Charge Balance Error Calculator
Chemistry
Free charge balance error calculator for water analyses. Converts mg/L to meq/L, sums cations and anions, reports the balance error against the ±5% criterion, and computes…
Groundwater Calculators
Browser-based tools for groundwater flow and water chemistry. Every calculator shows the equation it uses, cites where that equation came from, and tells you when it stops being valid.
Free groundwater calculators: Darcy’s law, the Theis solution for pumping tests, reference evapotranspiration by five methods, charge balance error, and concentration unit conversion from a mineral formula.
Most engineering calculators give you a number and nothing else — no equation, no source, and no warning when you have pushed a formula past the range it was derived for. Darcy’s law quietly stops describing reality above a pore Reynolds number of about 1, and nothing on the web tells you when you have crossed it. These tools do.
Nothing is uploaded. Every calculation runs in your browser.
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Why another calculator
Three things are different here, and each of them exists because getting them wrong is common in practice.
Every tool states where it stops working. A formula has a domain of validity, and outside it the answer is not merely imprecise — it is wrong. The Darcy calculator computes a pore Reynolds number and tells you which regime you are in. The Theis calculator reports whether the Cooper–Jacob approximation may be used at your radius and time. Tools that follow will do the same for their own limits.
Every equation is sourced. Not “as found in the literature”, but the actual paper or textbook, with the table number where a reference value came from. You should be able to check the work.
Quantities that are easy to confuse are shown side by side. Darcy flux and seepage velocity differ by a factor of 1/n; using one where the other belongs is the most frequent error in contaminant travel-time work. Both appear in the output, always.
The articles behind the tools
These calculators are the working end of the writing on this site. The Groundwater Science series derives the equations and then solves the same problems numerically with MODFLOW, FloPy and PHREEQC — the pumping test the Theis calculator evaluates at a point is fitted to a full drawdown curve in the series, and the water analysis this charge-balance tool validates is the input a speciation run begins with.