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 P.I. TAN. DIST. I TAN. DIST. E M P.C. 50 50 L.C. P.T. ½ D ½ D RADIUS RADIUS ½ I ½ I d D I R = L.C. 2 sin 1/2 I T = R tan 1/2 I = L.C. 2 cos 1/2 I L.C. 2 = 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 R = sec I/2, R - M 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 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