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Ratio Calculator

Simplify ratios and compute proportions.

Math & NumbersUpdated 2026-04-05• Author: CalcDock Team, Math reference editor• Reviewed by: CalcDock Team, Editorial review: GCD simplification + proportion cross-multiply (Apr 2026)

The Ratio Calculator helps you simplify ratios to their lowest terms, solve proportions for missing values, scale ratios up or down, and check if two ratios are equivalent. Ratios express the relationship between two quantities and appear everywhere in daily life: cooking recipes (double the batch), map scales (1:50,000), financial ratios (price-to-earnings), aspect ratios (16:9 for HD video), and mixing solutions (1 part concentrate to 4 parts water). This calculator handles all standard ratio operations with clear step-by-step results.

When this calculator helps most

Use to reduce A:B, solve A:B = C:x, or scale recipes while keeping proportions.

What each input means

Terms A : B — Two positive quantities in the same units before simplifying. (same-unit pair)
Proportion terms — Three known values in A:B = C:D to solve the fourth. (numbers)

Input mistakes to avoid

•Zeros break proportion solving — check inputs.
•Order matters: 2:3 is not 3:2.

Ratio Calculator

Value A

Value B

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Formula

Simplified ratio = A/GCD : B/GCD | Proportion: A/B = C/D → D = (B × C) / A

Examples

Simplify 24:36

Reduce the ratio 24:36 to its simplest form.

→ 2:3 (GCD = 12)

Scaling a Recipe from 4 to 10 Servings

Original recipe calls for 2:3 ratio of sugar to flour. Scale to 10 servings.

→ Scale factor: 2.5 → Sugar: 5 parts, Flour: 7.5 parts

Solve a Proportion: 5:8 = x:40

Find the missing value x in the proportion 5:8 = x:40.

→ x = 25 (because 5/8 = 25/40)

Map Scale Conversion

A map scale is 1:25,000. A distance of 4 cm on the map represents how many km in reality?

→ 4 cm × 25,000 = 100,000 cm = 1 km

How to read your results

→Simplest form divides both terms by GCD(A,B) — relatively prime integers.
→Cross-multiply for unknowns: A/B = C/D ⇒ A×D = B×C (watch for zero denominators).
→Scaling recipes multiplies every ingredient by the same factor to keep ratios.

What this result means

Simplified ratio shows relative size in lowest integers — physical meaning still needs correct units.

Common Pitfalls

⚠️Mixing units (miles vs km) in one ratio without converting.
⚠️Confusing odds (success:failure) with probability — different conventions.
⚠️Applying one ratio from a recipe when density or packing differs (liquids vs sifted flour).

Tips

✓Common aspect ratios: 16:9 (widescreen HD), 4:3 (standard SD), 1:1 (square), 9:16 (vertical video).
✓For cooking, scale all ingredients equally by multiplying by the same factor.
✓Always simplify ratios before comparing — 6:8 and 9:12 are both equivalent to 3:4.
✓Financial ratios like P/E are most useful when compared to industry peers, not in isolation.

How to check your results

✓Cross-multiply for proportions: A×x = B×C when structured as equality of fractions.

Warnings & Limitations

⚠️Medical or chemical mixing ratios may need safety data sheets — not only math.

What this calculator does not tell you

–Unit compatibility — convert to the same unit before forming a ratio.
–Non-linear mixing (volume vs mass in chemistry) without density.

Frequently Asked Questions

How do I simplify a ratio?

Find the Greatest Common Divisor (GCD) of both numbers and divide each by it. Example: 12:8 → GCD(12,8) = 4 → 12/4 : 8/4 = 3:2.

How do I solve a proportion for a missing value?

Cross-multiply and divide. If A:B = C:D and D is unknown: D = (B × C) / A. Example: 3:4 = 9:? → ? = (4 × 9) / 3 = 12.

How do I scale a recipe up or down using ratios?

Multiply all ingredient quantities by the same scale factor. Example: a recipe for 4 servings (2 cups flour, 1 cup sugar) scaled to 6 servings: multiply by 1.5 → 3 cups flour, 1.5 cups sugar.

What is the difference between a ratio and a fraction?

A ratio compares two related quantities (3:4 means 3 parts A for every 4 parts B). A fraction represents a part of a whole (3/4 means 3 out of 4 total). They use the same arithmetic but different conceptual interpretations.

What are common aspect ratios used in media?

16:9 — widescreen HD/4K video and monitors. 4:3 — older TV and monitors. 1:1 — square (Instagram posts). 9:16 — vertical video (stories/reels). 21:9 — ultrawide monitors.

What is a financial ratio?

Financial ratios compare two financial figures to assess performance. Common examples: P/E ratio (price-to-earnings), debt-to-equity ratio, current ratio (current assets / current liabilities). They help compare companies of different sizes.