BIZOMAT MAKEOS · Materials
Mixture Cost and Blending (Alligation)
What does this mixture cost per kilogram, or in what proportions do two ingredients blend to a target value?
Rule of mixtures (alligation): cost or any additive property per unit of a mixture of up to four ingredients by weighted average, and the proportions of two ingredients that blend to a target value (alligation alternate), with the quantities for a batch.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculation | choice | Average a mixture, or find blend proportions. |
| Mixture (quantity 0 = unused) | ||
| Quantity 1 | kg | Quantity of ingredient 1 (any consistent unit). |
| Value 1 (price per kg or property) | Its price per unit or its value of an additive property (for example a concentration). | |
| Quantity 2 | kg | Quantity of ingredient 2. |
| Value 2 | Its value. | |
| Quantity 3 | kg | Quantity of ingredient 3. |
| Value 3 | Its value. | |
| Quantity 4 | kg | Quantity of ingredient 4. |
| Value 4 | Its value. | |
| Blend | ||
| Value of ingredient A | Value of the first blend ingredient (for example concentration %). | |
| Value of ingredient B | Value of the second blend ingredient. | |
| Target value | Value wanted in the blend; must lie between the two. | |
| Batch size | kg | Total quantity to make. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Calculation
- What it is
- What to work out: the weighted average value of a mixture of up to four ingredients, or the shares of two ingredients that blend to a target value.
- Units and format
- Choose one of 2 options from the list: Value of a mixture; Blend two ingredients to a target.
- Example
- The form opens with “Value of a mixture” selected as a worked example. Choose the option that matches your case.
- Get it right
- The mixture option uses quantities and values 1 to 4; the blend option uses A, B, target and batch size.
Mixture (quantity 0 = unused)
What this means: Quantity 1
- What it is
- How much of the first ingredient goes into the mixture. It weights that ingredient’s value in the average.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Any unit works if all four quantities use the same one; a quantity of 0 leaves the ingredient out.
What this means: Value 1 (price per kg or property)
- What it is
- What one unit of the first ingredient is worth: its price per kilogram, or an additive property such as a concentration or density that mixes in proportion.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.7 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Only properties that mix linearly by quantity give a true average; strength or viscosity usually do not.
What this means: Quantity 2
- What it is
- How much of the second ingredient goes into the mixture, in the same unit as the other quantities.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set to 0 to leave this ingredient out.
What this means: Value 2
- What it is
- The price per unit or additive property value of the second ingredient, in the same terms as value 1.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.05 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not mix prices for one ingredient with property values for another.
What this means: Quantity 3
- What it is
- How much of the third ingredient goes into the mixture, in the same unit as the other quantities.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set to 0 to leave this ingredient out.
What this means: Value 3
- What it is
- The price per unit or additive property value of the third ingredient, in the same terms as value 1.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.99 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Prices should be on the same basis, for example all delivered and all excluding GST.
What this means: Quantity 4
- What it is
- How much of the fourth ingredient goes into the mixture, in the same unit as the other quantities.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set to 0 to leave this ingredient out.
What this means: Value 4
- What it is
- The price per unit or additive property value of the fourth ingredient, in the same terms as value 1.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A value is ignored when its quantity is zero.
Blend
What this means: Value of ingredient A
- What it is
- The property of the first blend ingredient that is being averaged, such as its concentration, grade or price per unit, used to find the blend shares.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same property and unit for A, B and the target.
What this means: Value of ingredient B
- What it is
- The matching property of the second blend ingredient, in the same property and unit as ingredient A. It must differ from A.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It does not matter whether A or B is the higher value.
What this means: Target value
- What it is
- The value you want the finished blend to have, in the same property and unit as the two ingredients.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must lie between the values of A and B; no blend of two ingredients can go outside them.
What this means: Batch size
- What it is
- The total quantity of blend you want to make. The tool splits it into the quantities of A and B by the calculated shares.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both ingredient quantities are proportional to the batch size; the shares do not change.
- Get it right
- The shares assume quantities add up; volumes of some liquids do not add exactly.
Method and formulas
- Mixture: value per unit = Σ (quantity × value) ÷ Σ quantity (handbook alloy example: $150.80 ÷ 85 lb ≈ $1.77 per lb).
- Blend: share of A = (v_B − v_T) ÷ (v_B − v_A); share of B = 1 − share of A.
- Example: the four ingredients average 1.7741 per unit.
Limitations
- Valid only for properties that mix linearly by quantity (cost, mass concentration); not for viscosity, strength or hardness.
- Process losses and mixing costs are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Cost an alloy or compound from its ingredients
- Blend two coolants, oils or powders to a target concentration
- Mix two grades to a target property or price
Who it is for
- Process engineers
- Buyers
- Foundry and mixing supervisors
What you get
- Value of the mixture per unit
- Blend proportions
- Quantities for the batch
Interpreting the result
- For coolants and solutions, blend by mass or volume consistently with how the concentration is defined.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 384. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
What well mixed means
In Blending Bulk Solids by the Numbers
What it covers: A blend's quality depends on the scale at which its user takes it. Define the scale of scrutiny, the composition variance and the perfectly segregated and random limits, and set the let-down ratio.
Method explained here · BIZOMAT original book
Molar mass averages, dispersity and regrind blends
In Polymer Chains by the Numbers
What it covers: Calculate number-, weight- and z-average molar masses from a distribution, see which properties follow which average, and blend regrind with virgin resin to a target without averaging the wrong way.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.