Apparent Depth Calculator (Why Pools Look Shallow)
How deep water looks from above compared with how deep it really is, and the size of Snell's window — the circle of sky a diver or fish sees overhead.
Results
What this tool does
Light leaving water bends away from the vertical, so the eye traces it back to a point that is too high: looking straight down, water appears only about three quarters as deep as it is, which is why people misjudge the depth of pools and rivers. Seen from below, the whole sky is squeezed into a bright circle — Snell's window — about 97° across, because of the critical angle; outside it the surface acts as a mirror. The apparent-depth figure is for looking straight down; at a slant water looks shallower still.
Formula
apparent depth = real depth × n_viewer ÷ n_water · Snell's window: θ_c = asin(n_viewer ÷ n_water), diameter = 2 d tan θ_c
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d | Real depth | m |
n1 | Refractive index of the water side | — |
n2 | Refractive index on the viewer's side (air ≈ 1) | — |
DA | Apparent depth, looking straight down | m |
SH | Looks shallower by | % |
WA | Snell's window — full cone angle | ° |
WD | Snell's window — diameter on the surface from that depth | m |
Worked example
- Real depth2 m
- Refractive index of the water side1.333
- Refractive index on the viewer's side (air ≈ 1)1
- Apparent depth, looking straight down1.500 m
- Looks shallower by25.0 %
- Snell's window — full cone angle97.2 °
- Snell's window — diameter on the surface from that depth4.54 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.