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Ratio Calculator — Simplify & Solve Ratios
Simplify ratios, solve proportions, and scale recipes or measurements. The fastest ratio calculator online with step-by-step solutions.
What is this calculator?
The Ratio Calculator simplifies ratios to their lowest terms, solves for a missing value in a proportion (a:b = c:d), and computes the decimal equivalent of a ratio. It uses the concept of equivalent ratios and cross-multiplication.
Formula
To simplify a ratio a:b, divide both terms by their greatest common divisor (GCD). To find d in a:b = c:d, use cross-multiplication: d = (b * c) / a. The decimal is a / b.
Example
For inputs a=8, b=12, c=6, the calculator simplifies 8:12 to 2:3, finds d = (12*6)/8 = 9, and shows decimal 8/12 = 0.6667.
How to use
- 1Enter the values for a and b (required). Optionally, enter a value for c to solve for d in the proportion a:b = c:d.
- 2Click Calculate. The tool computes the GCD of a and b to simplify the ratio, performs cross-multiplication if c is provided, and divides a by b for the decimal.
- 3The results show the simplified ratio (Simplified A : Simplified B), the missing value D (if c was entered), and the decimal representation of a/b.
Frequently Asked Questions
How do you simplify a ratio like 15:25?
Find the GCD of 15 and 25, which is 5. Divide both terms by 5: 15/5 = 3, 25/5 = 5, so the simplified ratio is 3:5.
What does the 'D (if C given)' output mean?
If you provide a value for c, the calculator solves the proportion a:b = c:d for d using cross-multiplication: d = (b * c) / a. This gives the fourth proportional.
Can I use this calculator for scaling recipes?
Yes. For example, if a recipe uses 2 cups flour to 3 cups sugar (2:3) and you want to use 4 cups flour, enter a=2, b=3, c=4 to find you need d=6 cups sugar.
What does the decimal output represent?
The decimal is the value of a divided by b. For a ratio 3:4, the decimal is 0.75, meaning a is 75% of b. It's useful for comparing quantities.
Is there an official standard for simplifying ratios?
Ratio simplification follows the mathematical principle of dividing by the greatest common divisor (GCD), which is a standard arithmetic method. There is no specific regulatory authority for ratio simplification.