Find a two-source mixture ratio
Alligation finds the proportions of a lower-concentration source and a higher-concentration source needed to reach a target between them. Enter all three concentrations on exactly the same basis, then enter the desired total amount. The calculator reports the high-to-low ratio and the amount of each source, followed by a weighted-average check that reproduces the target.
With sources at 20 and 50, a target of 30, and total amount 12 L, high-source parts are 30−20 = 10 and low-source parts are 50−30 = 20. The high-to-low ratio is therefore 1:2, giving 4 L of the higher source and 8 L of the lower source. Their weighted average is 30.
Understand the cross-difference method
The higher-source amount is proportional to target minus low, while the lower-source amount is proportional to high minus target. This apparent crossing keeps the weighted average balanced. Adding those differences gives high minus low, which becomes the total number of parts. Each source amount is its matching part count divided by total parts and multiplied by the requested mixture amount.
The target must lie strictly between the source concentrations. A target outside that interval cannot be produced by combining only those two sources, and an endpoint would require zero of one source rather than a genuine two-source mixture. The page rejects those cases instead of returning negative, infinite, or misleading proportions.
Keep concentration and amount bases consistent
Concentration entries may represent percent, mg/L, mol/L, or another linear measure, but all three must use the same definition and unit. Do not mix mass percent with volume percent or mg/L with mol/L. The amount unit may be volume or mass, provided the concentration definition and physical mixture make that basis appropriate throughout the calculation.
A volume-based calculation assumes the requested final amount can be allocated by the entered source volumes. Real liquids can contract or expand on mixing. A mass-based calculation avoids volume additivity but may require density before comparing with a volume recipe. Choose the basis specified by the problem or preparation method rather than changing units only because the numbers look convenient.
Verify the amounts and target
First add the two displayed source amounts; they should equal the requested total. Then multiply each amount by its concentration, add those contributions, and divide by total amount. The result should match the target within rounding. Moving the target closer to the high source should increase the high-source share, while moving it closer to the low source should increase the low-source share.
Alligation assumes concentration behaves linearly under the chosen basis and that no reaction, evaporation, precipitation, or phase separation changes composition. It is a compact weighted-average calculation, not proof that materials are compatible. If concentrations are supplied with uncertainty, keep appropriate significant figures and avoid interpreting a rounded ratio as a precision formulation.
Compatibility, safety, and privacy
Only combine materials when an authoritative procedure, product label, or qualified professional confirms that doing so is safe and appropriate. This calculator does not identify chemicals, check incompatibilities, validate a medical or industrial formulation, or replace required controls. It answers the arithmetic question after the user has established a legitimate two-source mixing basis.
The values are calculated in the current browser tab. NexaCurrent does not upload the quantities, formulas, chemical names, element choices, or other information entered here, and no account is needed. Copying is a deliberate action after the answer and working are visible. Refreshing or leaving the page clears the current calculation, so keep a copied result if it is needed for later study.