Have you ever wondered what a weather forecast means when it says “There is an 80% chance of rain”? I understand that it means that rain is pretty likely, but where has 80% come from? Let’s find out! @standupmaths @robeastaway @tkendalluk @mathsjem #mathschat

You might have some fair assumptions about how the percentages are calculated. Does it mean that 80% of a 24 hour period will be rainy? Does it mean that 80% of a town will be rained on? Has the day been run through a simulation and on 80% of the days it has rained?

If I’m honest, I thought it was the last one. Nowadays meteorologists can probably run data through a computer and get reliable results. But every time I teach probability we talk about weather forecasts and I have never questioned where the figure comes from...that ends today!

The % you see on a weather forecast is known as a Probability of Precipitation (or POP in weatherpeople lingo). The POP is describing the chance of rain at any point over an area and it is a number between 0 and 1. It is calculated by multiplying two variables known as C and A.

Let’s define those variables!

C = confidence that precipitation will occur somewhere in the forecast area.

A = % of the area that will receive measurable precipitation, if it occurs.

Measurable precipitation is defined as 0.25mm (0.01 inches for our imperial friends).

Obviously, being a percentage, A is a value between 0 and 1.

C is also measured between 0 and 1, where 0 is not confident at all and 1 is Kanye West levels of confidence.

Multiplying C and A gives another value between 0 and 1 and that’s the percentage we see on our forecasts!

For example, if a meteorologist is 70% sure that rain will occur over 50% of an area, the POP will be 0.7 x 0.5 = 0.35 or 35%.

Sometimes the weather forecast POP will be really high (like 90%) but you won’t get rained on. Why not? Because the forecaster might have absolute confidence that it’ll rain on 90% of an area and you happen to live in the other 10%.

Now, I’m no meteorologist and I’m not even going to attempt to explain where the C value comes from. Generally high confidence occurs when recent weather is behaving as it is expected to behave based on previous records. Maybe some professionals can jump in here and help out?!?

So next time you’re teaching probability and you or a student talks about “the chance of rain”, use it as an opportunity to explain POP and confidence intervals!

(As a post-script, my wife has told me that I’m incredibly boring and nobody cares about this stuff - hopefully Maths Twitter can prove her wrong!)