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CO₂ / pH / Alkalinity Calculator

pH, alkalinity, and dissolved CO₂ form a tightly coupled system. Once you fix any two, the third is mathematically determined by the carbonate equilibrium. This is the same equation used for planted-tank CO₂ injection but it works just as well for diagnosing why your reef tank pH won't climb above 7.9 (answer: too much CO₂ in the room air, not too little alkalinity).

CO₂ / pH / Alkalinity

pH
8.10
Alkalinity
8.00dKH
CO₂
2.23ppm
  • Below 5 ppm CO₂: pH may swing high in planted tanks; reef tanks at low CO₂ tend to read pH ~8.3+.

Formula: CO₂ [mg/L] = 15.7 × dKH × 10^(6.35 − pH). Carbonate first dissociation pK₁ = 6.35 at 25 °C.

How this is calculated

CO₂ [mg/L] = 15.7 × Alkalinity[dKH] × 10^(6.35 − pH)

where 6.35 = pK₁ (first carbonate dissociation constant at 25 °C)

Rearranged:
  pH  = 6.35 + log₁₀ (15.7 × dKH / CO₂)
  dKH = CO₂ × 10^(pH − 6.35) / 15.7

For a reef tank holding 8 dKH and pH 8.1, dissolved CO₂ is about 1.5 ppm. Drop pH to 7.8 at the same alkalinity and CO₂ climbs to 3 ppm — usually from poor room ventilation, not from coral consumption or any alkalinity problem. The fix isn't dosing more alk; it's opening a window or feeding the skimmer outdoor air.

Planted-tank hobbyists use this equation to inject CO₂ to 25–35 ppm. Reef tanks should run 1–3 ppm. Above 10 ppm starts stressing fish and corals.

FAQ

Why won't my pH go above 7.9 even with 9 dKH alk?
Room air CO₂. A typical indoor environment runs 800–1,500 ppm CO₂ (vs 420 ppm outdoor), and air exchange with the tank pulls dissolved CO₂ up. The fix: feed the skimmer air-pump line with outdoor air via airline tubing through a window, or run a CO₂ scrubber. Alkalinity is correct; the air is the problem.
Is high CO₂ harmful to coral?
Indirectly. Coral builds CaCO₃ skeleton — high dissolved CO₂ drops pH, which shifts the carbonate equilibrium away from CaCO₃ precipitation. SPS growth slows even when alk is in the green band. Long-term reef monitors usually correlate stunted SPS growth with low daytime pH.
Does temperature matter for this equation?
Yes, slightly. pK₁ = 6.35 is the 25 °C value; it shifts to 6.30 at 30 °C and 6.40 at 20 °C. For reef temperatures (76–82 °F) the error is under 5 % — negligible compared to test kit accuracy.
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Sources & references

  1. 01
    UKAPS — Water pH by dKH and CO₂ values (formula reference)
    https://www.ukaps.org/forum/threads/water-ph-by-dkh-and-co2-values.77203/
  2. 02
    Randy Holmes-Farley — Carbonate chemistry primer
    https://reefs.com/magazine/aquarium-chemistry-magnesium-in-reef-aquaria/

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