Math · Proportions
Ratio
Calculator
Simplify ratios, find missing values, scale ratios, and check proportions. Supports 2-part and 4-part ratios with step-by-step solutions and visual ratio bars.
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Simplified
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Scale Factor
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A as % of Total
Simplify & Analyze Ratio A : B
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Solve Proportion A : B = C : D
💡 Leave exactly ONE field empty — that is the unknown to solve for.
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Scale a Ratio to a New Value
Enter the original ratio A:B, then enter the new value for ONE part to find all scaled values.
Original Ratio
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Compare Two Ratios — Are They Equal?
Ratio 1
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Ratio 2
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Result
📚 Common Ratios Reference — Click to Load
1 : 1
Equal parts (50/50)
1 : 2
1/3 vs 2/3 split
1 : 3
25% vs 75%
2 : 3
40% vs 60%
3 : 4
Standard aspect ratio
4 : 3
Classic screen ratio
16 : 9
HD widescreen
1 : 4
20% vs 80%
3 : 1
75% vs 25%
5 : 3
Golden-ish split
8 : 5
Near golden ratio
21 : 9
Ultrawide screen
Understanding Ratios and Proportions
A ratio compares two or more quantities. Written as A:B, it tells you the relative size of A compared to B. Proportions state that two ratios are equal: A:B = C:D. Ratios are used everywhere — cooking recipes, map scales, financial analysis, screen resolutions, and engineering.
Key Ratio Formulas
Simplify: A:B → divide both by GCD(A,B)
Cross multiply: A/B = C/D → A×D = B×C
Find unknown D: D = B×C / A
Scale factor: k = New A / Original A → New B = k × Original B
A as % of total: A/(A+B) × 100
Decimal form: A/B
Real-World Ratio Examples
Screen resolutions (16:9 HD, 4:3 classic), map scales (1:50,000), cooking recipes (2 cups flour : 1 cup sugar), concrete mix (1:2:3 cement:sand:aggregate), financial ratios (P/E ratio, debt-to-equity), fuel mixture ratios, and gear ratios in engines.
What is the difference between a ratio and a fraction?
A fraction a/b represents "a out of b total" — it's a part of a whole. A ratio A:B compares A to B directly — it doesn't need to sum to 1. For example, a class of 12 boys and 18 girls has ratio 12:18 = 2:3. As fractions of the class: boys = 12/30 = 2/5 and girls = 18/30 = 3/5. The ratio tells you the comparison; fractions tell you the share of a whole.
How do you simplify a ratio with decimals?
Multiply both parts by a power of 10 to eliminate decimals first. For example, 1.5:2.5 — multiply both by 2 → 3:5. Or multiply by 10 → 15:25 → simplify by GCD(15,25)=5 → 3:5. You can also convert to fractions: 1.5/2.5 = 3/5, so the ratio is 3:5.
What is a proportion and how do you solve it?
A proportion states that two ratios are equal: A:B = C:D, equivalent to A/B = C/D. To find a missing value, use cross multiplication: A×D = B×C. Solve for the unknown algebraically. For example, 3:4 = ?:20 → 3×20 = 4×? → ? = 60/4 = 15.
How is ratio different from rate?
A ratio compares two quantities of the same type (3 boys : 5 girls). A rate compares two quantities of different types with different units (60 km per hour, $12 per kg). Rates are a special type of ratio where units matter. Unit rates express the ratio with a denominator of 1 (e.g., 60 km/1 hr = 60 km/h).
Please leave exactly ONE field empty to solve for it.
Ratio Scaling Calculator
| Original A | Original B | Original C | Original D |
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| Scale To (A): |