Repeated Water Change Dilution Calculator
Calculate concentration after repeated equal-fraction water changes and the whole change count needed to reach a reduction target.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply the same complete-mixing recurrence to each drain/refill and invert its geometric reduction where a target is reachable.
Cn=Csource+(Cinitial−Csource)(1−fraction)^n
Worked example
Starting at 100 mg/L with source 0, replacing 25% four times leaves 31.640625 mg/L. Reaching 10 mg/L needs nine complete changes under this model.
Assumptions and input details
Reduction scope requires initial concentration greater than source and target between them. Fractions 0–100%; entered change count 0–1e6. Water is fully mixed before every change, with no new solute, reactions, adsorption, evaporation or decay. The source concentration is approached asymptotically unless fraction is 100%. No chemical dose, organism suitability or water-quality recommendation is inferred.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
The 36 volume definitions distinguish US liquid, US dry and Imperial measures. Cups carry an explicit definition. Japanese shō is 2401/1331 L and a gō is one tenth of it; the explicitly labelled 180 mL rice cup is separate.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · UK Imperial definitions · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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