Strike and Dip from Three Points Calculator (Three-Point Problem)

What this tool does

Three points that are not in a line define a plane, and the three-point problem is how a geologist finds the attitude of a buried bed from three boreholes that reached its top. Give each point as east and north coordinates and the elevation at which the surface was met, all in the same unit. The dip is the steepest inclination, the dip direction is the compass bearing of the downhill direction, and the strike, by the right-hand rule, is 90° anticlockwise from it. Points that lie almost in a line give an unstable answer, so spread them out.

Formula

plane z = z₁ + a (x − x₁) + b (y − y₁) · dip = atan √(a² + b²) · dip direction = azimuth of (−a, −b) · strike = dip direction − 90°

Variables

Symbol	Meaning	Unit
`x1`	Point 1 — easting	m
`y1`	Point 1 — northing	m
`z1`	Point 1 — elevation of the surface	m
`x2`	Point 2 — easting	m
`y2`	Point 2 — northing	m
`z2`	Point 2 — elevation of the surface	m
`x3`	Point 3 — easting	m
`y3`	Point 3 — northing	m
`z3`	Point 3 — elevation of the surface	m
`DIP`	Dip	°
`DD`	Dip direction (azimuth from north)	°
`ST`	Strike (right-hand rule)	°
`SP`	Slope as a percentage	%

Worked example

Point 1 — easting0 m
Point 1 — northing0 m
Point 1 — elevation of the surface100 m
Point 2 — easting120 m
Point 2 — northing30 m
Point 2 — elevation of the surface80 m
Point 3 — easting40 m
Point 3 — northing150 m
Point 3 — elevation of the surface92 m

Dip9.3 °
Dip direction (azimuth from north)87 °
Strike (right-hand rule)357 °
Slope as a percentage16.5 %

Limitations

Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.