Apparent Dip Calculator (and True Thickness of a Dipping Bed)
The dip of beds seen in a cross-section that is not at right angles to the strike, and the true thickness of a dipping layer from a vertical borehole or from its outcrop width.
Results
What this tool does
Beds dip at their steepest at right angles to the strike; in any other direction the dip you see is smaller — tan(apparent dip) = tan(true dip) × sin β, with β the angle between the section and the strike. On a cross-section along the strike the beds look flat. Thickness has a similar trap: a vertical borehole through dipping beds, or a width measured on flat ground, overstates the real thickness by 1 ÷ cos δ or 1 ÷ sin δ, so the true thickness is smaller. Geologists need these corrections for every map and log.
Formula
tan(apparent dip) = tan(true dip) × sin β · t = T_vertical × cos δ · t = w × sin δ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dl | True dip of the beds | ° |
be | Angle between the section line and the strike of the beds | ° |
tv | Thickness measured down a vertical borehole | m |
wo | Width of the outcrop across the strike on flat ground | m |
AD | Apparent dip in that section | ° |
T1 | True thickness from the borehole | m |
T2 | True thickness from the outcrop width | m |
Worked example
- True dip of the beds40 °
- Angle between the section line and the strike of the beds30 °
- Thickness measured down a vertical borehole100 m
- Width of the outcrop across the strike on flat ground200 m
- Apparent dip in that section22.76 °
- True thickness from the borehole76.60 m
- True thickness from the outcrop width128.56 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.