Ice thickness follows the square root of accumulated cold. That relationship is over a century old, it is used in real engineering work, and it has a specific weakness that matters a great deal for anyone standing on early season ice.
Take a day, average its high and low temperature, and subtract that average from 32 degrees Fahrenheit. A day averaging 22 degrees contributes 10 freezing degree days. A day averaging 40 degrees contributes negative 8, because it takes heat back out of the sheet. Add those up across the winter and you get accumulated freezing degree days, usually written AFDD.
That single running total captures something a thermometer reading cannot. Ice does not care what the temperature is this morning. It cares how much heat has left the water since freeze up, and AFDD is a direct proxy for exactly that. It is also why a warm spell is genuinely destructive rather than merely a pause: those days subtract.
This site computes AFDD for each water from daily maximum and minimum temperature records at a nearby climate station, using the standard method of summing the daily differences from freezing across the season.
The relationship between AFDD and ice thickness is called the Stefan equation, after the physicist who derived it in 1891 for sea ice. In the form used by the US Army Corps of Engineers for practical work, thickness in inches equals a coefficient multiplied by the square root of AFDD in Fahrenheit degree days.
The coefficient carries all of the local reality: how much snow is insulating the sheet, whether the water is windswept or sheltered, whether there is current. Corps guidance uses values in the range of roughly 0.5 for a snow covered sheltered sheet up to around 0.8 for a windy lake with little snow. As a worked example from that guidance, a coefficient of 0.6 applied to 300 accumulated freezing degree days predicts a sheet about 10 inches thick.
The square root is the important part. It means ice growth decelerates. Getting the first four inches takes far less accumulated cold than adding the next four, because the ice itself insulates the water below from the air above. This is why a hard cold snap early in the season changes conditions dramatically and the same cold snap in February barely moves the number.
Published work on this method notes that it overpredicts thickness for newly formed thin ice. The error runs in the dangerous direction, and it runs that way precisely during the early season window when people are most eager to get out. Treat any early season estimate as optimistic.
Because the coefficient depends on snow and wind and shelter, a single number would be false precision. This site shows accumulated cold as the primary figure, which is a measurement rather than a model, and gives the modeled thickness only as a range across plausible coefficients.
Even that range assumes a uniform sheet, which never exists. Michigan DNR is direct about this: ice does not form at a uniform rate, and thickness can vary by feet within a few yards. A model built on a single air temperature record cannot know about the spring hole, the current seam, or the pressure ridge. Those are the things that actually put people in the water.
| Accumulated cold | What it implies | How to read it |
|---|---|---|
| 0 to 50 | Little or no ice expected | Early season or post thaw. Open water and skim ice. |
| 50 to 150 | Ice forming | The most dangerous window. The model is least reliable here and it errs optimistic. |
| 150 to 350 | Ice building | Sheets developing on shallow water. Deep and current driven water still unreliable. |
| 350 to 700 | Sustained cold | Established ice on shallow waters in a normal winter. Local variation still governs. |
| 700 and above | Hard winter accumulation | Deep water begins locking up. Michigan reaches this in colder years. |
These bands describe what the physics implies about formation, not whether any particular spot will hold you. Nothing in this table is a safety threshold.
Daily maximum and minimum temperatures come from the Applied Climate Information System, which serves the official daily climate record for United States stations. Current conditions come from the National Weather Service API. Great Lakes ice cover comes from NOAA GLERL, built on National Ice Center analyses.