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 1/2 I T = R tan 1/2 I = L.C. 2 cos 1/2 I L.C. -- = R sin I/2, D 1° = R = 5730, D 2° = 5730 -- 2 D = 5730 R M = R (1 - cos 1/2 I), = R - R cos I 2 E + R - = sec I/2, R - M R R = cos I 2 c = 2 R sin 1/2 d, d = c -- 2R L.C. = 2 R sin 1/2 I, E = R (sec 1/2 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 .0052 3/16 .0078 1/8 .0104 5/16 .0156 1/4 .0208 5/16 .0260 3/8 .0313 1/2 .0417 5/8 .0521 3/4 .0625 7/8 .0729 1 .0833 2 .1667 3 .2500 4 .3333 5 .4167 6 .5000 7 .5833 8 .6667 9 .7500 10 .8333 11 .9167