Mid-interval
Both simplified methods reach one-half the height range at exactly half the elapsed interval.
Boat Tide Height & Clearance Window Calculator
Created by: Liam Turner
Last updated:
Interpolate between user-entered official adjacent tide events, compare sinusoidal and rule-of-twelfths scenarios, and estimate threshold windows.
Boat Tide Height & Clearance Window Calculator
BoatingCompare two simplified interpolation methods between adjacent official tide events and estimate a user-entered threshold window.
Signed scenario applied to the whole curve; not a forecast.
What is a Boat Tide Height & Clearance Window Calculator?
This calculator interpolates between two official adjacent tide events entered by the user and estimates when an entered height threshold may be crossed.
NOAA provides official predictions by station, datum, units, and time zone; the tool does not fetch or reproduce those predictions.
Both sinusoidal and rule-of-twelfths methods are simplified and can differ from harmonic prediction and observed water level.
How the Boat Tide Height & Clearance Window Calculator Works
Elapsed time is normalized from zero at the first event to one at the second.
The sinusoidal method uses a half-cosine fraction. The twelfths method accumulates 1, 2, 3, 3, 2, and 1 twelfths over six equal time intervals.
A crossing is inverted from the selected method, and the at-or-above window is assigned according to whether the interval rises or falls.
Formulas and assumptions
Smooth fraction = (1 − cos(π × elapsed/duration)) ÷ 2
Height = start + fraction × (end − start) + observed offset
Twelfths increments = 1, 2, 3, 3, 2, 1
Example Calculations
Rising threshold
For one to five units over six hours, a three-unit sinusoidal threshold occurs at the three-hour midpoint.
Common Applications
- Teaching tide interpolation
- Approximate clearance-window comparison
- Method sensitivity
- Time-zone and datum briefings
Planning Tips
Use adjacent events from the correct official station.
Write the time zone and datum beside every value.
Use current predictions and observations for navigation.
Frequently Asked Questions
Does this calculator predict the tide?
No. It interpolates between two official adjacent high/low events entered by the user. Use current predictions for the correct station, date, units, time zone, and datum, plus observations and local corrections where appropriate.
What is sinusoidal interpolation?
It assumes a smooth half-cosine change between adjacent extrema. Real tides are harmonic and often asymmetric, so the result is an educational scenario rather than an official prediction.
What is the rule of twelfths?
It divides the height change into six equal time intervals with increments of 1, 2, 3, 3, 2, and 1 twelfths. It is a rough teaching approximation and can be poor for non-semi-diurnal or distorted tides.
How is the threshold window calculated?
The selected interpolation method estimates when entered height crosses the target. On a rising interval, the at-or-above window runs from crossing to the ending event; on a falling interval, it runs from the start to crossing.
What does observed offset do?
It adds one entered signed amount to both endpoint heights and the interpolated curve. It is a simple scenario, not a forecast that the observed difference will remain constant through the interval or at another location.
Can I use the window as permission to transit?
No. A height threshold is only one input. Datum compatibility, route depths, squat, waves, weather, current, traffic, bridge or lock operation, survey uncertainty, local rules, and alternatives remain essential.
Sources and References
- Royal Yachting Association. Anchoring with Care, accessed July 16, 2026; https://www.rya.org.uk/environment-and-sustainability/anchoring-with-care/.
- NOAA Center for Operational Oceanographic Products and Services. Tides & Great Lakes Water Levels, accessed July 16, 2026; https://www.tidesandcurrents.noaa.gov/water_level_info.html.
- NOAA Tides & Currents. NOAA Tide Predictions User Guide, accessed July 16, 2026; https://tidesandcurrents.noaa.gov/PageHelp.
- U.S. Coast Guard Office of Bridge Programs. Bridge Guide Clearances and bridge information, accessed July 16, 2026; https://www.dco.uscg.mil/Office-of-Bridge-Programs/.
- Geometry, clearance sign conventions, and interpolation assumptions are documented in each calculator.
Navigation limitation
Interpolation is a teaching and planning scenario, not an official tide prediction, observed water level, navigation instruction, or permission to transit.