0 to do a calculation to get an answer to a mathematical question:
1 to understand something or to find the answer to something by thinking about it:
[ + question word ] There will be a full investigation to work out what caused the accident.
[ + that ] Investigators needed several months to work out that a fraud had been committed.
2 If a problem or difficult situation works out, it gradually becomes better or satisfactory, and if you work it out, you make it better or satisfactory:
When we worked out how much it cost us to run a car, we decided to sell it.
I couldn't work out what was going on.
I couldn't work out what his expression meant.