Not the same as scaling
A naive approach would divide every value until the peak fits. That preserves the ratios and destroys the picture: everything gets darker, including the midtones and skin tones that were already correct.
Real tone mapping is non-linear. It leaves the lower range close to untouched, where most of the image lives, and applies increasing compression toward the top, where the highlights are. The result keeps faces looking right while rolling off the sun rather than clipping it to a flat disc.
The curve is not optional information
SMPTE ST 2084, the PQ curve, encodes absolute luminance: a code value means a specific number of nits. A display that cannot reach that number has to map it down, and a display that ignores the curve entirely does something much worse than mapping badly.
The failure you will actually see
Skipping tone mapping does not produce a darker picture. It produces a washed-out one. A player that reads PQ code values as if they were ordinary gamma sees the whole signal wrong: blacks lift toward grey, saturation drains, and the image looks worse than the SDR original it came from.
This is the single most common reason someone concludes an HDR conversion failed. Before re-exporting anything, check whether the display and player are actually applying the curve.
Doing it deliberately
When you need an SDR deliverable from an HDR master, the curve you choose matters, and so does the diffuse white level you map against. Converting HDR to SDR without the washed-out result walks through three working methods, including the LUT route that works on ffmpeg builds without zscale.
Questions people ask
Is tone mapping lossy?
Yes, in the direction that matters. Compressing a wider range into a narrower one discards distinctions that cannot be recovered from the result, which is why you keep the HDR master and derive SDR from it rather than the reverse.
Can I turn tone mapping off?
On a display, sometimes, and you should not want to. Without it, content graded above the panel's peak simply clips. What you can control is the player: if a player is applying the wrong transform rather than a good one, the fix is a different player, not disabling the step.