Part to Part Calculator

Calculate part-to-part ratios, compare quantities, and solve proportions

Calculate Part to Part Ratio

What do you want to do?

Part A (First Quantity)

Part B (Second Quantity)

Example:

Simplify 12:18 to 2:3

Results

Enter values to calculate part-to-part ratio

Understanding Part-to-Part Ratios

Part-to-part ratios compare different portions or components to each other, without referencing the total. Unlike part-to-whole ratios that compare a part to the total, part-to-part ratios compare two or more separate quantities directly.

Key Concepts:

Ratio Format: Written as A:B (e.g., 2:3, read as "2 to 3")
Simplified Form: Divide by GCD to get smallest whole numbers
Proportions: Two ratios that are equal (e.g., 2:3 = 4:6)
Decimal Form: First part divided by second (2:3 = 0.667)
Total Parts: Sum of all parts (2+3 = 5 total parts)

Common Applications:

Cooking: Recipe ratios (2 cups flour : 1 cup sugar)
Mixing: Paint colors, concrete mix (2 parts sand : 3 parts gravel)
Demographics: Gender ratios, age group comparisons
Finance: Investment allocations (60% stocks : 40% bonds)
Maps: Scale ratios (1 inch : 1 mile)
Chemistry: Molecular ratios, solution concentrations

Part-to-Part Ratio Formulas

Simplify Ratio

Divide both by GCD

Example: 12:18 → GCD=6 → 2:3

Decimal Ratio

Ratio = A ÷ B

Example: 2:3 = 2÷3 = 0.667

Find Part from Ratio

B = A ÷ (A_ratio ÷ B_ratio)

If ratio is 2:3 and A=10, then B=15

Total of Parts

Total = A + B

Example: 2:3 has 2+3 = 5 total parts

Part as Percentage of Total

% = (Part ÷ Total) × 100

In 2:3, first part = (2÷5)×100 = 40%

Equivalent Ratios

Multiply or divide both by same number

2:3 = 4:6 = 6:9 = 10:15

Common Part-to-Part Ratio Examples

Original Ratio	Simplified	Decimal	Total Parts	Common Use
2:3	2:3	0.667	5	Basic ratio
12:18	2:3	0.667	30	Proportional
16:9	16:9	1.778	25	Screen aspect
3:2	3:2	1.500	5	Photo ratio
1:1	1:1	1.000	2	Equal parts
4:1	4:1	4.000	5	Fuel mixture

Frequently Asked Questions

What is a part-to-part ratio?

A part-to-part ratio compares different portions or quantities to each other directly. For example, if there are 12 boys and 18 girls in a class, the boy-to-girl ratio is 12:18 (simplified to 2:3). This compares boys directly to girls, not to the total number of students. Part-to-part ratios are written as A:B and read as 'A to B'.

How do I simplify a ratio?

To simplify a ratio, divide both parts by their greatest common divisor (GCD). For example, to simplify 12:18: find GCD of 12 and 18 (which is 6), then divide both by 6: 12÷6 = 2 and 18÷6 = 3, giving you 2:3. The simplified ratio maintains the same proportional relationship but uses the smallest whole numbers possible.

What's the difference between part-to-part and part-to-whole ratios?

Part-to-part ratios compare separate components to each other (boys to girls = 12:18), while part-to-whole ratios compare one component to the total (boys to total students = 12:30). In the same example with 12 boys and 18 girls: part-to-part is 12:18 (boys:girls), while part-to-whole is 12:30 (boys:total) or 18:30 (girls:total).

How do I find a missing value in a proportion?

Use cross-multiplication or maintain the ratio. If the ratio is 2:3 and you know one new value, divide or multiply to find the other. For example, if the ratio is 2:3 and the first part is now 10, calculate: 10÷2 = 5 (multiplier), then 3×5 = 15 for the second part. So 10:15 maintains the 2:3 ratio. Alternatively, use the decimal ratio: if 2:3 = 0.667, then 10÷0.667 = 15.

How do I convert a ratio to a percentage?

First find the total of all parts, then divide each part by the total and multiply by 100. For ratio 2:3, total parts = 2+3 = 5. First part percentage = (2÷5)×100 = 40%. Second part percentage = (3÷5)×100 = 60%. Note that these percentages add up to 100% because they represent parts of the whole.

How do ratios work in cooking and mixing?

Cooking ratios maintain proportions when scaling recipes. If a recipe uses a 2:1 ratio of flour to sugar (2 cups flour : 1 cup sugar), you can scale it proportionally: 4:2, 6:3, or 10:5. The ratio stays the same. For mixing (like concrete at 2:3:1 for cement:sand:gravel), multiply each part by the same amount to get the quantities you need while maintaining the proper mixture.