Ratio Calculator — Solve, Simplify & Scale Any Ratio

Quick Start Guide

  1. Select mode: General (simplify, scale, solve, compare, or convert a ratio), Mix (scale real quantities like fuel or recipes), or Split (divide a total across weighted parts).
  2. Enter values: Ratio terms, quantities, or split parts depending on the selected mode and task.
  3. View results: See the simplified ratio, solved value, scaled equivalents, or split allocation — with an optional bar visualization.
  4. Show steps (optional): Turn on Show Steps to see the GCD or cross-multiplication worked out, line by line.

Understanding Ratios

What is a ratio?

A ratio compares two quantities, written A:B (for example 3:2). It shows how much of one thing there is relative to another. A ratio with more than two parts, like 2:3:5, compares several quantities at once.

How to simplify a ratio

Divide both terms by their greatest common divisor (GCD). For 12:18 the GCD is 6, so 12:18 simplifies to 2:3. A ratio is in lowest terms when its terms share no common factor other than 1.

Equivalent ratios and scaling

Multiplying or dividing both terms by the same number gives an equivalent ratio with the same value. 2:3, 4:6, and 8:12 are all equivalent. Scaling is how you resize a recipe or a drawing while keeping proportions.

Solving a proportion

A proportion says two ratios are equal: A:B = C:D. If one value is unknown, cross-multiply (A×D = B×C) and divide. For 2:3 = 8:x, x = (3×8)/2 = 12.

Comparing two ratios

Two ratios are equivalent when their cross-products match: A:B equals C:D if A×D = B×C. For example 4:6 and 2:3 are equivalent because 4×3 = 6×2 = 12.

Ratio to fraction, decimal, and percent

A ratio A:B is the fraction A/B. Divide for the decimal (3:2 = 1.5) and multiply by 100 for the percent (150%). To express each part's share of the whole, use A/(A+B) and B/(A+B) — for 3:2 that is 60% and 40%.

Part-to-part vs part-to-whole

A part-to-part ratio compares two parts (2:3 boys to girls). A part-to-whole ratio compares one part to the total (2 out of 5, or 40%). Mixing the two is a common mistake.

Common mistakes to avoid

Reversing the order (3:2 is not the same as 2:3); mixing units without converting to the same unit first; using zero when a ratio term should be greater than zero; and confusing part-to-part with part-to-whole.

Ratio vs. DTI vs. Aspect Ratio — which calculator do I need?

This calculator handles any two- or multi-term ratio you type in — recipes, mixes, business splits, or general proportions. For a ratio the industry already has a name and rules for, use the dedicated tool instead: the Debt-to-Income Calculator turns your monthly debts and income into the specific percentage lenders check for a mortgage, and the Aspect Ratio Calculator turns width and height into the pixel dimensions platforms and printers expect. Use this Ratio Calculator whenever your two numbers do not fit either of those molds.

Features

Simplify & Reduce: Reduce any ratio to its lowest terms (e.g. 12:18 → 2:3) and see the greatest common divisor used. Works with whole numbers and decimals.

Solve Missing Value: Find the unknown term in a proportion A:B = C:D by cross-multiplication. For example, 2:3 = 8:x solves to x = 12.

Scale & Equivalent: Multiply a ratio to an equivalent one (2:3 × 4 → 8:12) and see a quick equivalent-ratio table (1×, 2×, 3×, 4×, 5×, 10×).

Compare & Convert: Check whether two ratios are equivalent, and convert a ratio to a fraction, decimal, percentage, and each part's share of the whole.

Mix, Recipe & Fuel: Mix mode scales real quantities with unit conversion (gallons, liters, ounces, milliliters) for recipes, fuel/oil, and solutions.

Step-by-Step: Turn on Show Steps to see the GCD or cross-multiplication worked out, line by line, for learning and transparency.

Split a Total: Split a total across a multi-part ratio like 2:3:5 to get each share, with an animated proportion bar.

Export Data: Export your ratio calculations to JSON, CSV, or PDF format for record-keeping or sharing.

Common Use Cases

Simplify & Solve: reduce a ratio to lowest terms (12:18 → 2:3), solve a missing value in 2:3 = 8:x, and show the GCD or cross-multiplication steps.

Scale & Compare: scale a ratio to an equivalent (2:3 × 4 → 8:12) and check whether 4:6 and 2:3 are equivalent.

Convert Ratios: convert a ratio to a fraction, decimal, or percent, and see part-to-part vs part-to-whole shares.

Recipes, Fuel & Mixing: scale recipes using ingredient ratios and calculate gas/oil mixes (e.g., 50:1, 40:1).

Split a Total: distribute totals across weighted ratios (e.g. 2:3:5) to plan budget, campaign, or inventory allocation quickly.

Frequently Asked Questions

Divide both sides of the ratio by their greatest common divisor (GCD). For example, 12:18 simplifies to 2:3 by dividing both by 6. In General mode, pick Simplify — the calculator reduces any whole-number or decimal ratio to its lowest terms and shows the GCD.
Multiply both terms by the same number. For example, 2:3 scaled by 4 becomes 8:12, which is equivalent because it keeps the same value. The Scale task scales by any factor and shows an equivalent-ratio table (1×, 2×, 3×, 4×, 5×, 10×).
Use cross-multiplication. If A:B = C:x, then A×x = B×C, so x = (B×C) / A. Enter three known values in the Solve task and the calculator finds the fourth automatically — for example, 2:3 = 8:x gives x = 12.
Cross-multiply: A:B equals C:D when A×D = B×C. For example, 4:6 and 2:3 are equivalent because 4×3 = 6×2 = 12. The Compare task does this for you and tells you whether the two ratios are equivalent.
A ratio A:B is the fraction A/B. Divide to get the decimal (3:2 = 1.5), multiply by 100 for the percent (150%), or use A/(A+B) and B/(A+B) for each part’s share of the whole (60% and 40%). The Convert task shows all of these at once.
A part-to-part ratio compares two parts to each other (e.g., 2:3 boys to girls). A part-to-whole ratio compares one part to the total (e.g., 2 out of 5, or 40%). The Convert task’s share-of-total output turns a part-to-part ratio into part-to-whole percentages.
A ratio compares two quantities (e.g., 3:4). A proportion states that two ratios are equal (e.g., 3:4 = 6:8). Use the Solve task to find a missing value when one ratio is known and the other is partially known.
Add all parts (2+3+5=10), then divide the total by 10 to get one part, and multiply by each ratio number. For example, splitting $100 in a 2:3:5 ratio gives $20, $30, and $50. Use Split mode to do this for any number of parts.

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