HomeGuidesRatio Calculator Guide
Math Guide

Ratio Calculator Guide: Ratios, Proportions & Cross-Multiplication

Ratios and proportions are fundamental in finance, cooking, construction, and science. Master the key techniques and you'll solve most ratio problems in seconds.

Solving Proportions: Cross-Multiplication

If A:B = C:D, then A × D = B × C
Unknown = (known product) ÷ (opposite known)
3:5 = X:20
3 × 20 = 5 × X → 60 = 5X → X = 12
X = 12
X:8 = 15:24
X × 24 = 8 × 15 → 24X = 120 → X = 5
X = 5

Real-World Ratio Applications

Map scales
1:50,000 means 1 cm on map = 50,000 cm (500 m) in reality
Recipe scaling
Recipe for 4: 200g flour. Scale to 6: 200 × (6÷4) = 300g
Mixing solutions
Cement:sand 1:3 means 1 bag cement for every 3 of sand
Financial ratios
P/E ratio: price ₹100, EPS ₹10 → P/E = 10

Frequently Asked Questions

What is a ratio?

A ratio compares two or more quantities showing how many times one contains the other. Written as A:B or A/B. For example, a ratio of 3:5 means for every 3 of A, there are 5 of B. Ratios are used in maps, recipes, finance, and scale models.

How do I solve a proportion (A:B = C:D)?

Cross-multiply to find the missing value. If A:B = C:D, then A×D = B×C. For example, 3:5 = X:20 → 3×20 = 5×X → X = 60÷5 = 12.

How do I simplify a ratio?

Divide both parts by their Greatest Common Divisor (GCD). For 24:36: GCD is 12. Simplified: 2:3. For 15:25:30: GCD is 5. Simplified: 3:5:6.

What is a direct proportion?

In direct proportion, when one quantity increases, the other increases proportionally. If 5 workers complete a job in 8 hours, 10 workers (double) complete it in 4 hours (half). Written as A ∝ B or A = kB.

What is an inverse proportion?

In inverse proportion, when one quantity increases, the other decreases proportionally. More workers = less time to finish a job. If 4 workers take 12 days, 6 workers take 12 × (4÷6) = 8 days.

Related Calculators

Solve Any Proportion

Find the missing value in any A:B = C:D proportion instantly.

Open Ratio Calculator