Google Docs counts characters for you: click Tools, then Word count, or press Ctrl+Shift+C (⌘+Shift+C on a Mac). The box shows characters and characters without spaces, along with words and pages. Select a passage first to count only that part.
When to paste it here instead
Docs gives you the count, but not how close you are to the limit you are writing for. Paste the text into the counter above and it shows the room left for a title tag (60 characters), a meta description (160) and an X post (280). The count happens in your browser, so the text stays on your computer.
This character counter is free with no signup. SearchBlueprint, who make it, sell SEO planning: a plan that shows the searches your customers type and the page that should answer each one.