Tidal Height Formula — The 1/12 Rule
Calculate the height of tide at any time using the 1/12 rule.
Estimates water depth between high and low tide in 6 equal hourly steps.
The Formula
Height at hour n = LW + (Cumulative fraction) × Range
The 1/12 rule is a simple approximation used by sailors and coastal navigators to estimate the height of tide at any point between low water (LW) and high water (HW). It divides the tidal cycle into six equal one-hour intervals and assigns a fraction of the tidal range to each hour.
The 1/12 Rule Table
| Hour | Rise that hour | Cumulative rise | Height above LW |
|---|---|---|---|
| LW (hour 0) | — | 0/12 | LW height |
| Hour 1 | 1/12 of range | 1/12 | LW + 1/12 × Range |
| Hour 2 | 2/12 of range | 3/12 | LW + 3/12 × Range |
| Hour 3 | 3/12 of range | 6/12 | LW + 6/12 × Range (mid-tide) |
| Hour 4 | 3/12 of range | 9/12 | LW + 9/12 × Range |
| Hour 5 | 2/12 of range | 11/12 | LW + 11/12 × Range |
| Hour 6 | 1/12 of range | 12/12 | HW height |
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| HW | Height of High Water | metres |
| LW | Height of Low Water | metres |
| Range | HW − LW (total tidal range) | metres |
| n | Hours elapsed since Low Water (0–6) | hours |
Example 1
LW = 0.5 m at 06:00. HW = 4.5 m at 12:00. What is the height at 09:00?
Range = 4.5 − 0.5 = 4.0 m
Time elapsed since LW = 3 hours → cumulative fraction = 6/12 = 0.5
Height = 0.5 + 0.5 × 4.0 = 0.5 + 2.0
Height at 09:00 ≈ 2.5 m
Example 2
LW = 1.0 m, HW = 5.8 m. Vessel needs 2.5 m of water. When is it safe to enter?
Range = 5.8 − 1.0 = 4.8 m
Need: 2.5 m → 2.5 − 1.0 = 1.5 m rise needed = 1.5/4.8 = 0.3125 of range
0.3125 falls between hour 2 (3/12 = 0.25) and hour 3 (6/12 = 0.50)
Safe entry approximately 2 hours after Low Water
When to Use It
Use the 1/12 rule when you need a quick estimate of tidal height without official tidal curves:
- Determining whether a vessel with a given draft can safely enter a harbour or anchorage
- Planning passage through shallow water (deciding when to depart with the tide)
- Estimating freeboard and clearance under bridges at a specific time
- Quick mental arithmetic at sea without electronic aids
Limitations: The 1/12 rule assumes a regular, symmetrical semi-diurnal tide (two equal tides per day). It is less accurate for mixed or diurnal tides, and for shallow-water ports where tidal curves are irregular. Always use official tidal tables and curves for critical navigation decisions.