How do I compute the mix ratio (alligation alternate)?

Use cross-differences: parts of stock 1 = |C2 − Ct|, parts of stock 2 = |C1 − Ct|, then scale to any total.

What if the target concentration lies outside C1 and C2?

Alligation alternate requires Ct to be between C1 and C2. Otherwise, the blend is impossible without a third component (e.g., pure solvent).

Can I mix % and ppm in the same calculation?

No. Convert so all concentrations use the same unit (all % or all ppm) before calculating.

Do I need the total amount to get an answer?

No. The ratio is independent of total. Provide a total only if you want explicit quantities of each component.

What’s the difference between alligation alternate and medial?

Alternate finds the ratio of two sources to hit a target strength. Medial computes the resulting concentration from 2–5 sources via a weighted average.

Does density matter in these calculations?

This tool assumes like-for-like basis (all mL or all g). If density differs substantially, work in mass units—or convert volumes using density—before applying alligation.

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Alligation Calculator

Mix two or more solutions/solids at different strengths to get a target concentration (alligation alternate & alligation medial).

Background

Alligation (alternate) finds the ratio of two stocks (C₁ and C₂) to make a target strength C_t. The classic cross-difference gives parts of each stock. Alligation (medial) finds the resulting concentration from multiple components by a weighted average.

Enter mixture data

Mode:

Choose alternate for 2-source blend; medial for 2–5 sources.

Concentration unit:

Calculator treats inputs consistently; no unit conversion here.

Show:

Step-by-step working

Mini ratio chart

Round to sensible significant figures

Alligation Alternate (two stocks):

If total amount is provided, the calculator returns actual quantities; otherwise it returns the simplest ratio.

Alligation Medial (2–5 sources):

Quick picks:

Result:

No results yet. Enter inputs and click Calculate.

How to use this calculator

Alternate: enter C₁, C₂, target C_t (and optional total). Get ratio and quantities.
Medial: add 2–5 sources with amount + concentration. Get the resulting concentration.
Units are treated consistently (e.g., all % or all ppm). No auto-conversion.

Formula & Equation Used

Alternate (two sources): parts of 1 = |C₂ − C_t|; parts of 2 = |C₁ − C_t|; ratio = parts₁ : parts₂.

Medial (weighted average): C_mix = (Σ amountᵢ·Cᵢ) / (Σ amountᵢ).

Example Problems & Step-by-Step Solutions

Example — 10% & 2% → 5% (1000 mL)

Parts of 10% = |2 − 5| = 3; parts of 2% = |10 − 5| = 5 → ratio 3:5.
Total parts = 8 → Stock 10% = 1000×(3/8)=375 mL; Stock 2% = 625 mL.

Example — Medial of three batches

(200×12 + 300×8 + 500×5)/(200+300+500) = (2400+2400+2500)/1000 = 7.3%.

Frequently Asked Questions

Q: Can I mix % and ppm?

No. Convert first so all concentrations use the same unit.

Q: Does the total amount matter in alternate?

Only if you want actual quantities; otherwise the ratio alone is returned.

Q: Is density involved?

This tool assumes like-for-like basis (e.g., all mL or all g). Provide mass if density matters.

Solutions