Ratio Calculator
Solve ratios (A:B = C:?), simplify, scale up or down, and compare two ratios. Step-by-step working with a recipe scaling example.
About Ratio Calculator
Solve for missing ratio values, simplify ratios to lowest terms, scale up or down, and compare two ratios for equivalence. Four modes cover every common ratio problem with step-by-step working shown for each calculation.
How to Solve a Ratio Proportion
A proportion states that two ratios are equal: A:B = C:D. If you know three of the four values, you can find the missing one using cross multiplication.
A/B = C/D means A × D = B × C
Worked example: If 3:5 = 12:?, find the missing value
- Set up the proportion: 3/5 = 12/?
- Cross multiply: 3 × ? = 5 × 12
- 3 × ? = 60
- ? = 60 / 3 = 20
- Answer: 3:5 = 12:20
How to Simplify a Ratio
To simplify a ratio, divide both parts by their greatest common factor (GCF):
| Original Ratio | GCF | Simplified |
|---|---|---|
| 12:18 | 6 | 2:3 |
| 45:60 | 15 | 3:4 |
| 24:36:48 | 12 | 2:3:4 |
| 100:250 | 50 | 2:5 |
| 0.5:1.5 | - | 1:3 |
| 2.4:3.6 | - | 2:3 |
For decimal ratios, the calculator first converts to whole numbers by multiplying both sides by the appropriate power of 10, then simplifies. For finding the GCF directly, see the GCF and LCM calculator.
How to Scale a Ratio
Scaling multiplies both parts of a ratio by the same factor. The proportion stays the same but the quantities change.
Worked example: A recipe uses flour and sugar in a 3:2 ratio. You need 750g of flour. How much sugar?
- Scale factor: 750 / 3 = 250
- Sugar: 2 × 250 = 500g
- Scaled ratio: 750:500 (still 3:2)
Ratios, Fractions, and Percentages
Ratios, fractions, and percentages are all ways of expressing the same relationship:
| Ratio | Fraction (of total) | Percentage | Decimal |
|---|---|---|---|
| 1:1 | 1/2 each | 50% each | 0.5 each |
| 1:2 | 1/3 and 2/3 | 33.3% and 66.7% | 0.333 and 0.667 |
| 1:3 | 1/4 and 3/4 | 25% and 75% | 0.25 and 0.75 |
| 2:3 | 2/5 and 3/5 | 40% and 60% | 0.4 and 0.6 |
| 3:4 | 3/7 and 4/7 | 42.9% and 57.1% | 0.429 and 0.571 |
| 1:1:1 | 1/3 each | 33.3% each | 0.333 each |
Where Ratios Are Used
| Field | Example | Typical Ratio |
|---|---|---|
| Cooking | Rice to water | 1:2 (white rice), 1:1.5 (brown rice) |
| Concrete mixing | Cement:sand:gravel | 1:2:3 for general use |
| Photography | Image aspect ratios | 4:3, 16:9, 3:2, 1:1 |
| Maps | Scale | 1:50,000 means 1 cm = 500 m |
| Finance | Debt-to-income | Under 36% (or 9:25) is healthy |
| Chemistry | Molar ratios | 2H₂:O₂ → 2H₂O is 2:1:2 |
| Architecture | Golden ratio | 1:1.618 |
| Screen resolution | Display ratios | 16:9 (widescreen), 21:9 (ultrawide) |
Common Aspect Ratios in Detail
Screen and image ratios are among the most commonly looked-up ratios:
| Ratio | Decimal | Where Used |
|---|---|---|
| 1:1 | 1.000 | Instagram square, profile photos |
| 4:3 | 1.333 | Old TV, iPad, 1024×768 |
| 3:2 | 1.500 | 35mm film, many DSLR photos |
| 16:10 | 1.600 | MacBook displays, some monitors |
| 16:9 | 1.778 | HD/4K TV, YouTube, 1920×1080 |
| 21:9 | 2.333 | Ultrawide monitors, cinema |
| 9:16 | 0.563 | Phone vertical video, TikTok, Stories |
Comparing Two Ratios
Two ratios are equivalent (proportional) if they simplify to the same ratio. The compare mode converts each to a decimal to check:
Example: Are 15:25 and 21:35 equivalent?
- 15:25 = 15/25 = 0.6, simplifies to 3:5
- 21:35 = 21/35 = 0.6, simplifies to 3:5
- Yes, they are equivalent (both are 3:5)
For percentage calculations that build on ratio concepts, the percentage calculator handles common percentage problems. For more advanced fraction work, the fraction calculator does arithmetic with fractions directly.
All calculations run in your browser. No data is sent anywhere.
Frequently Asked Questions
How do I solve for a missing ratio value?
Use the Solve tab. Enter A, B, and C in the ratio A:B = C:?, and the calculator will find the missing value using cross multiplication: ? = (B x C) / A.
Can I simplify ratios with decimals?
Yes. The simplify mode handles decimal values by converting them to equivalent integers first, then dividing by the GCF to get the simplest whole-number ratio.
What does scaling a ratio mean?
Scaling multiplies both parts of the ratio by the same factor. A ratio of 2:3 scaled by 4 becomes 8:12. The proportion stays the same but the quantities change.
How do I compare two ratios?
Enter both ratios in the Compare tab. The calculator converts each to a decimal and checks if they are equivalent (proportional).
Can I use this for recipe scaling?
Yes. Enter the original ingredient ratio and the scale factor. If a recipe uses a 2:3 ratio of flour to sugar and you want to triple it, the result is 6:9.
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<a href="https://toolboxkit.io/tools/ratio-calculator/" title="Ratio Calculator - Free Online Tool">Try Ratio Calculator on ToolboxKit.io</a>