Ratio Calculator – Simplify, Scale and Compare Ratios
Simplify ratios to lowest terms, scale ratios, check equivalence, and solve for a missing value in a proportion.
📊 Math📐 a:b = (a/GCF):(b/GCF) | Scale: a×k : b×k
Ratio value A
Ratio value B
Scale factor (or 1)
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| Ratio Calculator – Simplify, Scale and Compare Ratios | a:b = (a/GCF):(b/GCF) | Scale: a×k : b×k | simplified ratio |
Step-by-Step Examples
Example 1
Simplify 12:8
12:8 → GCF = 4 → 3:2.
- GCF(12,8) = 4 | 12/4 : 8/4 = 3:2
✓ 3:2
Example 2
Scale 3:2 by 5
3:2 scaled by 5 = 15:10.
- 3×5 : 2×5 = 15:10
✓ 15:10
Example 3
Recipe Scaling
2:3 ratio of oil to flour × 4.
- Scaled: 8:12
✓ 8:12
Real-World Applications
Students
Simplify and work with ratios.
Cooks
Scale recipe ratios accurately.
Builders
Calculate material ratios for concrete, mortar.
Finance
Analyze financial ratios.
Common Mistakes to Avoid
⚠️
Confusing ratio and fraction
3:2 and 3/2 are related but different. The ratio 3:2 means 3 parts to 2 parts (5 total). The fraction 3/2 = 1.5.
⚠️
Not simplifying
Always divide both parts by their GCF to get the simplest ratio form.
Frequently Asked Questions
How to simplify a ratio? ▾
Find the GCF of both numbers and divide each by it. 15:25 → GCF=5 → 3:5.
Equivalent ratios? ▾
Two ratios are equivalent if one is a multiple of the other. 2:3 and 4:6 and 6:9 are all equivalent.
Ratio to percentage? ▾
Part A as % of total: a/(a+b) × 100. In 3:2, first part is 3/5 × 100 = 60%.
Related Calculators
Formula Explorer connections
Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.