1. To turn quickly or with agile precision, especially with limited room to maneuver. Primarily heard in UK. The steering is so good on this car that you can turn on a sixpence, even at high speeds. The striker turned on a sixpence, leaving the defender flailing past her.

2. By extension, to change focus, activity, opinion, or behavior very suddenly or abruptly. Primarily heard in UK. He's usually a nice guy, but his temper can turn on a sixpence sometimes. Politicians have no loyalty to their causes—they'll turn on a sixpence if it means they'll get more votes.