |
8.6603 |
95 |
9.7468 |
| 16 |
4.0000 |
36 |
6.0000 |
56 |
7.4833 |
76 |
8.7178 |
96 |
9.7980 |
| 17 |
4.1231 |
37 |
6.0828 |
57 |
7.5498 |
77 |
8.7750 |
97 |
9.8489 |
| 18 |
4.2426 |
38 |
6.1644 |
58 |
7.6158 |
78 |
8.8318 |
98 |
9.8995 |
| 19 |
4.3589 |
39 |
6.2450 |
59 |
7.6811 |
79 |
8.8882 |
99 |
9.9499 |
| 20 |
4.4721 |
40 |
6.3246 |
60 |
7.7460 |
80 |
8.9443 |
100 |
10.0000 |
5. RECIPROCALS (1/N)
1/N for N = 1 to 100.
| N |
1/N |
N |
1/N |
N |
1/N |
N |
1/N |
N |
1/N |
| 1 |
1.000000 |
21 |
0.047619 |
41 |
0.024390 |
61 |
0.016393 |
81 |
0.012346 |
| 2 |
0.500000 |
22 |
0.045455 |
42 |
0.023810 |
62 |
0.016129 |
82 |
0.012195 |
| 3 |
0.333333 |
23 |
0.043478 |
43 |
0.023256 |
63 |
0.015873 |
83 |
0.012048 |
| 4 |
0.250000 |
24 |
0.041667 |
44 |
0.022727 |
64 |
0.015625 |
84 |
0.011905 |
| 5 |
0.200000 |
25 |
0.040000 |
45 |
0.022222 |
65 |
0.015385 |
85 |
0.011765 |
| 6 |
0.166667 |
26 |
0.038462 |
46 |
0.021739 |
66 |
0.015152 |
86 |
0.011628 |
| 7 |
0.142857 |
27 |
0.037037 |
47 |
0.021277 |
67 |
0.014925 |
87 |
0.011494 |
| 8 |
0.125000 |
28 |
0.035714 |
48 |
0.020833 |
68 |
0.014706 |
88 |
0.011364 |
| 9 |
0.111111 |
29 |
0.034483 |
49 |
0.020408 |
69 |
0.014493 |
89 |
0.011236 |
| 10 |
0.100000 |
30 |
0.033333 |
50 |
0.020000 |
70 |
0.014286 |
90 |
0.011111 |
| 11 |
0.090909 |
31 |
0.032258 |
51 |
0.019608 |
71 |
0.014085 |
91 |
0.010989 |
| 12 |
0.083333 |
32 |
0.031250 |
52 |
0.019231 |
72 |
0.013889 |
92 |
0.010870 |
| 13 |
0.076923 |
33 |
0.030303 |
53 |
0.018868 |
73 |
0.013699 |
93 |
0.010753 |
| 14 |
0.071429 |
34 |
0.029412 |
54 |
0.018519 |
74 |
0.013514 |
94 |
0.010638 |
| 15 |
0.066667 |
35 |
0.028571 |
55 |
0.018182 |
75 |
0.013333 |
95 |
0.010526 |
| 16 |
0.062500 |
36 |
0.027778 |
56 |
0.017857 |
76 |
0.013158 |
96 |
0.010417 |
| 17 |
0.058824 |
37 |
0.027027 |
57 |
0.017544 |
77 |
0.012987 |
97 |
0.010309 |
| 18 |
0.055556 |
38 |
0.026316 |
58 |
0.017241 |
78 |
0.012821 |
98 |
0.010204 |
| 19 |
0.052632 |
39 |
0.025641 |
59 |
0.016949 |
79 |
0.012658 |
99 |
0.010101 |
| 20 |
0.050000 |
40 |
0.025000 |
60 |
0.016667 |
80 |
0.012500 |
100 |
0.010000 |
6. POWERS AND EXPONENTIALS
| n |
2^n |
e^n |
e^-n |
10^n |
| 0 |
1 |
1.0000 |
1.000000 |
1 |
| 1 |
2 |
2.7183 |
0.367879 |
10 |
| 2 |
4 |
7.3891 |
0.135335 |
100 |
| 3 |
8 |
20.0855 |
0.049787 |
1000 |
| 4 |
16 |
54.5982 |
0.018316 |
10000 |
| 5 |
32 |
148.4132 |
0.006738 |
100000 |
| 6 |
64 |
403.4288 |
0.002479 |
1000000 |
| 7 |
128 |
1096.6332 |
0.000912 |
10000000 |
| 8 |
256 |
2980.9580 |
0.000335 |
100000000 |
| 9 |
512 |
8103.0839 |
0.000123 |
1000000000 |
| 10 |
1024 |
22026.4658 |
0.000045 |
10000000000 |
| 11 |
2048 |
59874.1417 |
0.000017 |
100000000000 |
| 12 |
4096 |
162754.7914 |
0.000006 |
1000000000000 |
| 13 |
8192 |
442413.3920 |
