Ratio Calculator
Simplify ratios, solve for a missing value, scale a ratio, divide a quantity in a ratio or compare two ratios, with every step shown.
- Greatest common divisor
- 12
- Fraction (first ÷ second)
- 2/3
- Decimal (first ÷ second)
- 2/3 ≈ 0.6667
- Unit ratio
- 1 : 1.5
- Second per one of the first
- First share of total
- 40%
- 2 of 5 parts
- Second share of total
- 60%
- 3 of 5 parts
2/3 compares the first quantity with the second. It is not the first part’s share of the whole, which is 2/5 = 40%.
Visual comparison
Step-by-step solution
Step 1: Find the greatest common divisor (GCD)
Euclid’s algorithm: divide, keep the remainder, repeat until the remainder is 0. The last non-zero remainder is the GCD.
36 = 1 × 24 + 12
24 = 2 × 12 + 0
GCD(24, 36) = 12
Step 2: Divide both terms by the GCD
24 ÷ 12 = 2
36 ÷ 12 = 3
Step 3: Simplified ratio
24 : 36 = 2 : 3
Related tools: reduce and add fractions with the Fraction Calculator, find the greatest common factor with the GCF Calculator, turn a part of a total into a percentage with the Percentage Calculator, or resize screens and images with the Aspect Ratio Calculator.
A ratio compares two quantities, such as 18 boys to 24 girls, written 18 : 24 and simplified to 3 : 4. This ratio calculator simplifies a ratio to lowest terms and shows its GCD, fraction, decimal and percentage forms, solves equivalent ratios with a missing value (A : B = C : x), scales a ratio up or down, divides a quantity in a given ratio and tells you whether two ratios are equivalent.
Whole numbers, decimals and fractions are all accepted, and every answer includes a step-by-step solution built from your numbers and a simple visual of the parts.
What Is a Ratio?
A ratio compares two quantities by showing how many of one there are for each of the other. With 6 red and 9 blue marbles, the ratio of red to blue is written 6 : 9 and read “6 to 9”. Order matters: blue to red is 9 : 6.
- Equivalent ratios describe the same relationship. Multiplying or dividing both terms by the same non-zero number gives an equivalent ratio: 6 : 9, 2 : 3 and 20 : 30 are all equivalent.
- A simplified ratio is the equivalent ratio with the smallest whole numbers. Its terms share no common factor other than 1, so 6 : 9 simplifies to 2 : 3.
- Part-to-part ratios compare one part with another part (red : blue = 2 : 3).
- Part-to-whole relationships compare one part with the total. Red is 2 of every 2 + 3 = 5 marbles, so red is 2/5, or 40%, of the whole.
Ratio Formulas
For a ratio A : B, A is the first quantity and B is the second. Its value as a division, A ÷ B, says how many of the first there are for each one of the second.
Equivalent ratios and cross-multiplication
A : B = C : D means A/B = C/D
so A × D = B × C
A and B are the terms of the first ratio, C and D the terms of the second. Cross-multiplying turns the equal fractions into a simple equation, which is how you solve for a missing value: in 3 : 5 = 12 : x, 3 × x = 5 × 12, so 3x = 60 and x = 20.
Dividing a quantity in a ratio
Part 1 = Total × A ÷ (A + B)
Part 2 = Total × B ÷ (A + B)
The Total is the amount being shared, and A + B is the total number of parts. Dividing 100 in the ratio 2 : 3: there are 5 parts, each worth 100 ÷ 5 = 20, so the shares are 2 × 20 = 40 and 3 × 20 = 60.
Ratio to percentage
Each part’s percentage of the total is A ÷ (A + B) × 100. For 2 : 3, the first part is 2/5 = 40% and the second is 3/5 = 60%. These are shares of the whole: 2 : 3 does not mean the first quantity is 2/3 of the total, although it is 2/3 (≈ 66.7%) of the second quantity.
How to Simplify a Ratio
- Make both terms whole numbers. If a term has decimals, multiply both terms by 10, 100 and so on: 1.5 : 2.25 becomes 150 : 225.
- Find the greatest common divisor (GCD) of the two terms. For 24 : 36, the GCD is 12.
- Divide both terms by the GCD: 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 24 : 36 = 2 : 3.
If a term is 0, the ratio simplifies to 0 : 1 (or 1 : 0), meaning there is none of one quantity. 0 : 0 is undefined because it compares nothing. To find the GCD of larger lists of numbers, use the GCF Calculator.
Ratio Examples
Recipe: flour to sugar
A recipe uses flour and sugar in the ratio 3 : 1. You have 450 g of flour.
Scale factor = 450 ÷ 3 = 150
Sugar = 1 × 150 = 150 g
450 g : 150 g = 3 : 1
Scaling both terms by the same factor keeps the taste the same, whether you make one batch or ten.
Classroom: boys to girls
18 boys and 12 girls
GCD(18, 12) = 6
18 ÷ 6 = 3, 12 ÷ 6 = 2
3 : 2
For every 3 boys there are 2 girls. Boys are 3 of every 5 students, so 60% of the class (a part-to-whole share).
Money: sharing 1,000
Divide 1,000 (₹, $ or any currency) in the ratio 2 : 3
Total parts = 2 + 3 = 5
One part = 1,000 ÷ 5 = 200
2 × 200 = 400 and 3 × 200 = 600
400 and 600
The shares keep the 2 : 3 relationship (400 : 600 simplifies to 2 : 3) and add back up to 1,000.
Map scale
A map scale of 1 : 50,000. Two towns are 6 cm apart on the map.
1 : 50,000 = 6 : x
x = 6 × 50,000 = 300,000 cm
300,000 cm = 3 km
3 km on the ground
A map scale is a ratio with the same unit on both sides: 1 cm on the map stands for 50,000 cm in reality. Convert units only at the end.
Mixture: concentrate to water
Mix concentrate and water in the ratio 1 : 4 to make 2.5 litres
Total parts = 1 + 4 = 5
One part = 2.5 ÷ 5 = 0.5 L
Concentrate = 0.5 L, water = 4 × 0.5 = 2 L
0.5 L concentrate and 2 L water
Concentrate is 1 part in 5, or 20% of the mixture. Note that 1 : 4 is not “1/4 concentrate”: the fraction of the whole is 1/5.
Ratio vs Fraction vs Proportion vs Percentage
These ideas are related but answer different questions. A ratio A : B can be written as the fraction A/B to compare the two quantities, but that fraction is not the part of the whole unless B is the total. With 2 red and 3 blue balls:
| Concept | What it describes | Example |
|---|---|---|
| Ratio | Compares two quantities with each other (part to part), or a part with the whole. | 2 red : 3 blue |
| Fraction | One number divided by another; often a part of a whole. | Red is 2/5 of all the balls |
| Proportion | A statement that two ratios are equal. | 2 : 3 = 4 : 6 |
| Percentage | A fraction out of 100. | Red is 40% of all the balls |
For fraction arithmetic, use the Fraction Calculator; for percentages of a number, the Percentage Calculator; and for how much a value grew, the Percentage Increase Calculator.
Common Uses of Ratios
Cooking and baking
Scale a recipe up or down while keeping ingredients in the same proportion.
Sharing money and costs
Split profits, rent or bills between people according to what each contributed.
Maps, models and drawings
Convert between a scale drawing and real life, such as 1 : 50,000 on a map or 1 : 24 for a model.
Mixing and dilution
Mix paint, concrete, fuel or cleaning solutions in the right parts.
Screens and images
Aspect ratios such as 16 : 9 describe the shape of a screen or photo.
Finance and statistics
Compare quantities such as debt to income, students to teachers or wins to losses.
For screen and image dimensions, the Aspect Ratio Calculator works out matching widths and heights. To convert map or recipe amounts between units after scaling, use the Unit Converter.
How to Use the Ratio Calculator
- Choose a tool: simplify a ratio, solve A : B = C : D for a missing value, scale a ratio, divide a quantity in a ratio, or compare two ratios.
- Enter the ratio terms. Whole numbers, decimals (1.5) and fractions (3/4) are accepted; ratio terms cannot be negative.
- To solve for a missing value, fill in three of the four boxes and leave the unknown one empty (or type x).
- Read the highlighted answer, then the step-by-step working, which uses your numbers, and the visual comparison of the parts.
- In Simplify mode, also read the fraction, decimal and percentage forms: the percentages are each part’s share of the total.
Frequently Asked Questions
How do you simplify a ratio?
Divide both terms by their greatest common divisor (GCD). For 24 : 36, the GCD is 12, and 24 ÷ 12 = 2, 36 ÷ 12 = 3, so the ratio simplifies to 2 : 3. If the terms have decimals, first multiply both by 10, 100, and so on to make them whole numbers.
How do you calculate a ratio?
Write the two quantities in order with a colon between them, then simplify. With 18 boys and 24 girls, the ratio of boys to girls is 18 : 24, which simplifies to 3 : 4.
How do you solve an equivalent ratio?
Write A : B = C : D as A/B = C/D and cross-multiply: A × D = B × C. For 3 : 5 = 12 : x, 3x = 60, so x = 20. You can also scale: 12 is 3 × 4, so x = 5 × 4 = 20.
How do you find a missing value in a ratio?
Cross-multiply the two known diagonal terms and divide by the remaining known term. In 2 : 5 = x : 20, x = 2 × 20 ÷ 5 = 8.
How do you divide a number in a ratio?
Add the ratio terms to get the number of parts, divide the total by that number to find one part, then multiply each term by one part. 100 in the ratio 2 : 3: 5 parts, one part = 20, so the shares are 40 and 60.
How do you convert a ratio to a percentage?
Divide each term by the sum of the terms and multiply by 100. For 2 : 3, the parts are 2/5 = 40% and 3/5 = 60% of the total. These are shares of the whole, not the first term as a percentage of the second.
What is the difference between a ratio and a fraction?
A ratio compares quantities with each other (2 red : 3 blue); a fraction is a single number, often a part of a whole (red is 2/5 of the balls). A ratio A : B can be written as A/B to compare the two terms, but A/B is only the part of the whole when B is the total.
Can ratios contain decimals?
Yes. A ratio such as 1.5 : 2.25 is valid; to simplify it, multiply both terms by 100 to get 150 : 225, then divide by the GCD (75) to get 2 : 3. Fractions work the same way: 1/2 : 3/4 = 2 : 3.
Can a ratio contain zero?
One term can be zero: 0 : 5 means there is none of the first quantity, and it simplifies to 0 : 1. A ratio of 0 : 0 is undefined, because it compares nothing.
What is an equivalent ratio?
Equivalent ratios describe the same relationship, and you get one by multiplying or dividing both terms by the same non-zero number. 2 : 3, 4 : 6 and 20 : 30 are equivalent because 2/3 = 4/6 = 20/30.
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Last updated: September 29, 2026.