Solve ratios and proportions — find the missing value in a:b = c:d and simplify any ratio instantly.
The Ratio Calculator solves ratio and proportion problems — given three values of a proportion a:b = c:d, it finds the missing fourth value (d). It also simplifies the ratio a:b to its lowest terms.
Ratios and proportions are everywhere in mathematics, everyday life, and competitive exams. They're used for scaling recipes, mixing solutions, comparing prices, map reading, exchange rates, and countless word problems in competitive exams.
Ratio vs Proportion
A ratio (a:b) compares two quantities. A proportion (a:b = c:d) states that two ratios are equal. This calculator helps you find the missing value in any proportion.
Common Applications
- Recipe scaling: If a recipe serves 4 with 500g flour, how much for 10 people?
- Currency exchange: If ₹83 = $1, how many rupees is $250?
- Mixing solutions: If 3 parts water to 1 part concentrate makes 4L, how to make 10L?
- Map scaling: If 1 cm = 50 km on a map, how many km is 3.5 cm?
- Competitive exams: Ratio and proportion problems in SSC, IBPS, CAT, NMAT
1. Enter a and b: The first ratio (a:b).
2. Enter c: The known value in the second ratio (c:d).
3. Find d: The calculator solves a:b = c:d for d. Also shows the simplified form of a:b.
If a:b = c:d, then d = (c × b) / a
Simplified ratio: divide a and b by their GCD (Greatest Common Divisor)
Example: a=3, b=4, c=9 → d = (9 × 4) / 3 = 12
So 3:4 = 9:12 ✓ (both simplify to 3:4)
Cross-multiplication rule: a × d = b × c
Example 1 — Recipe: 2:3 = 8:d (8 cups flour, how much sugar if ratio is 2:3?) → d = 8×3/2 = 12 cups sugar
Example 2 — Exchange: 83:1 = d:250 (₹83 = $1, find rupees for $250) → d = 250×83/1 = ₹20,750
Example 3 — Simplify: 18:24 → GCD(18,24) = 6 → Simplified: 3:4