Tide Height Calculator
Tide level and state from high, low, hours.
What it does
Tides breathe on a 12.42 hour cycle. High water falls toward low over about six hours then climbs back, following a cosine curve closely enough for beach plans. Height at any hour sits between the two marks by that curve.
The tool above interpolates the marks. With high 2 m and low 0.5 m at 3 hours, water stands near 1.29 m with a 1.5 m range and Falling tide. At 9 hours the same marks give 1.84 m and Rising tide. The imperial mirror at 6.6 over 1.6 feet gives 4.23 feet at 3 hours.
Wind and rivers bend the curve. Onshore gales pile water above prediction while offshore winds and low pressure troughs hold it down, and river mouths add their own slope. Official tables beat sine math whenever bars or channels are involved.
This page estimates one semidiurnal cycle only. It does not replace tide tables, account for diurnal coasts, or clear any bar crossing. For boating, use the official predictions.
How to use
- Pick metric (m) or imperial (ft).
- Enter the high water mark.
- Enter the low water mark below high.
- Enter hours since high tide.
- Read height first, then range.
- Read rising or falling for plans.
Formula
- high
- High water mark in m or ft.
- low
- Low water mark in the same unit.
- t
- Hours since high water, 0 to 12.42.
Sine interpolation for one semidiurnal cycle of 12.42 hours. At zero hours the height is high water; near 6.21 it is low. Storm surge and river flow sit outside this curve.
Worked example
Example: 3 h after a 2 m high
Defaults: metric high 2 m with low 0.5 m at 3 h after high water. Semidiurnal period 12.42 h.
- Inputs (metric default): high 2 m with low 0.5 m at 3 h after high.
- Factor: (1 plus cos(2 pi times 3 / 12.42)) / 2 is 0.5265.
- Height: 0.5 plus 1.5 times 0.5265 is 1.29 m.
- Range: 2 minus 0.5 is 1.5 m range.
- At 3 h under 6.21 the state is Falling tide. Imperial 6.6 over 1.6 gives 4.23 ft. Tool shows the same.
Reference table
| Hours after high | Height | State |
|---|---|---|
| 3 h | 1.29 m | Falling tide |
| 9 h | 1.84 m | Rising tide |
| 0 h | 2 m | Falling tide |
| 6.21 h | 0.5 m | Rising tide |
| 6.6 over 1.6 ft at 3 h | 4.23 ft | Falling tide |
Limits
- Sine estimate. Surge and rivers excluded.
- Semidiurnal only. Diurnal coasts differ.
- One cycle. Multi day needs tables.
- No navigation clearance.
Common mistakes
- Reading marks without hours.
- Mixing meters with feet.
- Trusting sine math over tables at bars.
- Ignoring wind setup on shallow coasts.
- Assuming low at exactly 6 h (it is 6.21).
Try it yourself
Quick checks. Answers sit tucked under each question.
High 3 m with low 1 m at 9 h?
Factor is 0.42. Height is 1 plus 2 times 0.42 is 1.84 m with 2 m range. Rising tide.
6.6 over 1.6 ft at 0 h?
Height is 6.6 at 0 h exactly (high water) with 5 ft range. Falling tide just after.
Questions
How is tide height figured?
Low plus range times (1+cos(2 pi t/12.42))/2. Here 1.29 m.
What is tidal range?
High minus low. Here 1.5 m range.
Rising or falling?
Before 6.21 h falling, after rising. Here Falling tide.
Is this exact water?
No. Wind, pressure, and rivers shift real water from the sine curve.
Does this fit all coasts?
Yes for mixed semidiurnal coasts. Diurnal single tide coasts need other harmonics.
Is this safe for boating?
No. Rips, bars, and channels need local tables and advice.