How this calculator works
If each year is treated as an independent draw with the same probability, the chance of no white Christmas in a run of years is one minus the yearly chance raised to the number of years. The chance of at least one is the complement. Expected white Christmases are simply years times probability, and the chance of a run of three is the yearly chance cubed. Independence is an approximation: weather patterns such as El Nino and the North Atlantic Oscillation make some winters snowier than others, so real runs are more clustered than the binomial model predicts. The per-year probability should come from a local climate normal, not from this page.
Formula
chance of no white Christmas = (1 - p)^years, where p is the chance in one year. chance of at least one = 1 - (1 - p)^years. expected count = years x p. chance of three in a row = p^3.
Worked example
A town with a 30 percent chance of a white Christmas has a 0.7^10 = 0.02825 chance of none in ten years, so the chance of at least one is 97.18 percent. The expected number is 10 x 0.3 = 3 white Christmases, and the chance of three consecutive white Christmases is 0.3^3 = 2.7 percent. At a 50 percent yearly chance the ten year chance of at least one rises to 99.90 percent.
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Frequently asked questions
Where do I get the yearly probability?
Environment and Climate Change Canada publishes climate normals that let you count how often snow was on the ground on 25 December at a station. Many weather services publish a white Christmas probability directly for major cities. Use the nearest station with a long record.
What counts as a white Christmas?
Definitions vary. The common Canadian definition is at least 2 centimetres of snow on the ground at 7 a.m. on 25 December, while other services use 1 inch or any measurable snow. Match the definition of the probability you are using.
Why does the model assume independent years?
Independence keeps the arithmetic simple and is a reasonable first approximation. In reality, ocean and atmosphere patterns persist, so snowy Christmases cluster and the binomial model overstates the chance of long snow-free runs.
Does climate change affect these odds?
Yes, and the long-run normal is a moving target. A probability based on a 1981 to 2010 normal may be higher than the current odds in a warming climate. Use the most recent normal available and treat the result as a planning guide.