CURVE FORMULAE D = Degree of Curve 1° = 1-Degree of Curve 2° = 2-Degree of Curve P.C. = Point of Curve P.T. = Point of Tangent P.I. = Point of Intersection I = Intersection of Angle, Angle between Two Tangents L = Length of Curve, from P.C. to P.T. T = Tangent Distance E = External Distance R = Radius L.C. = Length of Chord M = Length of Middle Ordinate c = Length of Sub-Chord d = Angle of Sub-Chord R = L.C. 2 sin ½ I T = R tan ½ I = L.C. 2 cos ½ I L.C. 2 = R sin I 2 , D 1° = R = 5730, D 2° = 5730 2 , D = 5730 R M = R (1 - cos ½ I), = R - R cos I 2 E + R R = sec I 2 , R - M R = cos I 2 c = 2 R sin ½ d, d = c 2R L.C. = 2 R sin ½ I, E = R (sec ½ I - 1), = R sec I 2 - R Minutes in Decimals of a Degree 1' 0.167 2 0.333 3 0.500 4 0.667 5 0.833 6 1.000 7 1.167 8 1.333 9 1.500 10 1.667 11' 12 13 14 15 16 17 18 19 20 .1833 .2000 .2167 .2333 .2500 .2667 .2833 .3000 .3167 .3333 21' 22 23 24 25 26 27 28 29 30 .3500 .3667 .3833 .4000 .4167 .4333 .4500 .4667 .4833 .5000 31' 32 33 34 35 36 37 38 39 40 .5167 .5333 .5500 .5667 .5833 .6000 .6167 .6333 .6500 .6667 41' 42 43 44 45 46 47 48 49 50 .6833 .7000 .7167 .7333 .7500 .7667 .7833 .8000 .8167 .8333 51' 52 53 54 55 56 57 58 59 60 .8500 .8667 .8833 .9000 .9167 .9333 .9500 .9667 .9833 1.0000 Inches in Decimals of a Foot 1/16 3/32 1/8 3/16 1/4 5/16 3/8 1/2 5/8 3/4 7/8 .0052 .0078 .0104 .0156 .0208 .0260 .0313 .0417 .0521 .0625 .0729 1 2 3 4 5 6 7 8 9 10 11 .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167