Ratio Calculator
Solve proportions, simplify ratios, and scale values
How to Use This Ratio Calculator
- Choose your task: Solve Proportion, Simplify Ratio, or Scale Ratio
- For proportions (A:B = C:D): enter any 3 values, leave one blank to solve
- For simplifying: enter both numbers of the ratio to reduce to lowest terms
- For scaling: enter the original ratio and your scale factor
- Click the appropriate button to see results with step-by-step solution
Example: Doubling a recipe that uses 2:3 flour to sugar: Scale by 2 to get 4:6. Or solve the proportion 2:3 = 4:x to find x = 6 cups of sugar.
Tip: When solving proportions, cross-multiply: if A:B = C:D, then A x D = B x C. Solve for your unknown.
Why Use a Ratio Calculator?
Ratios and proportions are essential for scaling, comparing, and converting in everyday situations.
- Scale recipes up or down while maintaining ingredient proportions
- Convert map distances to real-world distances using scale ratios
- Calculate aspect ratios for resizing images without distortion
- Mix solutions and compounds in correct proportions (cleaning, concrete, etc.)
- Compare financial ratios like price-to-earnings or debt-to-income
- Solve unit conversion problems and cross-multiply proportions
Understanding Your Results
Ratios in simplest form have no common factors. Proportions show equivalent relationships.
| Result | Meaning | Action |
|---|---|---|
| Simplified ratio | Lowest terms | Both numbers share no common factor except 1 |
| Scale factor applied | Proportionally increased/decreased | New ratio maintains the same relationship |
| Solved proportion | Found the missing value | Verify by checking A x D = B x C |
Meaning: Lowest terms
Action: Both numbers share no common factor except 1
Meaning: Proportionally increased/decreased
Action: New ratio maintains the same relationship
Meaning: Found the missing value
Action: Verify by checking A x D = B x C
Note: Decimal form shows the ratio as a single number - useful for comparing multiple ratios.
About Ratio Calculator
Formula
A:B = C:D implies A x D = B x C Cross-multiplication: multiply the means (inner values) and extremes (outer values). Equal products confirm a valid proportion.
Current Standards: Ratios are typically simplified to lowest terms by dividing both numbers by their GCD (greatest common divisor).
Frequently Asked Questions
How do I simplify a ratio?
Find the GCD (greatest common divisor) of both numbers and divide each by it. For 24:36, GCD = 12, so 24/12 : 36/12 = 2:3. The calculator does this automatically and shows the GCD used.
What's the difference between ratio and rate?
A ratio compares quantities of the same kind (like 2 cups flour to 3 cups sugar). A rate compares different kinds of quantities (like 60 miles per hour or $15 per hour). Rates usually have units; ratios are unitless comparisons.
How do I use ratios to resize images?
Maintain the aspect ratio (width:height). If an image is 1920x1080 (16:9 ratio) and you want width = 800, solve 16:9 = 800:x. Cross-multiply: 16x = 7200, so x = 450 pixels height. This prevents distortion.
What if my proportion has decimals?
The calculator handles decimals fine. You can also multiply all numbers by a power of 10 to eliminate decimals first, then simplify. For example, 0.5:1.5 becomes 5:15 (multiply by 10), which simplifies to 1:3.
How do I scale a three-part ratio?
Multiply all three parts by the same factor. If a concrete mix is 1:2:3 (cement:sand:gravel) and you need 5 bags of cement, scale by 5: you need 10 bags sand and 15 bags gravel. The ratios stay equivalent.