Two-bearing intersection calculator

Calculate intersection easting and intersection northing with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use intersection easting and intersection northing to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Station A east (m)
0
Station A north (m)
0
A bearing (degrees)
45
Station B east (m)
100
Station B north (m)
0
B bearing (degrees)
315
Intersection easting (m)
50
Intersection northing (m)
50
Acute intersection angle (degrees)
90

Try another scenario

Station A east (m)
0.1
Station A north (m)
0
A bearing (degrees)
45
Station B east (m)
100
Station B north (m)
0
B bearing (degrees)
315
Intersection easting (m)
50.05
Intersection northing (m)
49.95
Acute intersection angle (degrees)
90
Calculation method

Calculation method

Intersection easting (m)

Solve A+t uA=B+s uB; require forward ray distances and nonparallel bearings.

Intersection northing (m)

Solve A+t uA=B+s uB; require forward ray distances and nonparallel bearings.

Acute intersection angle (degrees)

Solve A+t uA=B+s uB; require forward ray distances and nonparallel bearings.

Symbols and units
a
Station A east (m)
b
Station A north (m)
c
A bearing (degrees)
d
Station B east (m)
e
Station B north (m)
f
B bearing (degrees)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Calculation uses the entered values and stated mathematical model; quantities must use the labelled units. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. Solve A+t uA=B+s uB; require forward ray distances and nonparallel bearings.
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