ANGLE CONVERSIONS Radians into Degrees and Decimals of a Degree (Based on π radians = 180 degrees) Machinery's Handbook, 31st Edition
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Rad.
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10 57.2958 0.1 5.7296 0.01 0.5730 0.001 0.0573 0.0001 0.0057 20 1145.9156 2 114.5916 0.2 11.4592 0.02 1.1459 0.002 0.1146 0.0002 0.0115 30 1718.8734 3 171.8873 0.3 17.1887 0.03 1.7189 0.003 0.1719 0.0003 0.0172 40 2291.8312 4 229.1831 0.4 22.9183 0.04 2.2918 0.004 0.2292 0.0004 0.0229 50 2864.7890 5 286.4789 0.5 28.6479 0.05 2.8648 0.005 0.2865 0.0005 0.0286 60 3437.7468 6 343.7747 0.6 34.3775 0.06 3.4377 0.006 0.3438 0.0006 0.0344 70 4010.7046 7 401.0705 0.7 40.1070 0.07 4.0107 0.007 0.4011 0.0007 0.0401 80 4583.6624 8 458.3662 0.8 45.8366 0.08 4.5837 0.008 0.4584 0.0008 0.0458 90 5156.6202 9 515.6620 0.9 51.5662 0.09 5.1566 0.009 0.5157 0.0009 0.0516 100 5729.5780 10 572.9578 1.0 57.2958 0.10 5.7296 0.010 0.5730 0.0010 0.0573 Radians into Degrees, Minutes, and Seconds (Based on π radians = 180 degrees) Rad. Angle Rad. Angle Rad. Angle Rad. Angle Rad. Angle Rad. Angle 10 572 ° 57 ′ 28 ″ 1 57 ° 17 ′ 45 ″ 0.1 5 ° 43 ′ 46 ″ 0.01 0 ° 34 ′ 23 ″ 0.001 0 ° 3 ′ 26 ″ 0.0001 0 ° 0 ′ 21 ″ 20 1145 ° 54 ′ 56 ″ 2 114 ° 35 ′ 30 ″ 0.2 11 ° 27 ′ 33 ″ 0.02 1 ° 8 ′ 45 ″ 0.002 0 ° 6 ′ 53 ″ 0.0002 0 ° 0 ′ 41 ″ 30 1718 ° 52 ′ 24 ″ 3 171 ° 53 ′ 14 ″ 0.3 17 ° 11 ′ 19 ″ 0.03 1 ° 43 ′ 8 ″ 0.003 0 ° 10 ′ 19 ″ 0.0003 0 ° 1 ′ 2 ″ 40 2291 ° 49 ′ 52 ″ 4 229 ° 10 ′ 59 ″ 0.4 22 ° 55 ′ 6 ″ 0.04 2 ° 17 ′ 31 ″ 0.004 0 ° 13 ′ 45 ″ 0.0004 0 ° 1 ′ 23 ″ 50 2864 ° 47 ′ 20 ″ 5 286 ° 28 ′ 44 ″ 0.5 28 ° 38 ′ 52 ″ 0.05 2 ° 51 ′ 53 ″ 0.005 0 ° 17 ′ 11 ″ 0.0005 0 ° 1 ′ 43 ″ 60 3437 ° 44 ′ 48 ″ 6 343 ° 46 ′ 29 ″ 0.6 34 ° 22 ′ 39 ″ 0.06 3 ° 26 ′ 16 ″ 0.006 0 ° 20 ′ 38 ″ 0.0006 0 ° 2 ′ 4 ″ 70 4010 ° 42 ′ 16 ″ 7 401 ° 4 ′ 14 ″ 0.7 40 ° 6 ′ 25 ″ 0.07 4 ° 0 ′ 39 ″ 0.007 0 ° 24 ′ 4 ″ 0.0007 0 ° 2 ′ 24 ″ 80 4583 ° 39 ′ 44 ″ 8 458 ° 21 ′ 58 ″ 0.8 45 ° 50 ′ 12 ″ 0.08 4 ° 35 ′ 1 ″ 0.008 0 ° 27 ′ 30 ″ 0.0008 0 ° 2 ′ 45 ″ 90 5156 ° 37 ′ 13 ″ 9 515 ° 39 ′ 43 ″ 0.9 51 ° 33 ′ 58 ″ 0.09 5 ° 9 ′ 24 ″ 0.009 0 ° 30 ′ 56 ″ 0.0009 0 ° 3 ′ 6 ″ 100 5729 ° 34 ′ 41 ″ 10 572 ° 57 ′ 28 ″ 1.0 57 ° 17 ′ 45 ″ 0.10 5 ° 43 ′ 46 ″ 0.010 0 ° 34 ′ 23 ″ 0.0010 0 ° 3 ′ 26 ″ Minutes and Seconds into Decimal of a Degree and Vice Versa (Based on 1 second = 0.00027778 degree) Minutes into Decimals of a Degree Seconds into Decimals of a Degree Min. Deg. Min. Deg. Min. Deg. Sec. Deg. Sec. Deg. Sec. Deg. 572.9578 1 1 0.0167 21 0.3500 41 0.6833 1 0.0003 21 0.0058 41 0.0114 2 0.0333 22 0.3667 42 0.7000 2 0.0006 22 0.0061 42 0.0117 3 0.0500 23 0.3833 43 0.7167 3 0.0008 23 0.0064 43 0.0119 4 0.0667 24 0.4000 44 0.7333 4 0.0011 24 0.0067 44 0.0122 5 0.0833 25 0.4167 45 0.7500 5 0.0014 25 0.0069 45 0.0125 6 0.1000 26 0.4333 46 0.7667 6 0.0017 26 0.0072 46 0.0128 7 0.1167 27 0.4500 47 0.7833 7 0.0019 27 0.0075 47 0.0131 8 0.1333 28 0.4667 48 0.8000 8 0.0022 28 0.0078 48 0.0133 9 0.1500 29 0.4833 49 0.8167 9 0.0025 29 0.0081 49 0.0136 10 0.1667 30 0.5000 50 0.8333 10 0.0028 30 0.0083 50 0.0139 11 0.1833 31 0.5167 51 0.8500 11 0.0031 31 0.0086 51 0.0142 12 0.2000 32 0.5333 52 0.8667 12 0.0033 32 0.0089 52 0.0144 13 0.2167 33 0.5500 53 0.8833 13 0.0036 33 0.0092 53 0.0147 14 0.2333 34 0.5667 54 0.9000 14 0.0039 34 0.0094 54 0.0150 15 0.2500 35 0.5833 55 0.9167 15 0.0042 35 0.0097 55 0.0153 16 0.2667 36 0.6000 56 0.9333 16 0.0044 36 0.0100 56 0.0156 17 0.2833 37 0.6167 57 0.9500 17 0.0047 37 0.0103 57 0.0158 18 0.3000 38 0.6333 58 0.9667 18 0.0050 38 0.0106 58 0.0161 19 0.3167 39 0.6500 59 0.9833 19 0.0053 39 0.0108 59 0.0164 20 0.3333 40 0.6667 60 1.0000 20 0.0056 40 0.0111 60 0.0167 Example 3: Convert 11 ′ 37 ″ to decimals of a degree. From the “Min. into Dec. Deg.” table, 11 ′ = 0.1833 degree. From the “Sec. into Dec. Deg.” table, 37 ″ = 0.0103 degree. Adding, 11 ′ 37 ″ = 0.1833 + 0.0103 = 0.1936 degree. Example 4: Convert 0.1234 degree to minutes and seconds. From the “Min. into Dec. Deg.” table, 0.1167 degree = 7 ′ . Subtracting 0.1167 from 0.1234 gives 0.0067. From the “Sec. into Dec. Deg.” table, 0.0067 = 24 ″ so that 0.1234 = 7 ′ 24 ″ .
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