Soil Chemistry & Agricultural Hydrology
Soil Sodium Adsorption Ratio (SAR) & ESP Formula
Calculate USDA Salinity Lab Sodium Adsorption Ratio SAR = Na / SQRT((Ca + Mg) / 2) in meq/L, Empirical Exchangeable Sodium Percentage (ESP), and Normal / Saline / Sodic / Saline-Sodic soil class.
Diagnose clay dispersion hazard from meq/L cations—never raw mg/L ppm!
Excess monovalent Sodium (Na+) relative to divalent Calcium (Ca2+) and Magnesium (Mg2+) disperses clay aggregates, sealing soil pores and halting water infiltration! Under USDA Agriculture Handbook No. 60 (Richards, 1954), all soluble cations in saturated paste extract MUST first be expressed in milliequivalents per liter (meq/L = mg/L divided by equivalent weight: Na 23.0, Ca 20.04, Mg 12.15—never plug raw ppm mg/L into SAR!): Sodium Adsorption Ratio is SAR = Na / SQRT((Ca + Mg) / 2)! From SAR, the U.S. Salinity Lab regression predicts solid-phase Exchangeable Sodium Percentage ESP = (100 * (-0.0126 + 0.01475 * SAR)) / (1 + (-0.0126 + 0.01475 * SAR)), classifying soils across Electrical Conductivity EC_e = 4.0 dS/m and ESP = 15.0%!
Verify on Soluble_Sodium Na = 12.0 meq/L (B2), Soluble_Calcium Ca = 4.0 meq/L (B3), Soluble_Magnesium Mg = 4.0 meq/L (B4 -> (Ca + Mg) / 2 = 4.0, SQRT = 2.0), and Paste_Conductivity EC_e = 2.50 dS/m (B5): SAR equals 12.0 / 2.0 = 6.00 (E2); Predicted ESP is 7.05% (E3, < 15.0%); Protective Divalent Cation Share (Ca + Mg) / (Na + Ca + Mg) is 8 / 20 = 0.4000 (E4); and USDA Class is "Normal Soil (ECe < 4 & ESP < 15)" (E5)! Spike Na to 32.0 meq/L (SAR = 16.00, ESP = 18.26% >= 15.0%): at EC_e = 2.50 soil becomes "Sodic Soil (Gypsum Required)", and at EC_e = 6.00 it becomes "Saline-Sodic Soil"!
| USDA Soil Chemistry Metric (Na=12, Ca=4, Mg=4 meq/L, ECe=2.5 dS/m) | Formula | Verified Output |
|---|---|---|
| Sodium Adsorption Ratio (SAR) | Na / SQRT((Ca + Mg) / 2) | 6.00 (16.00 @ Na=32) |
| Predicted Exchangeable Sodium ESP | 100*k / (1 + k), k=-0.0126+0.01475*SAR | 7.05% (18.26% @ Na=32) |
| Divalent Cation Share | (Ca + Mg) / (Na + Ca + Mg) | 0.4000 (40.00%) |
| USDA Handbook 60 Classification | ECe >= 4 vs ESP >= 15 Matrix | Normal Soil (ECe < 4 & ESP < 15) |
USDA SAR & Empirical ESP Formula
Clamp ESP at MAX(0, ...) when Na = 0 (since the linear intercept -0.0126 produces a tiny -1.28% artifact at SAR = 0) and require Ca + Mg > 0!
=LET(na_c, B2, ca_c, B3, mg_c, B4, ec_e, B5, IF(OR(na_c < 0, ca_c < 0, mg_c < 0, ca_c + mg_c <= 0, ec_e < 0), "Invalid Cation Assay", LET(sr_v, na_c / SQRT((ca_c + mg_c) / 2), kp_e, -0.0126 + 0.01475 * sr_v, ROUND(MAX(0, (100 * kp_e) / (1 + kp_e)), 2))))Four-Quadrant USDA Salinity-Sodicity Classifier Formula
Distinguish Normal, Saline (leach with low-salt water), Sodic (amend with CaSO4 gypsum BEFORE leaching so clays do not deflocculate!), and Saline-Sodic profiles!
=IF(ISTEXT(E3), E3, IF(AND(B5 >= 4, E3 >= 15), "Saline-Sodic Soil", IF(E3 >= 15, "Sodic Soil (Gypsum Required)", IF(B5 >= 4, "Saline Soil (Leach Salts)", "Normal Soil (ECe < 4 & ESP < 15)"))))Try the example
Use the original values or change them to test your understanding.