Strike and Dip Calculator

Determine a plane’s true orientation from two apparent dip measurements.

Strike (Azimuth)

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What is Calculating Strike Using Dip?

In structural geology, calculating strike using dip is a fundamental technique used to determine the precise three-dimensional orientation of a planar feature (like a sedimentary bed, fault, or dyke) when direct measurement isn’t possible. Strike and dip are the two components that define this orientation. The strike is the compass direction of a horizontal line on the surface of the plane. The dip is the angle of inclination of that plane, measured downwards from a horizontal plane.

Often, geologists can only observe an apparent dip. This is the inclination of the plane as seen on a vertical surface that is not perpendicular to the strike line. Apparent dip is always less than or equal to the true dip. By measuring two different apparent dips along two different bearings (for example, on two different faces of a road cut or in different mine tunnels), we can mathematically calculate the plane’s true strike and true dip. This is a common problem, sometimes called the “two apparent dips problem”, and is crucial for creating accurate geological maps and cross-sections.

Calculating Strike from Two Apparent Dips: Formula and Explanation

The calculation is based on trigonometry. Given two apparent dip angles (α₁, α₂) and their respective azimuth bearings (β₁, β₂), we can determine the orientation of the true strike line (ψ_s).

The gradient vectors on the plane in the directions of the apparent dips can be projected onto a horizontal coordinate system. The strike line is, by definition, horizontal, meaning the gradient along its direction is zero. This principle leads to the core formula:

tan(ψ_s) = [tan(α₂)cos(β₁) – tan(α₁)cos(β₂)] / [tan(α₁)sin(β₂) – tan(α₂)sin(β₁)]

Once the strike (ψ_s) is known, the true dip (δ) can be found using one of the apparent dips:

tan(δ) = tan(α₁) / |sin(ψ_s – β₁)|

The dip direction is always 90 degrees from the strike direction. To learn more about this relationship, you might want to read up on stereonet analysis basics.

Variables Table

Description of variables used in the strike calculation. Units are auto-inferred as degrees.

Variable	Meaning	Unit	Typical Range
α1, α2	Apparent Dip Angles	Degrees	0° – 90°
β1, β2	Apparent Dip Bearings	Degrees (Azimuth)	0° – 360°
ψs	Strike Azimuth	Degrees (Azimuth)	0° – 360°
δ	True Dip Angle	Degrees	0° – 90°

Practical Examples of Calculating Strike

Example 1: Road Cut Observation

A geologist is examining a road cut. On the east-facing wall, she measures an apparent dip of 25° towards a bearing of 090° (East). On the north-facing wall, she measures an apparent dip of 15° towards a bearing of 000° (North).

• Inputs: Apparent Dip 1 = 25°, Bearing 1 = 90°; Apparent Dip 2 = 15°, Bearing 2 = 0°
• Results:
  • Calculated Strike: ~028° (N28°E) or 208° (S28°W)
  • Calculated True Dip: ~28.5°
  • Dip Direction: ~118° (SE)

This tells the geologist that the rock layer is striking roughly North-Northeast and dipping moderately to the Southeast. For a better understanding of how to take these initial measurements, a geological compass guide would be a useful resource.

Example 2: Mining Exploration

In a mine, a coal seam is observed in two different tunnels. In tunnel A, the seam appears to dip at 40° along a bearing of 210°. In tunnel B, it appears to dip at 35° along a bearing of 300°.

• Inputs: Apparent Dip 1 = 40°, Bearing 1 = 210°; Apparent Dip 2 = 35°, Bearing 2 = 300°
• Results:
  • Calculated Strike: ~264° (N84°W) or 084° (S84°E)
  • Calculated True Dip: ~48.7°
  • Dip Direction: ~354° (N)

This information is vital for the mining engineers to predict the location and orientation of the coal seam for future excavation. The process is similar to solving a classic three-point problem solver, but with dip information instead of elevation points.

How to Use This Strike and Dip Calculator

This calculator simplifies the process of calculating strike using dip data.