0.000002 |
10000000000000 |
| 14 |
16384 |
1202604.2842 |
0.000001 |
100000000000000 |
| 15 |
32768 |
3269017.3725 |
0.000000 |
1000000000000000 |
| 16 |
65536 |
8886110.5205 |
0.000000 |
10000000000000000 |
| 17 |
131072 |
24154952.7536 |
0.000000 |
100000000000000000 |
| 18 |
262144 |
65659969.1373 |
0.000000 |
1000000000000000000 |
| 19 |
524288 |
178482300.9632 |
0.000000 |
10000000000000000000 |
| 20 |
1048576 |
485165195.4098 |
0.000000 |
100000000000000000000 |
7. UNIT CONVERSION FACTORS
Length
| From |
To |
Multiply by |
| inches |
mm |
25.400 |
| feet |
metres |
0.3048 |
| yards |
metres |
0.9144 |
| miles |
km |
1.6093 |
| nautical miles |
km |
1.8520 |
| fathoms |
metres |
1.8288 |
Area
| From |
To |
Multiply by |
| sq feet |
sq metres |
0.0929 |
| acres |
hectares |
0.4047 |
| sq miles |
sq km |
2.5900 |
Volume
| From |
To |
Multiply by |
| imp gallons |
litres |
4.5461 |
| US gallons |
litres |
3.7854 |
| cubic feet |
litres |
28.317 |
| fluid ounces (imp) |
ml |
28.413 |
Mass
| From |
To |
Multiply by |
| pounds |
kg |
0.4536 |
| ounces |
grams |
28.350 |
| tons (long) |
tonnes |
1.0160 |
| tons (short) |
tonnes |
0.9072 |
Temperature
| Conversion |
Formula |
| °F to °C |
(°F − 32) × 5/9 |
| °C to °F |
°C × 9/5 + 32 |
| °C to K |
°C + 273.15 |
Pressure
| From |
To |
Multiply by |
| psi |
kPa |
6.8948 |
| bar |
kPa |
100.00 |
| atm |
kPa |
101.33 |
| mmHg |
kPa |
0.1333 |
Energy
| From |
To |
Multiply by |
| BTU |
kJ |
1.0551 |
| calories |
joules |
4.1868 |
| kWh |
MJ |
3.6000 |
| hp·hr |
MJ |
2.6845 |
8. PHYSICAL AND
MATHEMATICAL CONSTANTS
| Constant |
Symbol |
Value |
| Pi |
π |
3.1415926536 |
| Euler’s number |
e |
2.7182818285 |
| Speed of light |
c |
299,792,458 m/s |
| Gravitational acceleration (std) |
g |
9.80665 m/s² |
| Boltzmann constant |
k |
1.380649 × 10⁻²³ J/K |
| Avogadro number |
Nₐ |
6.02214 × 10²³ /mol |
| Universal gas constant |
R |
8.31446 J/(mol·K) |
| Stefan-Boltzmann constant |
σ |
5.6704 × 10⁻⁸ W/(m²·K⁴) |
| Atmospheric pressure (std) |
P₀ |
101,325 Pa |
| Water density (4°C) |
ρ |
1000.0 kg/m³ |
| Absolute zero |
|
−273.15 °C |
| Nautical mile |
|
1,852 m (by definition) |
| Knot |
|
1 nautical mile/hour = 0.5144 m/s |
These tables were generated computationally and are
mathematically exact to the precision shown. Any computer with
basic programming capability can regenerate, extend, or reformat
these tables — the computation is trivial. Higher-precision
tables, additional functions, and specialized engineering tables
can be produced the same way. Ideally, these are precomputed and
printed before any disruption occurs. See Doc #10 (Nautical
Almanac) and Doc #11 (Sight Reduction Tables) for navigation
applications, and Doc #17 (Engineering Reference Tables) for
engineering applications.