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