Use this chemistry calculator to reproduce a named relationship with explicit quantities and units for study, laboratory planning, or an independent numerical check.

Madelung constant

Optional number input.

Interionic distance (nm)

Required number input.

Charge product z+ times z-

Required integer input.

Estimate electrostatic Madelung energy U = -138.935*A*|z+z-|/r for an ion pair, with interionic distance r in nanometres; short-range repulsion is not included. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Lattice energy (kJ/mol)

The resulting lattice energy returned as a number.

• Crystallographic calculations assume the stated ideal lattice, indexing, wavelength, occupancy, and unit-cell geometry. Defects, strain, texture, thermal expansion, mixed phases, and instrumental corrections are outside the compact model.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check units and significant figures, compare the result with limiting cases, and use measured or source-specific constants where available. Laboratory, safety, and regulatory decisions require validated methods and appropriate uncertainty analysis.

• DLVO Interaction Energy Estimate

  Combine a user-specified exponentially screened electrostatic repulsion with the non-retarded sphere–plate van der Waals term −AR/(6h). This is a simplified DLVO energy model, not a stability verdict for arbitrary colloids.

• Analytical Detection Limit

  Estimate a detection limit from response standard deviation and calibration slope using the stated 3.3σ/slope convention. This is one common calibration-based estimate, not a universal regulatory limit.

• Analytical Relative Standard Deviation

  Calculate relative standard deviation from a supplied sample standard deviation and mean: RSD%=100s/|mean|. The mean cannot be zero; this is a precision measure, not an accuracy estimate.