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. T = R tan ½ I = L.C. 2 sin ½ I 2 cos ½ I L.C. = 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 sec I/2, R - M cos I/ R = sec 2, R = cos 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' .0167 11' .1833 21' .3500 31' .5167 41' .6833 51' .8500 2 .0333 12 .2000 22 .3667 32 .5333 42 .7000 52 .8667 3 .0500 13 .2167 23 .3833 33 .5500 43 .7167 53 .8833 4 .0667 14 .2333 24 .4000 34 .5667 44 .7333 54 .9000 5 .0833 15 .2500 25 .4167 35 .5833 45 .7500 55 .9167 6 .1000 16 .2667 26 .4333 36 .6000 46 .7667 56 .9333 7 .1167 17 .2833 27 .4500 37 .6167 47 .7833 57 .9500 8 .1333 18 .3000 28 .4667 38 .6333 48 .8000 58 .9667 9 .1500 19 .3167 29 .4833 39 .6500 49 .8167 59 .9833 10 .1667 20 .3333 30 .5000 40 .6667 50 .8333 60 1.0000 Inches in Decimals of a Foot 1/16 3/32 1/8 5/32 1/4 9/32 5/16 11/32 3/8 7/16 1/2 .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