Bayes’ theorem, no homework required

Casual Bayes

A pocket calculator for “how worried should I actually be?” — right in your browser. You give it three plain-English numbers; it gives you the honest updated probability, and shows its work.

Everything is local — nothing is sent anywhere. It’s the web version of the casual_bayes command-line tool.

One yes/no question, one piece of evidence. This is the classic Bayes update. Type percentages (20%) or decimals (0.2) — both work.

The base rate. “1% of people my age have this disease.”
“The test catches 90% of real cases.”
The number everyone forgets. “The test wrongly flags 9% of healthy people.”

Fill in the numbers on the left — or pick one of the worked examples below — and the updated probability appears here, live.

Try it on a real problem

Each card loads its numbers into the calculator above, so you can see the setup and then poke at it. Change one number and watch how much the answer moves.

The only three numbers you need

Every problem on this page boils down to the same three questions.

prior — the base rate

Before any evidence at all, how common is the thing you’re worried about?

“About 1% of people my age have this disease.”

likelihood — the hit rate

If the thing is true, how often does this clue show up?

“The test catches 90% of real cases.”

false-positive — the cry-wolf rate

If the thing is false, how often does the clue show up anyway?

“The test also flags 9% of perfectly healthy people.”

The trap everyone falls into: a test can be “90% accurate” and still be wrong most of the time it goes off — if the thing it’s testing for is rare. Rare things stay rare even after a positive result. That gap between “accuracy” and “what a positive result actually means for you” is the whole reason this tool exists.
The other trap — double counting: in “several clues” mode, the clues must be genuinely independent. If two of your clues are secretly the same signal (a sketchy domain and a sketchy link are both just “sketchy sender”), the math will make you far too confident. When in doubt, use fewer, truly separate clues.