How I make ffmpeg hit an exact file size (the bitrate math nobody explains)

Every few weeks I hit the same wall: I have a 300 MB screen recording, and something on the other end wants it under 8 MB . Discord, an email attachment, a bug tracker, a form that silently rejects anything bigger. The usual advice is "just use HandBrake" or "run ffmpeg with a lower CRF." But CRF doesn't take a target size — it takes a quality knob . So you export, check the size, it's 11 MB, nudge the knob, export again, now it's 5 MB and looks like a potato, nudge back… It's a binary search you run by hand, one full encode per guess. The thing is, hitting an exact size isn't a guessing game at all. It's arithmetic you can do before you encode. I ended up wrapping that arithmetic into a little Rust CLI ( DeepShrink ), but the math is the interesting part, and almost nobody writes it down. So here it is. The one insight everything rests on File size is (roughly) bitrate × duration . A bitrate is bits per second. A duration is seconds. Multiply them and the seconds cancel, leaving bits — the size of the file. That's it. That's the whole trick. Normally you treat bitrate as the input and size as whatever falls out. Flip it around: fix the size, measure the duration, and solve for the bitrate. You know the duration (ffprobe will tell you), and you know the size you want (the platform's limit). The only unknown is the bitrate — and now it's a single division away. bitrate = size_in_bits / duration_in_seconds Everything below is just this equation with the real-world messiness added back in. Building the budget, step by step Say I want a 60-second clip to fit Discord's 8 MB limit. 1. Turn the target size into bits. Sizes are in bytes, bitrate is in bits, so multiply by 8. (I'll use 1 MB = 1,000,000 bytes here to keep the mental math clean; if your platform means mebibytes, same method, different constant.) target_bits = 8_000_000 bytes × 8 = 64_000_000 bits (64 Mbit) 2. Reserve a little for container overhead. An .mp4 isn't pure video and audio — there's a container, a m