Ratio Calculator

Ratio & Proportion Calculator Guide: Simplify Ratios & Solve Proportions

A ratio calculator simplifies ratios, solves proportions, and converts between part-to-part and part-to-whole forms. It is handy for recipes, maps, photography, chemistry, and finance.

What is Ratio Calculator?

The ratio calculator reduces ratios to lowest terms, scales them to a target total, and solves unknowns in a:b = c:d using cross-multiplication.

How to Use the Ratio Calculator

1. Enter a ratio a:b to simplify or scale.
2. Use proportion mode to solve a:b = c:x or x:b = c:d for the unknown.
3. Provide a total to convert parts into quantities (part-to-whole).
4. Calculate and view steps (GCD, scaling factor).
5. Switch units (cups, liters, inches, cm) to keep measurements consistent.

Formulas & Methods

• Simplify: a:b -> (a/g):(b/g) where g = gcd(a,b).
• Proportion: a/b = c/d ⇒ ad = bc ⇒ unknown x = (b*c)/a etc.
• Scale to total T: for a:b, sum s = a + b; quantities = (a/s)*T and (b/s)*T.
• Multiple parts: for a:b:c, use s = a + b + c; each = (part/s)*T.

Assumptions & limitations

• Units must be consistent before applying ratios.
• For negative or zero terms, interpret carefully; many ratio contexts assume positives.

Examples

Example A — Simplify
18:24 -> gcd = 6 -> 3:4.

Example B — Proportion
3:5 = x:25 -> x = 25*3/5 = 15.

Example C — Scale to total
2:3:5 for T = 1000 units -> parts = 200, 300, 500.

| Task | Input | Output | |---|---|---| | Simplify | 42:56 | 3:4 | | Resize recipe | 1:2:4 to 7 cups | 1.17, 2.33, 4.67 cups | | Map scale | 1:24,000, 3 in | 6,000 ft (1.136 mi) |

Pro Tips & Best Practices

• Compute GCD first to avoid large numbers.
• Keep units aligned (all cups or all milliliters).
• For recipes, round to workable measures while preserving ratios.
• For photography, remember aspect ratios (e.g., 3:2, 16:9) when cropping.

Related Calculators

• Basic Calculator
• Percentage Calculator
• Fraction Calculator
• Speed Calculator

FAQ

Q: How do I simplify a ratio?

A: Divide both terms by their greatest common divisor (GCD).

Q: How do I solve a proportion?

A: Use cross-multiplication: a:b = c:d implies ad = bc.

Q: How do I scale a ratio to a total?

A: Find the sum of parts and multiply each part by total/sum to get part-to-whole amounts.

Q: How do I convert between fractions and ratios?

A: a:b equals a/b; multiply or divide both terms to scale.

Q: What about mixing problems?

A: Use ratios to maintain proportions when combining ingredients or solutions.

Call to Action

Type a ratio or proportion and get simplified forms, scaled quantities, and step-by-step solutions—perfect for mixing, resizing, and planning.