CO2 from KH and pH calculator, temperature-corrected

How the estimate works

Dissolved CO2 and bicarbonate are linked by the first dissociation of carbonic acid. In water where carbonate is the only significant buffer, the balance can be written as

[CO2] = [HCO3⁻] × 10^(pK1 − pH)

Carbonate hardness (KH) is a measure of alkalinity, the water’s acid-neutralizing capacity, which comes from bicarbonates, carbonates and hydroxides ^[2]. One German degree is defined as 10 mg/L of calcium oxide equivalent, or 17.848 mg/L as CaCO3 ^[3], which corresponds to 0.35665 mmol/L of bicarbonate alkalinity. Seachem’s product directions use the same relationship rounded: 1 meq/L is about 2.8 dKH ^[4]. Multiplying by the molar mass of CO2, 44.009 g/mol ^[5], gives

CO2 (mg/L) = 15.696 × KH (dKH) × 10^(pK1 − pH)

pK1 depends on temperature. The calculator uses the temperature function published by Plummer and Busenberg (1982) for the CO2–water system ^[1]; it gives pK1 = 6.382 at 20 °C, 6.352 at 25 °C and 6.337 at 28 °C. Warmer water therefore holds slightly less CO2 at the same KH and pH reading.

The chart shortcut

Most aquarium CO2 charts use CO2 ≈ 3 × KH × 10^(7 − pH). At 25 °C the equilibrium above works out to 3.53 × KH × 10^(7 − pH), so the chart figure is about 15 % lower than the temperature-corrected estimate. Neither is “the” right value: the chart’s factor of 3 corresponds to a pK1 of about 6.28, below the 6.33–6.38 this temperature function gives between 20 and 30 °C, and both treat the water as an ideal dilute solution. The calculator prints both so you can compare a reading with a chart you already use.

Reference table at 25 °C

CO2 in mg/L from the temperature-corrected formula (pK1 = 6.352):

KH (dKH)	pH 6.4	pH 6.6	pH 6.8	pH 7.0	pH 7.2	pH 7.4
2	28	18	11	7	4	3
3	42	27	17	11	7	4
4	56	35	22	14	9	6
6	84	53	34	21	13	8
8	112	71	45	28	18	11

Each 0.2 pH step changes CO2 by a factor of 1.58, and each full pH unit by a factor of 10. That is why the calculator also shows the result for a pH reading 0.1 higher and lower: a 0.1 error in pH alone moves the estimate by +26 % or −21 %.

Where it breaks

The formula assumes that bicarbonate is the only thing holding the pH up. When something else buffers the water, the measured pH no longer reflects CO2 alone:

• Other buffers. Phosphate buffers, humic and tannic acids from wood, peat and leaves, and many nutrient-rich aqua soils all shift pH without changing CO2.
• pH products. Commercial pH-adjusting buffers do the same by design.
• Measurement. Liquid pH tests are read by eye in steps of 0.2 or more; a calibrated meter is far better, but the 0.1 sensitivity above still applies.
• Timing. CO2 rises after injection starts and falls when plants photosynthesize and the gas escapes at the surface, so a single reading describes one moment.

For water with other buffers, a drop checker isolates a sample of known KH from the tank water and avoids most of these problems; the drop checker guide shows the same arithmetic applied there.

Targets in grower data

Tropica rates plants by CO2 need and defines the ratings on every plant page: a medium need is 6–14 mg/L and a high need approximately 15–25 mg/L ^[6]. Its fertilizer guide gives slightly different bands, about 10–15 mg/L for plants marked “Medium” and 15–30 mg/L for “Advanced”, and recommends adding CO2 until the pH in its KH/pH table is reached ^[7]. The calculator’s lower table shows the pH that corresponds to 10, 20 and 30 mg/L at your KH and temperature.