geology · structural
Apparent Dip from True Dip
tan(α) = tan(δ) × sin(β)
click formula to derive ↑
Inputs
°
°
Description
Computes the apparent dip seen in a vertical section or cross-section that is not perpendicular to strike, given the true dip of the plane and the angle (structural bearing) between the strike and the section direction. Apparent dip is always less than or equal to true dip for the same plane.
Variables
| Symbol | Unit | Description |
|---|---|---|
| α | ° | Apparent Dip |
| δ | ° | The true (maximum) dip of the plane, measured perpendicular to strike. |
| β | ° | The horizontal angle, measured from the strike direction, to the vertical section or observation line for which the apparent dip is wanted. |
Assumptions
- The surface is genuinely planar over the section of interest.
- β is the acute angle (0-90°) between the strike line and the section/observation direction.
- True dip has already been established (e.g., from a three-point solution or a field measurement) — this calculator converts it to what would be seen in an oblique section; it does not derive true dip from an apparent dip.
Limitations
- Not valid across a fold hinge or fault, where the planar-attitude assumption breaks down.
- Sensitive to error in β when true dip is small — a small error in the assumed strike direction noticeably shifts the computed apparent dip at gentle true dips.
- Reports the magnitude of apparent dip only; confirming which side of the section the dip appears on requires knowing the actual 3-D geometry.
- The formula tan(α) = tan(δ) × sin(β) is corroborated across multiple independent secondary structural-geology sources. Ragan's textbook (4th ed.) was directly read and confirmed to define exactly these three variables and to reference an 'Eq. 1.7' relating them, but the specific page containing that equation itself was not reached this session — treat the formula as secondary-source-corroborated, not a page-checked citation from Ragan directly.
Use Cases
- → Cross-section construction: When drafting a geologic cross-section that isn't perpendicular to strike, find the dip that will actually appear on the section face.
- → Correcting an obliquely measured dip: Convert a dip measured obliquely (e.g., along a road cut not perpendicular to strike) for comparison against a true-dip value obtained independently.
Related Calculations
Region Notes
Global
Apparent dip is always ≤ true dip for the same plane — if a calculated apparent dip exceeds an independently known true dip, check whether β was measured as the angle from strike (correct) rather than from the dip direction.
References
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