Recipes
Keep ingredient proportions consistent when changing the number of servings.
Ratio Calculator
Solve equivalent ratios, find a missing value, scale proportions, and see each ratio visually.
Solve A:B = C:DScale ratiosVisual explanations
Solve a Proportion
Enter three positive values and leave the value you want to calculate empty.
Completed proportion
3 : 4 = 600 : 800
D = 800
Calculation steps
D = (B × C) ÷ A
D = (4 × 600) ÷ 3 = 800
- Simplified A:B
- 3 : 4
- First term normalized
- 1 : 1.333333
- Second term normalized
- 0.75 : 1
- First term as share of total
- 42.857143%
A: 3 · B: 4
A
B
How Ratio Calculations Work
Equivalent ratios describe the same relationship. For B = C:D, cross multiplication gives A × D = B × C.
A = (B × C) ÷ D
B = (A × D) ÷ C
C = (A × D) ÷ B
D = (B × C) ÷ A
Scaling formulas
Enlarge: A × factor : B × factor
Shrink: A ÷ factor : B ÷ factor
Worked example: 3:4 = 600:800
D = (4 × 600) ÷ 3 = 800, so 3:4 and 600:800 are equivalent ratios.
Understanding Ratios
A ratio compares two quantities. The notations B, “A to B,” and A/B can all describe the same comparison when the context is clear.
Maps and models
Scale drawings relate a measured distance to a real-world distance.
Rates and odds
Compare quantities such as miles per hour or favorable to unfavorable outcomes.
Screens and video
Aspect ratios compare display width with height, such as 16:9.
Common Screen and Video Aspect Ratios
| Format | Aspect ratio | Resolution |
|---|---|---|
| 480p | 3:2 | 720×480 |
| 576p | 5:4 | 720×576 |
| 720p | 16:9 | 1280×720 |
| 1080p/FHD | 16:9 | 1920×1080 |
| 4K UHD | 16:9 | 3840×2160 |
| XGA | 4:3 | 1024×768 |
| WXGA | 16:10 | 1280×800 |
| WQXGA | 16:10 | 2560×1600 |
Ratio Simplification, Scaling, and Proportions
How do I calculate a missing value in a ratio?
Write the relationship as A:B = C:D, cross multiply to get A × D = B × C, then divide by the coefficient attached to the missing value.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For example, 12:16 simplifies to 3:4 after both terms are divided by 4.
How do I scale a ratio up or down?
Multiply both terms by the same positive factor to enlarge a ratio, or divide both terms by the same positive factor to shrink it.
How do I convert a ratio to a percentage?
For a two-part ratio A:B, the first term is A ÷ (A + B) × 100 percent of the total. The second term makes up the remainder.
What is an equivalent ratio?
Equivalent ratios express the same relationship with different numbers, such as 3:4 and 6:8. Multiplying or dividing both terms by the same nonzero value preserves equivalence.
Can ratios contain decimals?
Yes. Decimal ratios are valid, and they can often be rewritten as whole-number ratios by multiplying both terms by a power of ten before simplifying.
What is an aspect ratio?
An aspect ratio compares width to height. A 16:9 display is 16 units wide for every 9 units high, regardless of its actual pixel dimensions.
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