Article — Mixing Ratio Calculator
Mixing Ratio Calculator: Blend Two Solutions to a Target Concentration
A mixing ratio is the proportion in which two components combine to form a mixture. The final concentration follows the mass-balance formula C_f = (C1 V1 + C2 V2) / (V1 + V2). To hit a target concentration, the alligation shortcut gives the parts ratio directly: (C2 − C_target) parts of A to (C_target − C1) parts of B.
The math is the same whether you are diluting concentrated bleach, formulating epoxy, blending two-stroke fuel, or preparing a buffer in the lab. The mixing ratio calculator handles the two most common cases: predicting the result of combining known volumes, or solving for the volume needed to reach a chosen concentration.
What a mixing ratio means
Two solutions of the same solute but different concentration can be combined to make a third solution. The total amount of solute is conserved: whatever was dissolved in the two starting solutions ends up in the final blend. Dividing the total solute by the total volume gives the final concentration.
Mixing ratio is usually expressed in parts by volume (1:1, 7:3, 50:1) or by mass, depending on the industry. Paint and resin labels favor volume; pharmacy labels often favor weight; gas mixtures use mole fractions. The calculator works in any consistent unit so long as the two concentration inputs match and the two volume inputs match.
The mixing ratio mass balance
The fundamental formula is a one-line mass balance:
C_f = (C1 V1 + C2 V2) / (V1 + V2) final concentrationV2 = V1 (C_t − C1) / (C2 − C_t) solve V2 for targetA: B = (C2 − C_t): (C_t − C1) alligationBoth inputs must use the same concentration unit (both percent by mass, both mol/L, both ppm), but the calculator does not care which one as long as you stay consistent. Mass-balance assumes the volumes add: V_total = V1 + V2.
Alligation: the parts shortcut
The alligation cross is a memorable mental shortcut taught in pharmacy and culinary courses. Write the higher concentration on top and the lower concentration on the bottom; the target sits in the middle. Subtract diagonally: the difference between the target and the lower concentration is the parts of higher needed, and the difference between higher and target is the parts of lower needed.
For a 25% target from 10% (A) and 50% (B) stocks, the parts are (50 − 25): (25 − 10) = 25: 15, simplified to 5: 3. So 5 mL of A for every 3 mL of B will give exactly 25%.
Mixing ratio worked examples
Diluting bleach. Commercial household bleach is roughly 5.25% sodium hypochlorite. To make a 0.5% disinfecting solution, the alligation gives parts of bleach: parts of water = (0 − 0.5): (5.25 − 0.5) in absolute value = 0.5: 4.75, about 1: 9.5. So one part bleach to about nine parts water.
Two-stroke fuel. A 50:1 ratio means 50 parts gasoline to 1 part oil. For one liter of fuel: 1000 mL / 51 = 19.6 mL of oil per liter. The ratio is volumetric and the "additivity" assumption is fine because the oil is a small fraction.
Pharmacists used alligation tables in the 1600s, long before the concept of molar concentration existed. The rule survives in modern compounding pharmacies, where blending two stock creams or two strengths of a pediatric syrup to a custom dose is still done with a paper-and-pencil cross.
Mixing ratio units and volume additivity
The simple mass balance assumes V_total = V1 + V2. For most dilute aqueous solutions this is accurate to better than 1%. The textbook exception is ethanol + water: 50 mL ethanol plus 50 mL water gives about 96 mL of solution, not 100 mL, because the molecules pack more tightly together. Concentrated sulfuric acid plus water shrinks even more, and releases a large amount of heat to boot.
| Pair | Volume contraction | Note |
|---|---|---|
| Water + water | 0% | Trivial reference |
| Salt + water (dilute) | < 1% | Negligible for most lab work |
| Ethanol + water (50/50) | ~ 4% | Notable; use mass for precision |
| H2SO4 + water (concentrated) | ~ 5-7% | Plus large exotherm; safety risk |
Common mixing ratios in industry
- 70% isopropyl alcohol: 7 parts 99% IPA + 3 parts water
- 1:10 bleach disinfectant: 1 part 5.25% NaClO + 9 parts water = ~0.5% NaClO
- 50:1 two-stroke fuel: 19.6 mL of 2T oil per 1 L gasoline
- 2:1 epoxy: 2 parts resin + 1 part hardener by volume; cure depends on exact ratio
- 1:3 cement mortar: 1 part Portland cement + 3 parts sand by volume
- 0.9% saline: 9 g NaCl per liter of water (isotonic)
- Phosphate buffer (1x PBS): typically a 1:10 dilution of 10x stock
Mixing ratio mistakes and pitfalls
The single most common slip is trying to reach a target concentration outside the range of the two stocks. You cannot blend a 5% and a 20% solution to make 25%; mass balance forbids it. The target must lie between the two starting concentrations. To go below the lowest stock, mix with pure solvent. To go above the highest, find a more concentrated source or evaporate.
Mixing 100 mL of "5% w/w" with 100 mL of "5% w/v" does not give 5%. The two definitions diverge with density. Always confirm whether percentages are by weight, by volume, or weight-to-volume before you plug into the calculator. Mixing apples-and-oranges concentrations is the leading source of compounding errors.
Other regular slips: ignoring volume contraction in alcohol-water blends, assuming the mixing ratio for two-component adhesives is volumetric when the label specifies mass, forgetting the diluent (water) is itself the "other solution" in a dilution problem, and not stirring long enough to homogenize before measuring concentration.
Mixing ratio safety: order matters
For most cosmetic and food applications the order of addition does not matter. For concentrated acids and bases it matters a great deal. Adding water to concentrated sulfuric acid causes the surface to flash to boiling almost instantly, splashing acid out of the container. The opposite order, slowly adding concentrated acid to a larger volume of water, lets the released heat dissipate into the bulk.
"A.A. - Add Acid to water, Always." The same applies to dissolving concentrated NaOH or KOH; pour the solid into water with stirring, never the other way. Even non-acid solutes can release heat: dissolving anhydrous calcium chloride is exothermic enough to use as a hand warmer.