Sqrt Curve

Understanding the Sqrt Curve in Color Grading

The sqrt curve is a specific tonal mapping function that uses the square root of the input signal to distribute highlights more gracefully than a standard log or gamma curve. It shows up in DaVinci Resolve, Baselight, and various LUT generation tools. The basic idea is that the curve compresses the upper range of your image while leaving the lower midtones relatively untouched, which tends to match how film stocks behave in their highlight roll-off regions. The mathematical operation is straightforward: output = sqrt(input), where input is normalized between 0 and 1. This means shadows get very little compression while highlights get progressively more. A pixel at 0.5 luminance becomes roughly 0.707, but a pixel at 0.9 becomes about 0.949. That 0.049 difference might look small on paper but in practice it gives you headroom to pull back blown-out highlights without crushing the midtones into a muddy mess. Where this matters most is when you are working with Log footage from cameras like the ARRI Alexa or RED, which already have a lot of highlight information baked in. If you just apply a standard Rec.709 transform to that footage, those highlight areas tend to clip harshly. The sqrt curve softens that transition in a way that feels more natural to the eye.

Setting It Up in DaVinci Resolve

I run this in Resolve about once per project now. Here is the practical way to do it without buying any extra plugins. Open the Color page and add a Curves node. In the curves panel, switch the curve type from Parabolic to Logarithmic first, then right-click on the curve points and manually place controls. Start by anchoring the black point at 0,0 and the white point at 1,1. Then add a control point around 0.6 on the input axis and lift it to roughly 0.75 on the output axis. Add another point at 0.85 input and bring it to about 0.93 output. This approximates the sqrt behavior well enough for most delivery workflows. If you want the exact curve rather than an approximation, you can use the Custom3DL export option in Resolve. Generate a 33x33 or 65x65 3D LUT that maps the sqrt function across all three color channels simultaneously, then load that LUT into a Look node. This gives you the mathematically precise curve instead of eyeballing it with spline points.

Getting a Ready-Made Sqrt Curve LUT

There are a couple of free options online if you do not want to build your own. The most reliable source I have found is the OpenColorIO community configs repository on GitHub. Search for sqrt_curve.3dl or sqrt_lut.zip in that repo and download whichever version matches your bit depth needs. A 17x17 LUT is fine for SDI output or final delivery, but if you are doing further grade work after applying it, go with a 65x65 at minimum. Anything smaller introduces visible banding in smooth gradient shots, especially skies. Another option is to generate one yourself with a tool like Qtfaststart or the command-line utility lutcreate from the OCIO suite. The command is roughly: lutcreate --type 3dl --size 65 sqrt_out = sqrt(in) > sqrt_curve_65.3dl

This produces a standards-compliant 3D LUT you can drop into any NLE. I keep a folder of self-generated curves on my local drive rather than relying on whatever free pack someone uploaded three years ago. Those old packs sometimes have the R and B channels swapped or use the wrong gamma assumption underneath.

One Problem You Will Hit and How I Fixed It

Here is a specific issue that cost me an afternoon on a recent project. I applied a sqrt curve LUT to Log C footage from a Sony Venice 2, then went to grade the shadows. The image looked fine until I pushed the shadows up in a dim interior scene, at which point the sqrt curve introduced a subtle magenta cast in the darkest areas. It was almost imperceptible in the midtones but completely obvious once I started lifting blacks. The cause turned out to be that the sqrt curve I was using was built on a linear input assumption, but the Venice 2 outputs in S-Log3, which is a variant of the SGT (S-Gamut3) transfer function, not pure linear. Applying a linear sqrt LUT directly to S-Log3 footage meant the curve was operating on the wrong gamma space. The fix was simple: I inserted a S-Log3 to Rec.709 EOTF node before the sqrt curve, applied the sqrt mapping in the proper linear-light space, and then let the sqrt curve do its highlight compression. The magenta cast disappeared entirely. This is the kind of thing that does not show up in any tutorial because everyone assumes you already know your footage is in the right color space before you touch the curve.

When the Sqrt Curve Is the Right Call

Use this when your source material has extended highlights that need gentle compression without losing contrast in the midtones. It is particularly effective for outdoor scenes with bright skies, window light in interior setups, or any shot where specular highlights carry important information rather than acting as pure burnout. It is not a cure-all. If your footage is already HDR mastered content in PQ or HLG, applying a sqrt curve on top will generally look wrong because those transfer functions already handle highlights differently. The sqrt curve belongs in a traditional SDR or wide-gamut S-log workflow, not as a universal fix for every lighting problem.

Common Pitfalls to Avoid

Do not stack the sqrt curve with another highlight compression curve unless you actually need the extra squashing. I have seen people apply a sqrt curve and then follow it with a film emulation LUT that also compresses highlights, which double-crushes the top end and makes the image look flat and lifeless within three seconds of looking at it. Another mistake is applying the sqrt curve before primary color correction. If you are going to shift your whites or adjust the exposure, do that first. The sqrt curve assumes a certain input range, and if you change the exposure after applying it, the highlight behavior shifts in ways that are hard to predict. Linear workflow order matters here: exposure adjustment first, then sqrt curve, then creative grading. Also check whether your deliverable format supports the highlight detail the sqrt curve preserves. If you are delivering to a platform that aggressively recompresses video, like some social media uploads, all that extra highlight information gets crushed by the encoder anyway. In those cases you might as well skip the sqrt curve and save yourself the grading complexity.

Alternatives Worth Knowing

If the sqrt curve does not fit your project, the ARIB Base T10 curve is worth evaluating. It handles highlight roll-off in a similar direction but with a different mathematical profile that some colorists find more predictable. There is also the SPG (Standard Picture Gamma) curve built into Baselight, which combines sqrt-like behavior with built-in contrast management. If you are working primarily in Resolve and need something closer to a film look, the ARRI LogC3 to V3 conversion already includes highlight behavior that overlaps with what the sqrt curve does, so applying both would be redundant. The sqrt curve is a useful tool in the right situation. It is not a magic bullet, and it will not fix bad exposure or a poorly lit set. But when you have clean Log footage with recoverable highlights and need a straightforward way to compress the top end without sacrificing midtone contrast, it does exactly what it claims to do without introducing artifacts or requiring expensive plugins.