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 I/2 T = R tan I/2 = L.C. / 2 cos I/2 L.C. / 2 = R sin I/2, D 1° = R = 5730, D 2° = 5730/2, D = 5730/R M = R (1 - cos I/2), = R - R cos I/2 (E + R) / R = sec I/2, (R - M) / R = cos I/2 c = 2 R sin d/2, d = c / 2R L.C. = 2 R sin I/2, E = R (sec I/2 - 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 | .2167 | 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 |