Ratio of 3 Numbers Calculator
Simplify, normalize, scale, divide, or complete an equivalent three-part ratio with live checks and a ready-to-download Excel workbook.
Inputs
Live results
1 : 2 : 4
The ratio is reduced by dividing every term by 100.
0.01
700
7
100
Term-by-term comparison
| Original term | Original value | Result term | Result value | Applied factor |
|---|---|---|---|---|
| A | 100 | D | 1 | 0.01 |
| B | 200 | E | 2 | 0.01 |
| C | 400 | F | 4 | 0.01 |
Each result term is its matching original term multiplied by the same scale factor. That shared multiplier is the defining check for an equivalent ratio.
How to use this ratio of 3 numbers calculator
What this calculator does
This calculator transforms a three-part ratio written as A : B : C into a new ratio D : E : F while preserving the relationship among all three terms. It can reduce a ratio to its simplest whole-number form, normalize one chosen term to 1, multiply or divide every term by the same factor, or calculate an equivalent ratio from one known result term. Ratios compare relative quantities; they do not by themselves identify units, totals, probabilities, or causation. For a formal introduction to ratio notation and interpretation, see the OpenStax lesson on ratios and rates.
When to use it
Use the tool when scaling a recipe with three ingredients, comparing a three-color mixture, resizing a design specification, allocating a total among three groups, or checking whether two three-term ratios are proportional. It is also useful for classroom work where you need to show the same ratio in several forms, such as 100 : 200 : 400, 1 : 2 : 4, and 2 : 4 : 8.
How to calculate
- The calculator opens with the demonstration ratio 100 : 200 : 400 and immediately simplifies it to 1 : 2 : 4. The Excel download is already available for this example.
- Choose an Operation. For a basic reduction, leave it on Simplify ratio. Select a normalization option to make A, B, or C equal to 1. Select multiply or divide to reveal Factor k. Select equivalent ratio to reveal Known result term and Known result value.
- Replace A, B, and C with your values. Results update live. Read the large Resulting ratio D : E : F, then use the supporting metrics and term-by-term table to verify the transformation.
- Select Download Excel to export the current validated inputs and results as a real .xlsx workbook. Reset clears the demonstration and all data fields; Excel export is then disabled until a complete valid ratio is entered again.
Input guide
Operation is required and controls the mathematical transformation. Simplify removes the greatest common divisor after decimal places are aligned; normalization divides every term by A, B, or C; multiply and divide apply the same positive factor; equivalent ratio derives the factor from one known D, E, or F value. A common mistake is changing only one term, which destroys proportionality.
A, B, and C are required non-negative decimal numbers. Enter plain U.S.-style numbers such as 12, 1.5, or 1,250.75; use a decimal point, not a decimal comma, and do not use scientific notation. Up to six decimal places are accepted, each value must not exceed 1,000,000,000, and at least one term must be positive. Zero is valid when the other terms define a meaningful ratio, such as 0 : 2 : 4. Increasing one source term changes its relative share and therefore changes the simplified or normalized result.
Factor k is required only for multiply and divide. It is a positive number such as 2, 0.5, or 1,000. Multiplying by 2 turns 1 : 2 : 4 into 2 : 4 : 8; dividing by 2 turns it into 0.5 : 1 : 2. A zero or negative factor is rejected because it does not produce the intended equivalent scaling operation.
Known result term is required for the equivalent-ratio mode and identifies whether your known target is D, E, or F. The selected term must correspond to a positive source term: D uses A, E uses B, and F uses C. Known result value is the positive target amount, for example D = 2. The calculator divides the target by its matching source term to find the common multiplier, then applies that multiplier to all terms. Selecting a source term that is zero is a common error because no finite multiplier can turn zero into a positive target.
Output guide
Resulting ratio D : E : F is the transformed three-part ratio. It is an exact proportional identity within the calculator's supported decimal precision, not a recommendation. Scale factor is the single multiplier applied to A, B, and C. A value below 1 reduces every term, a value above 1 enlarges every term, and 1 means the ratio is unchanged. Original total and Result total are sums of the three terms; they are useful for comparing scale, but the totals do not affect whether the ratios are equivalent. Common divisor / basis shows the divisor used for simplification, the source term used for normalization, Factor k for multiply or divide, or the selected source term in equivalent-ratio mode.
The summary pills repeat the active operation, resulting ratio, and human-readable scale action. The Term-by-term comparison table maps A to D, B to E, and C to F. Its Applied factor column should be identical in every row. That equality is the practical proportionality check described in the OpenStax guide to proportions.
Worked example
The startup example uses A = 100, B = 200, and C = 400 with Simplify ratio. The greatest common divisor is 100, so each term is divided by 100:
100 ÷ 100 : 200 ÷ 100 : 400 ÷ 100 = 1 : 2 : 4The displayed scale factor is 0.01, the original total is 700, and the result total is 7. Every table row confirms the same multiplication: 100 × 0.01 = 1, 200 × 0.01 = 2, and 400 × 0.01 = 4. The greatest common factor explanation shows why dividing all terms by the largest shared factor produces the simplest whole-number form.
How the ratio model works
Two three-term ratios are equivalent when one common finite multiplier converts every source term into its matching result term. In symbols, D = A × k, E = B × k, and F = C × k. The calculator never scales terms independently. Simplification is a special case: decimal places are first aligned so the terms can be treated as integers, their greatest common divisor is found, and all three are divided by that divisor. If the divisor is 1, the ratio is already in simplest whole-number form.
Normalization is also a special case of common scaling. To normalize A to 1, the multiplier is 1 ÷ A. The same idea applies to B or C. Because division by zero is undefined, a zero term cannot be selected as the normalization basis. Equivalent-ratio mode follows the same rule: if D is known, k = D ÷ A; if E is known, k = E ÷ B; and if F is known, k = F ÷ C.