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. 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' 0.0167 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 3/32 .0078 1/8 .0104 3/16 .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