Plenty of sites claim a tool "runs in your browser" or "never uploads your file" because it's good marketing, whether or not it's true. You don't have to take that claim on faith — every browser has a panel built in that shows exactly what left your machine, and checking it takes less time than reading the privacy policy that made the claim in the first place.
The actual check
Open developer tools (F12, or right-click → Inspect), go to the Network tab, and clear it. Then use the tool — compress the image, format the text, whatever it claims to do locally. If the file itself appears as outgoing request data, it left your device; the destination and payload size tell you exactly what was sent. If the network tab stays empty of anything resembling your input during the operation, nothing left the browser. This takes about a minute and doesn't require reading a single line of code.
What legitimately does need a network request
Not everything can run locally, and that's not automatically a red flag. DNS lookups, WHOIS records, IP geolocation, and live currency conversion all require querying an external data source that doesn't exist in your browser — there's no local copy of the DNS root to check against. The honest version of these tools says so on the page, names roughly what's being sent, and doesn't route unrelated data (like a file you uploaded for a different feature) through the same request.
Why local processing is also just faster
Beyond privacy, skipping the round trip to a server removes upload time, server queuing, and download time for the result — for anything under a few megabytes, a client-side tool usually finishes before a server-side equivalent has confirmed the upload succeeded. The privacy benefit and the speed benefit come from the same architectural decision, which is one reason it's worth checking for rather than assuming either way.
Where client-side processing hits a wall
Very large files can run into the browser's own memory limits before any server would — a multi-gigabyte video is a case where a browser tab crashing is more likely than a privacy leak. If a tool needs to chunk a large file or warns about size limits, that's usually a sign it's genuinely processing locally and hitting a real hardware ceiling, not evidence of anything being hidden.