Tidal Calculations Cheat Sheet
For RYA Day Skipper and Yachtmaster theory exams
Tides are where Day Skipper theory students lose the most marks. Almost always because they confuse heights with streams, get lost in secondary-port corrections, or panic and skip the Rule of Twelfths. This is the cheat sheet — what you actually need to know, in the order the exam asks for it.
The five terms to know cold
- Chart Datum (CD)
- The level below which the tide rarely falls. Charted depths are measured from here. Calculations always start from CD.
- MHWS / MLWS
- Mean High / Low Water Springs. The average height of HW / LW on spring tides over many years. Found in the almanac.
- MHWN / MLWN
- Same but for neap tides. Springs have a bigger range than neaps.
- Tidal Range
- Height of HW minus height of LW for that tide. The bigger the range, the faster the tidal stream. Springs = big range. Neaps = small range.
- Height of Tide
- Height of water above CD at a given time. What you add to charted depths to get actual water depth.
The one formula that runs everything
Depth of water = Charted depth + Height of tide
That is it. Every height question is a variation. The work is finding the Height of Tide at the right time and place — the formula itself is trivial. If the chart says 1.5 m at that spot and the Height of Tide is 4.2 m, the actual water depth right now is 5.7 m.
The Rule of Twelfths (the core technique)
The tide does not rise or fall at a steady rate. It rises slowly, then quickly, then slowly. The Rule of Twelfths splits the rise into six hours and assigns each hour a fraction of the range:
| Hour from LW | Fraction of range | Cumulative |
|---|---|---|
| 1st hour | 1/12 | 1/12 |
| 2nd hour | 2/12 | 3/12 |
| 3rd hour | 3/12 | 6/12 |
| 4th hour | 3/12 | 9/12 |
| 5th hour | 2/12 | 11/12 |
| 6th hour | 1/12 | 12/12 |
Memory aid: 1-2-3-3-2-1. The middle two hours are when most of the tide moves. The first and last hours barely move. This is why anchorages dry slowly at first and then suddenly.
Worked example
Question: LW at Dover is at 0600 with a height of 0.8 m. HW is at 1215 with a height of 6.8 m. What is the height of tide at 0900, and what is the depth of water at a spot charted 1.2 m?
- Range = 6.8 − 0.8 = 6.0 m
- Time from LW = 0900 − 0600 = 3 hours (so we include hours 1, 2, and 3 of the rise)
- Cumulative fraction = 1/12 + 2/12 + 3/12 = 6/12 = 1/2
- Rise from LW = 1/2 × 6.0 = 3.0 m
- Height of Tide = 0.8 + 3.0 = 3.8 m
- Depth of water = 1.2 + 3.8 = 5.0 m
Answer: 5.0 metres. You will find this is exactly the form most exam questions take. The numbers change; the procedure does not.
Tidal heights vs tidal streams — they are different
This is the most common confusion. They are completely separate calculations using different reference data:
Tidal Height
How deep the water is at a given time. Used for deciding when to enter a harbour, drying-out anchorages, bar crossings. Look up in the almanac tidal-curve tables. Uses HW/LW heights and the Rule of Twelfths.
Tidal Stream
How fast and in what direction the water is flowing. Used for passage planning, ETAs, fair-tide departures. Look up in the tidal stream atlas or chart diamonds. Two values: rate (knots) and direction (degrees true).
The exam will ask you both in the same question. Read the question twice. If it asks “depth” or “height,” you need heights. If it asks “rate,” “set,” “drift,” or “direction,” you need streams.
Secondary ports — the shortcut
Standard ports have full tidal curves. Secondary ports are smaller harbours nearby with a published correction table referring back to a standard port. The correction has four parts:
- HW time difference (e.g. −0010)
- LW time difference (e.g. +0005)
- HW height difference (e.g. −0.3 m)
- LW height difference (e.g. −0.1 m)
Procedure: Get the standard port HW and LW times and heights from the almanac. Apply the four corrections to get the secondary port HW and LW. Now use the Rule of Twelfths on the secondary-port values.
The exam trap: many students apply the corrections in the wrong direction. Read the sign carefully — a “−0010” means earlier, “+0010” means later. A “−0.3 m” means the secondary port has lower HW than the standard port, not higher.
Common mistakes
Mistake 1: Forgetting that charted depths are below CD
A drying height (shown on charts in italics, e.g. “1.2” with an underline) is height above CD — so the water covers it only when the Height of Tide is greater than 1.2 m. Read the chart carefully.
Mistake 2: Using the wrong tide
If the question asks about 0900 and HW is at 1215, you are in the rising tide between LW and HW. Make sure your “hour from LW” calculation uses the most recent LW, not yesterday's.
Mistake 3: Forgetting BST / DST
UK almanacs publish times in UT (GMT). In summer (British Summer Time), add one hour. Many wrong answers come from a one-hour shift in either direction. Always check the timezone note on the page.
Mistake 4: Rule of Twelfths between hours
The rule is a fraction-of-the-range model that works in whole hours. For times that fall between hours (e.g. 0930), use the 12-hour graphical method or interpolate — but most exam questions are set on whole hours to keep this clean. If you get a fractional hour, treat it as the nearest hour for an approximate answer, then check your working.
Mistake 5: Adding when you should subtract (and vice versa)
On a falling tide, the rise from LW is happening backwards — but the formula still gives you a positive cumulative number. Always ask: am I rising or falling? On a falling tide, the height at time T = HW height − (cumulative fraction × range).
Springs vs neaps — the cycle
Springs occur around full and new moons. Neaps occur around the first and last quarter moons. The cycle is roughly 14 days:
- Spring tides — big range, fast streams, low LW, high HW
- Neap tides — small range, slow streams, water doesn't move as much
- Memory aid: “Spring up high, neap down low.” Springs spring up to the higher of the highs and the lower of the lows.
Practise this now
Reading is not enough. The Day Skipper and Yachtmaster theory exams give you 4–6 tidal questions; you cannot fake your way through them. Drill until the procedure is automatic: