Ratio Calculator
Simplify ratios, scale them up or down, solve for a missing value, and compare two ratios instantly.
How to Use This Calculator
- Choose a mode — Simplify, Scale, Solve for X, or Compare
- Enter your values — whole numbers or decimals both work
- Click Calculate to see the simplified ratio, decimal, percentage, and step-by-step math
Mode
Simplify a Ratio
📐 How to Simplify a Ratio
- Find the GCF: Find the greatest common factor of both numbers. For 8:12, the GCF of 8 and 12 is 4.
- Divide both sides: Divide A and B by the GCF. 8 ÷ 4 : 12 ÷ 4 = 2:3.
- Solving proportions (A:B = C:X): Cross-multiply: X = (B × C) ÷ A. For 4:8 = 6:X, X = (8 × 6) ÷ 4 = 12.
- Comparing ratios: Convert each to a decimal (A ÷ B) and compare — 3:4 = 0.75 and 6:8 = 0.75, so they're equivalent.
🔢 Common Ratio Simplifications
Frequently Asked Questions
How do you simplify a ratio?
Find the greatest common factor (GCF) of both numbers, then divide each side by it. For 8:12, the GCF is 4, so 8÷4:12÷4 simplifies to 2:3.
How do you solve a proportion like A:B = C:X?
Cross-multiply and divide: X = (B × C) ÷ A. For example, if 4:8 = 6:X, then X = (8 × 6) ÷ 4 = 12.
How do you know if two ratios are equivalent?
Cross-multiply both ratios. If A:B and C:D are equivalent, then A × D equals B × C. For 3:4 and 6:8, 3×8=24 and 4×6=24, so they're equivalent.
How do you convert a ratio to a percentage?
Divide the first number by the second, then multiply by 100. A ratio of 3:4 is 3÷4 = 0.75, or 75%.
What's the difference between a ratio and a fraction?
A ratio (A:B) compares two separate quantities, while a fraction (A/B) usually represents a part of a whole. Mathematically they simplify the same way, but a ratio like 2:3 doesn't imply 2 is part of a total of 3 — it compares two distinct amounts.
How do you scale a ratio up or down?
Multiply both sides of the ratio by the same scale factor. Scaling 2:3 by a factor of 5 gives 10:15 — the relationship between the two numbers stays the same.