Log Curve Comparison Plotter

Why log encodings exist

Digital sensors capture light linearly — double the photons, double the voltage — but they only have a limited number of code values to spend on it: 1024 levels at 10-bit, 4096 at 12-bit. Store a wide-range sensor's output linearly and half of every available code value ends up describing the single brightest stop, while the stop nearest black — where the eye is most sensitive to banding — gets almost nothing. A log curve fixes the allocation by compressing the signal logarithmically, so each stop of exposure gets a roughly even share of code values across the sensor's usable range. That protects shadow detail from quantizing into visible bands and leaves headroom above middle gray to hold highlights that haven't clipped yet. It's also why raw log footage looks flat and desaturated on a monitor: the curve is deliberately not matched to a display. A LUT, camera-native display transform, or a color-managed pipeline (ACES and similar) has to undo the log encoding — and apply the matching color gamut — before the image reads as normal contrast.

Reading this chart

The x-axis is scene exposure in stops relative to 18% middle gray, from −8 to +8; the linear input every formula below actually takes is x = 0.18 × 2^stops. The y-axis is the encoded signal as a percentage of the code range (0–100%). A flatter part of a curve spends fewer code values per stop of exposure at that part of the range — every one of these five curves flattens progressively into the highlights, which is the compression doing its job of protecting clipped-adjacent detail. Toggle curves with the legend checkboxes, and drag the exposure slider to drop a vertical cursor at any stop: every enabled curve reports its exact signal percentage and 10-bit code value (signal × 1023, rounded) at that exposure, live.

Where mid-gray lands, and why it differs

All five curves are calibrated so an 18% grey card (x = 0.18, "0 stops") lands somewhere in the middle third of the code range — but not at the same value, because each manufacturer chose its own headroom-to-shadow ratio:

LogC4 places mid-gray noticeably lower than the others (27.8% vs. roughly 39–42%) because the ALEXA 35's LogC4 curve was redesigned to hold more highlight stops above middle gray than LogC3 did — pushing gray down frees more of the upper code range for the extra highlight latitude the newer sensor captures. That is also why S-Log3 and LogC footage graded side by side without a proper conversion look mismatched in contrast even before you touch color: their formulas simply place the same scene exposure at different numbers.

The formulas, and where they come from

Every curve here is implemented from its manufacturer's published transfer-function reference, not eyeballed off a chart image: ARRI's LogC3 technical white paper (the piecewise log/linear curve ARRI has shipped since the Alexa Classic, parameterized by exposure index); ARRI's LogC4 technical white paper (the newer, EI-independent curve built for the ALEXA 35's extended range); Sony's S-Log3 technical summary (shared across the current VENICE and FX camera lines); Panasonic's V-Log/V-Gamut technical reference (used on the VariCam and S1H/S5 lines); and RED's Log3G10 white paper (RED's current default log space, paired with REDWideGamutRGB).

Worked example: S-Log3 at +3 stops

Take +3 stops of exposure: linear x = 0.18 × 2³ = 1.44. Sony's formula for x ≥ 0.01125 is y = (420 + log10((x + 0.01) ÷ 0.19) × 261.5) ÷ 1023. Plugging in: (1.44 + 0.01) ÷ 0.19 = 7.632; log10(7.632) ≈ 0.8826; × 261.5 ≈ 230.8; + 420 = 650.8; ÷ 1023 ≈ 0.636 → 63.6%, roughly code value 651 of 1023. Drag this plotter's slider to +3 stops with only S-Log3 enabled and you'll read the same figure — the whole point of building this from the published formula instead of a rendered reference image.

Why you can't just "convert" between logs with one LUT

A log curve is only half the story: it maps scene-linear exposure to code values, but it says nothing about which colors those code values represent. Every log curve is paired with a specific wide color gamut — LogC3/LogC4 with ARRI Wide Gamut 3/4, S-Log3 with S-Gamut3/S-Gamut3.Cine, V-Log with V-Gamut, Log3G10 with REDWideGamutRGB — and a correct conversion has to undo both the curve and the gamut together (an IDT into a common working space, or a vendor-supplied 3D LUT built for that exact pairing). Feeding S-Log3 footage through a LUT built for LogC will get the exposure roughly in the right place because the anchor table above shows the curves aren't wildly different, but colors will shift, because the underlying primaries don't match.

Dynamic range isn't in the curve

The dynamic-range chips shown per curve — LogC4 17 stops (ALEXA 35), LogC3 14+ stops (ALEXA Mini), S-Log3 16 stops (VENICE 2), V-Log 14+ stops (VariCam/S1H), Log3G10 17+ stops (V-RAPTOR) — are manufacturer specifications, not anything this chart derives from the encoding math. A log curve is a pure transfer function from linear light to code value; by itself it has no dynamic range at all, because it has no noise floor and no clipping point. Those numbers belong to the sensor, measured under each manufacturer's own criteria for usable stops above and below middle gray (typically some signal-to-noise threshold in the shadows and a clipping threshold in the highlights) — criteria that differ enough between manufacturers that the stop counts aren't strictly comparable to each other, even though they're all real, published figures.

1. Switch on the log encodings you want overlaid: ARRI LogC3 and LogC4, Sony S-Log3, Panasonic V-Log and RED Log3G10.

2. Drag the exposure slider along the axis of stops relative to 18% middle gray.

3. Read each curve's encoded signal percentage and 10-bit code value at that stop, then compare display-side curves in the Gamma / EOTF Curve Comparator.