1. Enter Apparent Dip Angle 1: Input the first measured dip angle in degrees (a value between 0 and 90).
2. Enter Bearing of Dip 1: Input the compass direction (azimuth) for the first measurement in degrees (0-360).
3. Enter Apparent Dip Angle 2: Input the second measured dip angle.
4. Enter Bearing of Dip 2: Input the compass direction for the second measurement.
5. Review the Results: The calculator instantly provides the Strike (in both azimuth and quadrant format), the True Dip angle, and the Dip Direction. The results will update in real-time as you type.
6. Interpret the Chart: The visualizer provides a top-down view. The red and blue lines show your input bearings, and the thick green line shows the calculated strike direction, helping you visualize the plane’s orientation.

Key Factors That Affect Strike and Dip Calculations

• Measurement Accuracy: Small errors in measuring either the apparent dip angle or its bearing can lead to significant errors in the calculated true strike and dip. A reliable compass-clinometer is essential.
• Planarity of the Surface: The calculation assumes the geological feature is a perfect plane. If the surface is curved (e.g., part of a fold), the calculated orientation is only valid for the specific location of the measurements.
• Scale of Observation: Strike and dip can vary at different scales. A measurement over a few meters might not represent the overall structure of a formation that spans kilometers.
• Magnetic Declination: Compass bearings must be corrected for magnetic declination to get a true geographic azimuth. Failure to do so will skew the strike direction.
• Data Entry Errors: Double-check that the dip angles and bearings are entered correctly into the calculator. Swapping the two values is a common mistake. Understanding the difference between what is true dip and apparent dip is critical.
• Verticality of Exposure: The apparent dip must be measured on a truly vertical surface. If the cliff or wall face is itself inclined, the measurement will not be a true apparent dip, leading to errors.

Frequently Asked Questions (FAQ)

Why are there two possible strike directions 180° apart?

A strike line is a horizontal line with a direction. It can be described by its bearing in one direction (e.g., 045°) or the exact opposite direction (225°). Both are correct. Geologists use conventions like the “Right-Hand Rule” to be consistent. This calculator provides the primary azimuth and its reciprocal.

What happens if my two apparent dip bearings are the same?

If the bearings are the same or 180° opposite, you are measuring dips along the same line. This makes a solution impossible as it creates a division-by-zero scenario in the formula. You need two measurements in different directions.

Is apparent dip always less than true dip?

Yes. The true dip is the maximum possible angle of inclination. Any other dip measurement on that plane, viewed from a different angle, will be shallower. The only exception is if your apparent dip measurement happens to be in the direction of the true dip, in which case they are equal.

Can I use Quadrant bearings (e.g., N45E) as input?

This calculator is designed for Azimuth bearings (0-360°). You will need to convert your quadrant bearings to azimuth first (e.g., N45E = 45°; S30W = 210°; N20W = 340°).

What does a result of “NaN” or “–” mean?

This indicates an invalid input or an impossible calculation. Ensure your dip angles are between 0 and 90, bearings are between 0 and 360, and that you have provided four valid numerical inputs.

How does this relate to reading geological maps?

This calculation is the mathematical basis for how geologists determine the symbols you see on maps. Field data (often apparent dips) are processed to determine the true orientation, which is then plotted using a strike and dip symbol. It is a key skill in reading geological maps.

What if one of my apparent dips is 0?

An apparent dip of 0° means you have found the strike line itself! The bearing of that measurement is the strike direction. The calculator will handle this correctly.

Is this calculator useful for folded rock layers?

Yes, but with a caveat. It tells you the orientation of the plane at the point of measurement. For a fold, you would need to take multiple measurements along the curve to map out how the strike and dip change. This is essential for fault plane analysis and understanding deformational history.

Related Tools and Internal Resources

For more in-depth analysis, explore these related geological tools and guides:

• Three-Point Problem Solver: Calculate strike and dip from three points with known elevations.
• Stereonet Analysis Basics: A guide to using stereonets for visualizing and solving structural geology problems graphically.
• Geological Compass Guide: Learn the proper techniques for measuring strike and dip in the field.
• What is True Dip?: An article explaining the fundamental difference between true dip and apparent dip.
• Reading Geological Maps: A tutorial on interpreting the symbols and structures found on geological maps.
• Fault Plane Analysis: Advanced techniques for analyzing fault data to understand tectonic stress fields.