Ratio Calculator
Simplify ratios, compare them, and scale to any target value
Ratio Calculator
Simplify and solve ratios
Simplify a ratio A:B to its lowest terms
Divide both A and B by their GCDWhat is a Ratio Calculator?
A Ratio Calculator is a math tool that helps you compare two or more quantities and express their relationship in a simple form. A ratio shows how much of one thing there is compared to another. Ratios are commonly written using a colon, such as 3:2, or as a fraction, such as 3/2.
Ratios are used in everyday life and many fields: cooking recipes (2 cups flour to 1 cup sugar), mixing solutions (1 part concentrate to 4 parts water), map scales, financial comparisons, and geometry. They are especially useful when you need to scale something up or down while keeping the same relationship between values.
A ratio calculator can simplify ratios, create equivalent ratios, and help solve 'missing value' problems (often called proportion problems). It saves time and reduces mistakes when working with large numbers or decimals.
How to Use This Ratio Calculator
- Enter the ratio values -- Input the two (or more) numbers you want to compare (example: 24 and 36)
- Choose an option (if available) -- such as simplify ratio, find equivalent ratio, or solve for missing value
- Click 'Calculate' -- the calculator processes the ratio
- Review the simplified ratio -- example: 24:36 becomes 2:3
- Use the result -- apply the ratio for scaling recipes, mixing, comparing quantities, or solving proportions
Tips:
- Ratios work best when the values represent the same type of measurement (e.g., both in grams, both in dollars)
- If you use decimals, the calculator may convert them to a simplified whole-number ratio
- If a ratio is used to scale something (like a recipe), make sure you multiply or divide both parts by the same factor
Ratio Formulas
Ratio Simplification
To simplify a ratio a:b, divide both numbers by their greatest common divisor (GCD):
Simplified = (a / gcd(a,b)) : (b / gcd(a,b))
Example: a = 24, b = 36
gcd(24, 36) = 12
24:36 → (24/12):(36/12) = 2:3
Equivalent Ratios
Multiply or divide both parts by the same number k:
(a:b) → (a × k : b × k)
2:3 × 5 → 10:15
Proportions (Missing Value)
A proportion compares two equal ratios: a/b = c/d
Solve using cross-multiplication:
a × d = b × c
If d is unknown: d = (b × c) / a
Example Calculations
Example 1: Simplify a Ratio
Input: 24:36
GCD: gcd(24, 36) = 12
Calculation: 24 ÷ 12 = 2, 36 ÷ 12 = 3
Result: 2:3
Example 2: Create an Equivalent Ratio
Input: 3:8, scaled by 4
Calculation: 3 × 4 = 12, 8 × 4 = 32
Result: 12:32 (simplifies back to 3:8)
Example 3: Recipe Scaling (Real-World Use)
Setup: A drink mix uses a ratio of 1:5 (concentrate : water)
Problem: If you have 3 cups of concentrate, how much water?
Calculation: 1 part → 5 parts, so 3 parts → 3 × 5 = 15 parts
Result: 15 cups of water
Example 4: Solve a Proportion (Missing Value)
Problem: Solve for x in 2/3 = 10/x
Cross-multiply: 2x = 3 × 10 = 30
Solve: x = 30 ÷ 2 = 15
Result: x = 15
Frequently Asked Questions
What's the difference between a ratio and a fraction?
A fraction represents a part of a whole (3/4). A ratio compares two quantities (3:4). Ratios can be written as fractions, but they often represent comparisons rather than parts.
How do I simplify a ratio?
Divide both parts by their greatest common divisor (GCD). For example, 18:24 simplifies to 3:4 because gcd(18,24) = 6, and 18/6 = 3, 24/6 = 4.
Can ratios include more than two numbers?
Yes. You can have ratios like 2:3:5, often used to compare three quantities (for example, ingredient proportions). Simplification usually divides all terms by their common factor.
What does a ratio like 1:5 mean?
It means for every 1 unit of the first quantity, there are 5 units of the second. For example, 1 cup of concentrate to 5 cups of water.
What is a proportion, and why is it useful?
A proportion states that two ratios are equal (a/b = c/d). It's useful for scaling, converting, and solving for unknown values in real-world situations like recipes, maps, and unit conversions.
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What Is a Ratio?
A ratio expresses the relationship between two quantities. Written as A:B (or A/B), it shows how many times one value contains the other. Ratios appear everywhere in daily life: aspect ratios on screens (16:9), recipe measurements (1:2 flour to sugar), financial leverage ratios in investing, and map scales (1:50,000) that let you measure real-world distances from a printed page.
This calculator simplifies ratios to their lowest terms by dividing both parts by their greatest common divisor (GCD). It also compares two ratios to check whether they are equivalent, and scales a ratio to match any given total — so you can instantly find how much of each part you need when the target quantity changes.
How to Use the Ratio Calculator
- Enter the two values of the ratio — A and B.
- Select the operation: simplify, compare, or scale.
- For scaling, enter the target total you want to reach.
- Click Calculate to see the simplified or scaled result instantly.
Formulas & Reference
Simplify A:B — divide both by GCD(A, B)
Example: 12:8 → GCD = 4 → 3:2
Equivalent ratios — cross-multiply to check
A:B = C:D if A × D = B × C
Scale to total T:
Part A = (A / (A + B)) × T
Part B = (B / (A + B)) × T
Part-to-whole:
A / (A + B) = fraction of total for AA ratio A:B is equivalent to the fraction A/(A+B) as a part of the total, or A/B as a direct comparison between the two parts.
Worked Examples
Simplify 15:10
GCD(15, 10) = 5. Divide both sides: 15 ÷ 5 = 3, 10 ÷ 5 = 2. Simplified ratio: 3:2. This means for every 3 units of A there are 2 units of B.
Mix 3:5 cement to sand for 40 kg total
Total parts = 3 + 5 = 8. Cement = (3/8) × 40 = 15 kg. Sand = (5/8) × 40 = 25 kg. Check: 15 + 25 = 40 kg. ✓
Aspect ratio 1920:1080 simplified
GCD(1920, 1080) = 120. Divide both: 1920 ÷ 120 = 16, 1080 ÷ 120 = 9. Result: 16:9 — the standard widescreen aspect ratio used on almost every modern display.