Ratio Calculator
Simplify ratios to lowest terms, solve missing proportion values (A : B = C : D), and split monetary amounts by ratio shares.
Ratio Terms (A : B)
Enter positive integer or decimal terms to reduce the ratio to simplest integer form.
Simplified Ratio
How Ratios and Proportions Are Calculated
Pure mathematical formulas for ratio simplification, cross-multiplication proportion solving, and proportional partitioning.
1. Ratio Simplification Formula
To simplify a ratio A : B, divide both numbers by their Greatest Common Divisor (GCD). If inputs contain decimals, multiply by powers of 10 first to convert them to whole numbers.
When to use: Use to express proportions, recipes, aspect ratios, or scale models in their most concise integer form.
2. Proportion Cross-Multiplication Formula
In any proportion where two ratios are equal (A : B = C : D), the product of the extremes (A and D) is equal to the product of the means (B and C).
When to use: Use when scaling dimensions, converting currency/units, or calculating missing quantities in proportional systems.
3. Proportional Split Formula
To split a total sum across ratio parts (R1 : R2 : ... : Rn), first sum all parts to find the total parts. Then multiply the total amount by each part's fraction of the sum.
When to use: Use for sharing business profits, dividing inheritance, splitting bills, or mixing ingredients proportionally.
Practical Calculation Examples
Real-world scenarios illustrating step-by-step numbers, inputs, and verified outputs.
Example 1: Simplify Integer Ratio 12 : 18
Simplify 12 : 18 to lowest terms using GCD.
Example 2: Simplify Decimal Ratio 1.5 : 2.5
Normalize decimals and simplify 1.5 : 2.5.
Example 3: Solve Proportion 2 : 3 = 4 : ?
Find unknown D in proportion 2 : 3 = 4 : D.
Example 4: Solve Reverse Proportion 4 : 8 = ? : 24
Find unknown C in proportion 4 : 8 = C : 24.
Example 5: Split ₹1,000 in Ratio 2 : 3
Partition ₹1,000 proportionally into 2 parts.
Example 6: Split ₹1,000 in 3-Part Ratio 2 : 3 : 5
Partition ₹1,000 proportionally into 3 parts.
Frequently Asked Questions
Clear answers to common questions about simplifying integer and decimal ratios, solving proportions, and dividing amounts proportionally.
What is a ratio calculator?
A ratio calculator is a mathematical tool that compares quantities, reduces ratios to their simplest integer form (A : B), solves missing terms in equivalent proportions (A : B = C : D), and splits amounts into proportional shares.
How do I calculate a ratio using a calculator?
To calculate a ratio, select the mode that matches your goal: use 'Simplify Ratio' to reduce a two-part ratio, 'Solve Proportion' to find an unknown fourth value, or 'Split Amount' to divide a total amount into multiple proportional parts.
How do I find a ratio from two numbers?
To find the ratio between two numbers, enter the two values as Part A and Part B in the 'Simplify Ratio' mode. The calculator computes their Greatest Common Divisor (GCD) and divides both terms to display the simplest integer ratio along with its decimal equivalent.
How do I simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of all terms and divide each term by the GCD. For example, for 12 : 18, dividing both terms by 6 gives the irreducible ratio 2 : 3.
How do I solve a proportion using a ratio calculator?
In the 'Solve Proportion' mode, enter the three known values in the equation A : B = C : D. The calculator uses cross-multiplication (A × D = B × C) to solve for the missing term automatically (e.g., in 2 : 3 = 4 : D, D = (3 × 4) ÷ 2 = 6).
How do you divide an amount in a given ratio?
1) Sum the ratio parts to determine the total number of shares. 2) Divide the total amount by the sum of parts to find the value of one share. 3) Multiply the single-share value by each individual ratio part.
Can I split an amount into more than two parts?
Yes. You can add up to 10 ratio parts (such as 2 : 3 : 5). Each share is computed proportionally using Part = (Total × Part Ratio) / Total Ratio Sum.
How do you simplify ratios with decimal numbers?
Multiply all terms by 10, 100, or 1,000 until they are whole numbers, then divide by their GCD. For example, 1.5 : 2.5 multiplied by 10 becomes 15 : 25, which simplifies by 5 to 3 : 5.
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