Ratio Calculator Guide: How to Solve Proportions (2026)
Quick Answer
- *Solve proportions with cross-multiplication: a/b = c/d → a×d = b×c.
- *Simplify ratios by dividing both parts by their greatest common divisor.
- *Scale ratios by multiplying both parts by the same factor.
- *Unit rates express a ratio per one unit for easy comparison.
What Is a Ratio?
A ratio compares two quantities by division. The ratio 3:4 means “for every 3 of one thing, there are 4 of another.” Ratios can be written as 3:4, 3/4, or “3 to 4.” They describe relative size, not absolute amounts.
Simplifying Ratios
Divide both parts by their greatest common divisor (GCD). The ratio 24:36 has a GCD of 12, so it simplifies to 2:3. For decimals like 1.5:2.5, multiply both by 2 to get 3:5.
Solving Proportions
A proportion states two ratios are equal: a/b = c/d. To find a missing value, cross-multiply:
Example
If 3 apples cost $2.40, how much do 7 apples cost?
- 3/2.40 = 7/x
- 3x = 2.40 × 7 = 16.80
- x = 16.80 ÷ 3 = $5.60
Scaling Ratios
To scale a ratio to a specific total, divide the target by the sum of ratio parts, then multiply each part.
Mix concrete in a 1:2:3 ratio (cement:sand:gravel). You need 180 kg total:
- Sum of parts: 1 + 2 + 3 = 6
- Scale factor: 180 ÷ 6 = 30
- Cement: 1 × 30 = 30 kg
- Sand: 2 × 30 = 60 kg
- Gravel: 3 × 30 = 90 kg
Unit Rates
A unit rate has a denominator of 1. It answers “how much per one unit?”
| Comparison | Calculation | Unit Rate |
|---|---|---|
| 360 miles in 6 hours | 360 ÷ 6 | 60 mph |
| $4.50 for 3 lbs | 4.50 ÷ 3 | $1.50/lb |
| 120 words in 2 min | 120 ÷ 2 | 60 wpm |
Real-World Applications
- Cooking: Scale a recipe from 4 servings to 10. Multiply every ingredient by 10/4 = 2.5.
- Maps: A 1:50,000 scale means 1 cm on the map = 50,000 cm (500 m) in reality.
- Finance: Price-to-earnings ratio (P/E) compares stock price to earnings per share.
- Architecture: Scale models use ratios like 1:100 to represent buildings.
- Chemistry: Stoichiometric ratios determine how much of each reactant is needed.
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Try the Free Ratio Calculator →Frequently Asked Questions
How do you solve a proportion with a missing value?
Cross-multiply: a/b = c/d → a × d = b × c, then solve. Example: 3/4 = x/20 → x = 15.
How do you simplify a ratio?
Divide both numbers by their GCD. 12:18 simplifies to 2:3. For decimals, multiply by a power of 10 first.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (3:4). A proportion states two ratios are equal (3/4 = 6/8). Proportions let you find unknowns.
How do you scale a ratio up or down?
Multiply or divide both parts by the same number. To scale 2:3 to a total of 25: scale factor = 25 ÷ 5 = 5, giving 10:15.
What is a unit rate?
A ratio with denominator 1. If 300 miles takes 5 hours, the unit rate is 60 mph. Unit rates make comparisons straightforward.