Alligation Medial Calculator

Blend solutions with confidence. See the concentration, volume and solute balance together.

Solution parameters

Concentration basis

Use the same solute and compatible concentration basis for every component.

Solution 1Stock solution

Concentration · C1% w/vVolume · V1

Solution 2Stock solution

Concentration · C2% w/vVolume · V2

Solution 3Optional · 0 volume to omit

Concentration · C3% w/vVolume · V3

Measured final volume & advanced settings

Use measured final volumeMeasured final volume

Replaces the sum of stock volumes in medial mode. Input-volume shares still refer to the source mixture.

Solute molar mass (optional)g/mol

Molar mass enables mass ↔ molarity conversion for the same solute. No density or % v/v ↔ mass conversion is assumed.

Conservation, not a compatibility check.
Assumes no reaction or solute loss and additive volumes unless a measured final volume is supplied.

FINAL MIXTURE CONCENTRATION10.00 % w/v

10.00 g per 100 mL · 100.0 mg/mL

Total volume500 mL

Total solute50.0 g

Components3 solutions

Your mixture, visualized

Mass conserved

Solution 1 · 40%Solution 2 · 40%Water · 20%

Glassware and liquid levels are illustrative, not calibrated. Colors identify streams; actual solutions may be colorless.

Adding water changes concentration, not solute mass.

The 50.0 g of solute is spread across 500 mL of final solution.

Solute & volume balance

Σ CᵢVᵢ ÷ Σ Vᵢ

Component	Concentration	Volume	Solute mass	Volume share
Solution 1	20% w/v	200 mL	40.0 g	40.0%
Solution 2	5% w/v	200 mL	10.0 g	40.0%
Pure water	0% w/v	100 mL	0.0 g	20.0%
Final mixture	10.00% w/v	500 mL	50.0 g	100.0%

For % v/v, the solute total is volume-equivalent; for molarity, it is moles. Mass conversion requires the solute’s molar mass.

How alligation medial works

C_mix = (C₁V₁ + C₂V₂ + C₃V₃) / (V₁ + V₂ + V₃)

(20 × 200 + 5 × 200 + 0 × 100) ÷ 500
= 10.00% w/v

Concentrations must share the same basis. A volume-weighted calculation does not apply directly to % w/w.

Need a target concentration?

Alternate mode

Example: mix 20% and 5% stocks to make 500 mL at 10% w/v.

20% stock1 part166.67 mL

5% stock2 parts333.33 mL

High : low = (target − low) : (high − target).
The target must lie between the stock concentrations.

Frequently asked questions

What is the difference between medial and alternate alligation?

Medial calculates the concentration of known quantities. Alternate finds the proportions of two stocks needed to reach a specified intermediate concentration.

Can I mix % w/v, % v/v and molarity directly?

No. These describe different quantities. Only compatible units can be combined; molarity-to-mass conversion requires molar mass, while volume-to-mass conversion needs density information.

What if the volumes are not additive?

Use an experimentally measured final volume when appropriate. The simple sum of stock volumes is an approximation for mixtures with contraction or expansion.

Does this confirm that a mixture is safe or chemically compatible?

No. Compatibility, stability, sterility and suitability for a particular preparation need separate verification.

Enable JavaScript for live calculations. The static example is 20% w/v × 200 mL + 5% w/v × 200 mL + water × 100 mL = 500 mL at 10% w/v, containing 50 g of solute. Formula, example and FAQs remain available.

Sources & Reference Guides

USPPharmaceutical calculationsGeneral Chapter 〈1160〉 · public chapter overview.IUPACGold Book terminologyMass concentration and amount concentration.

Independent reference material · No institutional endorsement or preparation approval.

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