Check before you convert
This is the one source where the honest answer is usually "you do not need this". Since the iPhone 12, the Camera app records Dolby Vision profile 8.4 by default, which is an HLG-based HDR format. If your clip came off a recent iPhone with default settings, it is already HDR.
Verify rather than guess:
ffprobe -v error -select_streams v:0 \
-show_entries stream=color_transfer,color_primaries,pix_fmt \
-of default=nw=1 clip.mov
color_transfer=arib-std-b67 means HLG, so the clip is HDR. smpte2084 means PQ, also HDR. bt709, or an empty field, means SDR and conversion is worth doing.
The four cases where an iPhone clip really is SDR
HDR Video is switched off. Settings, then Camera, then Record Video, then the HDR Video toggle. Plenty of people turn it off deliberately because HDR clips look wrong when shared to apps that do not handle them.
iPhone 11 or earlier. No Dolby Vision recording. Everything from these devices is SDR.
A screen recording. iOS screen recordings capture the composited interface, not the camera, and they are SDR. See converting a screen recording.
The clip has been through another app. Plenty of editing and sharing apps re-encode to SDR on export, silently. A clip that was HDR on the phone can arrive on your desktop as BT.709. This is the most common case, and it is why checking the actual file beats reasoning about the device.
What conversion gives you
Where the source really is SDR, converting produces a 10-bit HDR10 file: BT.2020 primaries, PQ transfer, resolution and frame rate unchanged. Note that this is HDR10 rather than the Dolby Vision the phone would have recorded, which is the more portable format of the two. See what the converter outputs.
A note on sharing
An HDR clip shared into an app that does not tone-map will look washed out, and this is the reason many people conclude HDR is broken on their phone. The file is fine; the receiving app is reading the curve as ordinary gamma. Tone mapping covers why.
Questions people ask
How do I turn HDR recording off?
Settings, then Camera, then Record Video, then the HDR Video toggle. Turning it off is a reasonable choice if your footage keeps arriving washed out in apps that do not tone-map, though the better fix is usually the destination rather than the capture.
Why does my iPhone HDR clip look bad when I share it?
The receiving app is reading the PQ or HLG curve as ordinary gamma, so blacks lift and colour drains. The file is fine. Verify it with ffprobe before concluding otherwise, and share a download link rather than an in-app attachment when the HDR version matters.