Plane from three elevations calculator

Calculate plane dz/dEast and plane dz/dNorth with your own figures.

Your numbers

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

Use plane dz/dEast and plane dz/dNorth to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Three controls JSON [[east,north,elevation],...]
[[0,0,100],[100,0,110],[0,100,120]]
Query easting
25
Query northing
40
Plane dz/dEast
0.1
Plane dz/dNorth
0.2
Plane intercept
100
Query elevation
110.5

Try another scenario

Three controls JSON [[east,north,elevation],...]
[[1,0,100],[100,0,110],[0,100,120]]
Query easting
25
Query northing
40
Plane dz/dEast
0.10101
Plane dz/dNorth
0.20101
Plane intercept
99.89899
Query elevation
110.464646
Calculation method

Calculation method

Plane dz/dEast

Solve z=pE+qN+r through three noncollinear controls.

Plane dz/dNorth

Solve z=pE+qN+r through three noncollinear controls.

Plane intercept

Solve z=pE+qN+r through three noncollinear controls.

Query elevation

Solve z=pE+qN+r through three noncollinear controls.

Symbols and units
a
Three controls JSON [[east,north,elevation],...]
b
Query easting
c
Query northing

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 z=pE+qN+r through three noncollinear controls.
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