PI() radians = 180 degree
2 PI() radians = 360 degree
PI()/2 radians = 90 degree
Example
X (degree) 90 It must be ≤ 90 or ≤ -90
X (radians) 1.5707963268
X (degree) 90
Pi ∏ 3.1415926536
Pi /2 1.5707963268
Sin 1 Sin of an Angle (Angle must be in radians)
Arc Sin (radians) 1.5707963268 Arc Sin of a number in radians in the range -Pi/2 to Pi/2
Angle (degree) 90
tan 1.6324552E+16
arc tan (radians) 1.5707963268
Angle( degree) 90
180 3.141593
3.1415926536
180
3.1415926536
1.5707963268
1 1
1.5707963268 #VALUE!
90 #VALUE!
Excel:
=ACOS( SIN(lat1)*SIN(lat2) + COS(lat1)*COS(lat2)*COS(lon2-lon1) ) * 6371000 (m)
(or with lat/lon in degrees):
=ACOS( SIN(lat1*PI()/180)*SIN(lat2*PI()/180) + COS(lat1*PI()/180)*COS(lat2*PI()/180)*COS(lon2*PI()/180
CI60XC351 CI13XC912 P1
degree 39.81359722 39.80336 39
-84.1336556 -84.1061 -84
radian 0.694878359 0.6947
-1.4684093 -1.46793
2.610 Km 2.610 Km
2616.3 mts from radian formula 6371000
2616.3 mts fron degree formula 1 deg Lat = 111194.9 mts
0.010233333 1137.894749292
-0.02758056 -2383.353127324
2641.055961163
Bearing β = atan2(Y,X)
X X = cos θb * sin ∆L
Y Y = cos θa * sin θb – sin θa * cos θb * cos ∆L
Kansas City: 39.099912, -94.581213 39.099912 -94.5812
St Louis: 38.627089, -90.200203 38.627089 -90.2002
4.38101
X 0.059676687
Y -0.0068126195
Bearing 1.6844630626
B in degree 96.51262423
m)
/180)*COS(lon2*PI()/180-lon1*PI()/180) ) * 6371000 (m)
P2 P1 P2
40 39 39
-84 -84 -85
2.610 Km
1633349
1 deg Lat = 86414.25 mts
0.682422 -1.65075358
0.67417 -1.57429053
0.076463049
Calculating Bearing or Heading angle between two points:
So if you are from GIS field or dealing with GIS application, you should know bearing and how to calculat
tool for bearing:
Let ‘R’ be the radius of Earth,
‘L’ be the longitude,
‘θ’ be latitude,
‘β‘ be Bearing.
Denote point A and B as two different points, where ‘La’ is point A longitude and ‘θa’ is point A latitude,
measured from North direction i.e 0° bearing means North, 90° bearing is East, 180° bearing is measured
Note: If bearing is denoted with +ve or –ve initials whose values lies between 0° to 180°, then –ve is deno
Formula to find Bearing, when two different points latitude, longitude is given:
Bearing from point A to B, can be calculated as,
β = atan2(X,Y),
where, X and Y are two quantities and can be calculated as:
X = cos θb * sin ∆L
Y = cos θa * sin θb – sin θa * cos θb * cos ∆L
Lets us take an example to calculate bearing between the two different points with the formula:
Kansas City: 39.099912, -94.581213
St Louis: 38.627089, -90.200203
So X and Y can be calculated as,
X = cos(38.627089) * sin(4.38101)
X = 0.05967668696
And
Y = cos(39.099912) * sin(38.627089) – sin(39.099912) * cos(38.627089) * cos(4.38101)
Y = 0.77604737571 * 0.62424902378 – 0.6306746155 * 0.78122541965 * 0.99707812506
Y = -0.00681261948
So as, β = atan2(X,Y) = atan2(0.05967668696, -0.00681261948)
β = 96.51°
This means, from Kansas City if we move in 96.51° bearing direction, we will reach St Louis.
w bearing and how to calculate bearing with formula. Let us look on formula and
e and ‘θa’ is point A latitude, similarly assume for point B. Bearing would be
ast, 180° bearing is measured to be South, and 270° to be West.
en 0° to 180°, then –ve is denoted for South and West sides.
iven:
nts with the formula:
os(4.38101)
.99707812506
l reach St Louis.
Point A Point B Lat A (deg) Long A (deg) Lat B (deg) Long B (deg) La A (rad)
CI60XC351 CI13XC912 39.81359722 -84.13365556 39.80336389 -84.106075 0.694878359
CI13XC912 CI60XC351 39.80336389 -84.106075 39.81359722 -84.13365556 0.694699753
CI13XC912 CI03XC352 39.80336389 -84.106075 39.77738056 -84.14188333 0.694699753
CI13XC912 CI14XC285 39.80336389 -84.106075 39.82595278 -84.06907222 0.694699753
Long B (rad) Lat B (rad) Long B (rad) ∆L (deg) ∆L (rad) X Y Bearing (rad)
-1.468409301 0.694699753 -1.46792793 0.027581 0.000481 0.00037 -0.00018 2.0205966992
-1.46792793 0.694878359 -1.4684093 -0.02758 -0.00048 -0.00037 0.000179 -1.120687769
-1.46792793 0.694246259 -1.4685529 -0.03581 -0.00062 -0.00048 -0.00045 -2.327375688
-1.46792793 0.695094004 -1.46728211 0.037003 0.000646 0.000496 0.000394 0.899056858
Bearing(deg) Bearing Abs (deg) OK
115.8 115.8
-64.2 295.8
-133.3 226.7
51.5 51.5
Point A Point B Lat A (deg) Long A (deg) Lat B (deg) Long B (deg) La A (rad)
CI60XC351 CI13XC912 39.81359722 -84.13365556 39.80336389 -84.106075 0.694878359
CI13XC912 CI60XC351 39.80336389 -84.106075 39.81359722 -84.13365556 0.694699753
CI13XC912 CI03XC352 39.80336389 -84.106075 39.77738056 -84.14188333 0.694699753
CI13XC912 CI14XC285 39.80336389 -84.106075 39.82595278 -84.06907222 0.694699753
Long B (rad) Lat B (rad) Long B (rad) ∆L (deg) ∆L (rad) X Y Bearing (rad)
-1.468409301 0.694699753 -1.46792793 0.027581 0.000481 0.00037 -0.00018 2.0205966992
-1.46792793 0.694878359 -1.4684093 -0.02758 -0.00048 -0.00037 0.000179 -1.120687769
-1.46792793 0.694246259 -1.4685529 -0.03581 -0.00062 -0.00048 -0.00045 -2.327375688
-1.46792793 0.695094004 -1.46728211 0.037003 0.000646 0.000496 0.000394 0.899056858
Bearing(deg) Bearing Abs (deg) OK Sec Point A Point A Azim Sec Point B Point B Azimut
115.8 115.8
-64.2 295.8
-133.3 226.7 270 35
51.5 51.5 3 270 1 35
M=(A - 90)N=(A + 90)P(B - 30) Q(B + 30) Front or Back? P-B relat to Az A P-B relat to Az A
180 360 5 65 Back 218.5 141.5
Az B relat to Az A Az B relat to Az A
235.0 125.0
Angle Condition 1
