Hydroponic Nutrient Calculator: Salt Weights, ppm and EC

The recipe benchmarks are Hoagland and Arnon, Circular 347, revised January 1950, printed p. 31 (attached OCR page 22). Solution 1 uses 1, 5, 5 and 2 mmol/L of KH₂PO₄, KNO₃, Ca(NO₃)₂ and MgSO₄. Solution 2 substitutes NH₄H₂PO₄ at 1 mmol/L, with 6 mmol/L KNO₃ and 4 mmol/L Ca(NO₃)₂.

Salt allocation. Convert elemental mass concentrations to molar concentrations. Match Ca, Mg and P first. Remaining nitrogen is the target less two nitrogen atoms per calcium nitrate and any nitrogen from ammonium phosphate. Use the smaller remaining N and K requirement as KNO₃; fill remaining K with K₂SO₄. All masses remain nonnegative. Sulfur follows from the sulfate salts, so it is reported against a comparison target. The procedure is a stated priority rule, not a least-squares optimizer. Salt mass is concentration × molar mass × final volume. Molecular masses are derived from the named chemical formulas and conventional rounded atomic weights.

Stock dilution. For multiplier f, make each assigned stock to V/f and dose that entire volume into a final batch V. Thus a 100× A/B pair supplies 10 mL A and 10 mL B per final liter. A and B together displace 2% of the final volume; do not add them to an already full reservoir.

Conductivity. McCleskey et al. (2012), equations 7–9 and Table 1, printed pp. 371–372: κ = Σ λᵢmᵢ, I = ½Σmᵢzᵢ², and λᵢ = λᵢ⁰(T) − Aᵢ(T)√I/(1+Bᵢ√I). Apply the published ion coefficients for Ca²⁺, Mg²⁺, K⁺, NH₄⁺, NO₃⁻ and SO₄²⁻. This implementation uses the original Table 1 calcium polynomial, rather than a later alternative fit.

A reduced mass-action calculation removes neutral CaSO₄ and MgSO₄ pairs using the temperature expressions in the attached USGS phreeqc.dat snapshot and Davies activities (A approximated as 0.509). A sulfate mass balance is solved by bisection and ionic strength is iterated. H₂PO₄⁻ uses the Nernst–Einstein relation F²D/(RT) with PHREEQC D₂₅ = 0.846×10⁻⁹ m²/s; its temperature response follows the K⁺ limiting-conductivity ratio as an explicit approximation. Ion molalities are approximated from molarity using 1 kg water per liter. This reduced model is not a full PHREEQC/WATEQ implementation.

• Pure Ca(NO₃)₂·4H₂O, KNO₃, KH₂PO₄ or NH₄H₂PO₄, MgSO₄·7H₂O, and K₂SO₄. No fertilizer-grade ammonium nitrate blend or purity correction.
• Low-mineral source water. Custom targets represent required additions; the tool does not include background ions or estimate their conductivity from a blank EC.
• Final pH is approximately 5–6.5, with phosphate represented as H₂PO₄⁻ and ammonium as NH₄⁺. No pH prediction or acid/base dosing is performed.
• CaSO₄ and MgSO₄ association are included; phosphate complexes, KSO₄⁻, H⁺/OH⁻ contributions, and other species are omitted. Phosphate mobility outside 25 °C is approximate.
• Iron, trace elements, chelates, acids, disinfectants and other additives are excluded. The calculated macronutrient mixture is not a complete plant feed.
• The drawing is an original schematic of the recommended separate-stock procedure, independent of the deliberately incompatible combined-stock assessment option.

Salt mass balances apply to the displayed pure chemical forms and a positive final volume. The nitrogen and potassium priorities cannot meet every custom profile; warnings and the achieved profile disclose the mismatch. Sulfur is comparison only.

EC is a screening estimate for 15–30 °C, ionic strength ≤0.05 mol/kg, and dilute nutrient additions in low-mineral water. The single-salt conductance reference cases do not establish an error bound for a complete mixture. Do not transfer the original paper’s natural-water accuracy claim to this reduced speciation model. Verify actual EC and pH after mixing.

Separate calcium from concentrated phosphate and sulfate. Add A and B individually into the reservoir water, mix, then top up to final volume. Stock separation is qualitative compatibility guidance, not a precipitation or mixed-salt solubility calculation. Check solubility at the coldest storage temperature, particularly above 100×. Do not infer crop suitability from an EC number.