Sea Level Rise Projection Calculator

How this sea level rise calculator works

Sea level rise is one of those topics where the difference between a rough guess and a transparent estimate matters. If you are thinking about a seawall, a waterfront road, a drainage upgrade, a floodable park, or even just how a familiar shoreline may change over time, you usually want two answers. First, how much total sea level rise might accumulate between now and a future year? Second, how fast might the annual rise rate be by the time you reach that future year? This calculator is built to answer both questions with a compact model that is easy to inspect.

The page uses four inputs: a start year, a projection year, an initial rise rate in millimeters per year, and an acceleration term in millimeters per year squared. Those values define a simple quadratic projection. In plain language, the model starts with today’s annual rate and allows that rate to increase or decrease steadily over time. That is useful because many climate planning conversations are not really about a single year’s rise. They are about what happens when a modest change in the yearly rate compounds across decades.

This is a planning calculator, not a full coastal engineering model. It is best for scenario exploration, early screening, and quick communication. You can run a low, middle, and high assumption set; compare how much the end result changes; and decide whether a more detailed local analysis is warranted. The output is especially helpful when you want to explain why long time horizons are so sensitive to acceleration, even when the acceleration number itself looks small at first glance.

What each input means

Start year is the baseline year from which the projection begins. If your local observation record or planning document uses a different baseline than the calendar year you are in, enter that baseline here. The model treats this as year zero for the projection interval, so the gap between the start year and the projection year is what really drives the calculation.

Projection year is the future year you want to evaluate. A longer horizon generally produces a much larger cumulative rise because the model keeps adding rise every year and, when acceleration is positive, the annual rate itself also grows over time. If the projection year is not later than the start year, the calculator will ask you to correct the input because the model needs a forward-looking interval.

Initial rise rate (mm/year) is the annual sea level rise rate at the start year. Think of this as the slope of the curve at the beginning of the projection. If you have a planning report that says local relative sea level is currently rising at 3.3 millimeters per year, that is the number you would enter here. It is a rate, not a total. Entering centimeters or total rise to date would overstate the result.

Acceleration (mm/year²) describes how much the annual rate changes each year. A value of 0 means the rate stays constant, producing a straight-line trend. A positive value means the annual rise rate increases over time, which bends the curve upward and makes late-century totals much larger. A negative value would represent deceleration, which is mathematically allowed here, though many climate risk scenarios focus on zero or positive acceleration.

Because this calculator is about physical change over time, unit discipline matters. The rate input is in millimeters per year, and the acceleration input is in millimeters per year squared. The result panel reports cumulative rise in centimeters and the ending rate in millimeters per year. That mix is intentional: centimeters are easier to read for cumulative totals over many decades, while millimeters per year remain a natural unit for annual rates.

Formula used by the calculator

The model uses elapsed time, written here as Δt, where Δt = projection year − start year. If the annual rise rate starts at r₀ and changes by a constant acceleration a each year, then cumulative rise is the area under that changing rate curve. In this simplified model, the cumulative rise in millimeters is:

The projected annual rate in the target year is:

Those two expressions are the heart of the calculator. The first tells you the total accumulated rise over the interval. The second tells you how steep the annual rise rate has become by the final year. If acceleration is zero, the first equation collapses into the familiar rate times time relationship. When acceleration is positive, the squared time term becomes increasingly important, which is why long-range projections can separate dramatically even when two scenarios start from nearly the same present-day rate.

It can also help to view the calculator in the more general language of inputs and outputs. The result is still a function of the variables you supply, and this page preserves that broader mathematical framing:

For this sea level tool, the concrete variables are the start year, end year, initial rate, and acceleration. The general notation matters because it reminds you that the output changes only as the chosen inputs and assumptions change. If your scenario is local relative sea level rather than global mean sea level, then the numbers you feed into the model should already reflect that local context.

Worked example

Suppose you keep the default example values: start year 2020, projection year 2100, initial rise rate 3.3 mm/year, and acceleration 0.1 mm/year². The elapsed time is 80 years. The constant-rate part of the projection contributes 3.3 × 80 = 264 millimeters. The acceleration term contributes 0.5 × 0.1 × 80² = 320 millimeters. Add those together and the cumulative projected rise is 584 millimeters, or 58.4 centimeters.

The ending annual rate is easier to compute: 3.3 + 0.1 × 80 = 11.3 mm/year. That means the model is not just saying sea level rises by 58.4 centimeters over the full period. It is also saying that by 2100 the annual rate has increased from 3.3 mm/year to 11.3 mm/year under the same constant-acceleration assumption. This distinction is useful when you compare adaptation options. A site that can tolerate the total rise but not the higher late-period rate may still need earlier action.

If you want a quick reality check, ask two questions. First, does the sign make sense? With positive acceleration, both the total and the ending rate should be higher than a no-acceleration case. Second, does the scale make sense? A long horizon plus positive acceleration should yield a notably larger cumulative total than simply multiplying the starting rate by the number of years.

How acceleration changes the picture

The table below holds the start year, end year, and initial rate constant while changing only the acceleration term. This makes it easier to see why long-term coastal planning discussions often focus on acceleration rather than current rate alone.

This is the main lesson of the calculator: time and acceleration interact. People sometimes focus on the starting rate because it is intuitive, but for long horizons the acceleration term can contribute as much as or more than the straight-line portion of the estimate.

How to interpret the result panel

After you click Project, the calculator shows a cumulative rise total, the projected annual rate in the target year, and a milestone table at 10-year checkpoints. Read the cumulative rise as the model’s estimate of total change between the two years. Read the ending rate as the speed of ongoing rise at the end of the period, not as another total to be added on top.

The milestone table is there to make the curve easier to understand. Because the model includes acceleration, the increments between decades usually get larger as you move further into the future. That is often more informative than looking only at the final number. If one decade adds noticeably more than the one before it, the table is showing the accelerating nature of the scenario directly.

A helpful workflow is to run three cases: a conservative acceleration, a central estimate, and a higher-end stress test. The exact numbers depend on your source data, but the habit is valuable because it shows whether your decision is robust. If a drainage threshold or freeboard allowance changes little across scenarios, the decision is relatively stable. If the threshold is crossed only in the high case, you have identified where uncertainty really matters.

Assumptions and limitations

This calculator is intentionally simple. That simplicity makes it fast and transparent, but it also means the output is only as complete as the assumptions behind it. The calculation assumes a constant acceleration term over the whole interval. Real sea level behavior can be shaped by changing emissions pathways, ice-sheet dynamics, ocean circulation, thermal expansion, and local land motion, none of which must stay constant through time.

The result is also not a flood depth estimate. Sea level rise and coastal flooding are related, but they are not the same thing. A site can experience damaging flood events because of tides, storm surge, wave setup, rainfall, drainage limitations, and groundwater response long before the mean water level alone reaches a critical threshold. If your decision is about building elevation, evacuation routes, critical utilities, or insurance exposure, you usually need local hazard data in addition to a mean sea level projection.

Another important distinction is global versus local relative sea level rise. Local sea level can rise faster or slower than the global average because land itself may sink or rise, ocean circulation may shift, and shoreline processes may redistribute sediment. If your planning source already includes subsidence or uplift, you can enter a locally appropriate rate and acceleration. If it does not, the calculator cannot add those missing processes for you.

Finally, remember that this tool is best used for comparison and communication. It is excellent for asking questions such as, “How much extra rise comes from acceleration over 60 or 80 years?” or “What happens if our baseline rate is a millimeter per year higher?” It is not meant to replace formal guidance from regional climate assessments, coastal agencies, or engineering standards. In other words, this calculator helps structure the conversation; it does not end the conversation.