Ratio Calculator
Find the missing term in a ratio comparison (A:B = C:D) using cross-multiplication. Enter three known values to instantly solve for the fourth — ideal.
Formula
A/B = C/D → D = B × C / A
Enter three of the four terms in a ratio comparison A:B = C:D. Cross-multiplying (A × D = B × C) and solving for the unknown term gives you a ratio equivalent to the first, scaled to a new size.
Worked Examples
Example 1: Scaling a recipe
Problem:A recipe uses a flour-to-water ratio of 5:3. You have 12 cups of flour — how much water do you need?
Solution:Set up 5:3 = 12:D. Cross-multiply: 5 × D = 3 × 12 = 36, so D = 36/5 = 7.2.
Result:You need 7.2 cups of water
Example 2: Reading a map scale
Problem:A map has a scale of 1:25,000. A measured distance on the map is 4.4 cm — what is the real-world distance?
Solution:Set up 1:25,000 = 4.4:D. D = (25,000 × 4.4)/1 = 110,000 cm = 1.1 km.
Result:Real-world distance = 1.1 km
Frequently Asked Questions
What does it mean to find an equivalent ratio?
An equivalent ratio scales every term of a ratio by the same factor, so the underlying proportional relationship stays identical — 2:3, 4:6, and 20:30 are all equivalent ratios because each is 2:3 multiplied by 1, 2, and 10 respectively. Ratio Calculator finds the missing fourth term (D) that keeps A:B equivalent to C:D, which is exactly the technique used to scale a ratio up or down to a new size.
How do I scale a recipe using ratios?
Treat the original recipe amounts as A:B and the amount you actually have of one ingredient as C, then solve for D. For example, if a recipe calls for 2 cups flour to 1 cup sugar (A:B = 2:1) and you only have 3 cups flour (C = 3), solving 2:1 = 3:D gives D = 1.5 cups sugar — keeping the same flour-to-sugar ratio at a different batch size.
How are ratios used in scaling maps and models?
Map scales and architectural/engineering models are expressed as ratios, such as 1:50,000 (1 unit on the map equals 50,000 of the same unit in real life) or 1:24 for a scale model car. Given a measured distance on the map or model, Ratio Calculator finds the real-world equivalent (or vice versa) by treating the scale as A:B and the known measurement as C.
How do I simplify a ratio to its lowest terms?
Divide both terms of the ratio by their greatest common factor (GCF). For example, 24:36 has GCF 12, so dividing both terms by 12 gives the simplified ratio 2:3. A ratio is in lowest terms once its two terms share no common factor other than 1 (i.e., they are coprime).
Why does the calculator need exactly three values to find a ratio?
A ratio comparison (A:B = C:D) is a single equation with one degree of freedom once three of the four terms are known — cross-multiplying (A×D = B×C) lets you solve directly for the missing term. With only two values you can express a ratio but can't yet find an equivalent one; you need a third reference value to anchor the scale.
Can ratios compare more than two quantities at once?
Yes — compound ratios like 2:3:5 compare three or more quantities simultaneously (common in mixing concrete, paint colors, or financial allocations). Ratio Calculator solves the standard two-term-to-two-term case (A:B = C:D); for three-part ratios, apply the same scale factor to every term individually.
Where do ratios show up in everyday life?
Ratios appear in aspect ratios for screens and photos (16:9, 4:3), gear and pulley ratios in mechanical engineering, price-per-unit comparisons at the grocery store, mixing ratios for cleaning products or concrete, and financial ratios like debt-to-income used by lenders.
How do I split a total amount between people in a given ratio?
Add the ratio terms to get the number of equal shares, divide the total by that sum to find the value of one share, then multiply each term by it. Splitting 600 in the ratio 2:3 gives 2 + 3 = 5 shares, one share = 600 / 5 = 120, so the parts are 240 and 360. This share method is what profit-sharing agreements, inheritance splits, and concrete mix designs rely on.
What is the difference between a ratio and a rate?
A ratio usually compares two quantities measured in the same unit, so the units cancel and the result is dimensionless, like a 16:9 aspect ratio or a 3:1 gear ratio. A rate compares quantities in different units and keeps them, such as kilometres per hour or dollars per kilogram. A unit rate is simply a rate rewritten so the second term is 1, which makes price-per-unit comparisons straightforward.
How do I resize an image without distorting its aspect ratio?
Enter the original width and height as A:B and the new width you want as C; the calculator returns the height D that preserves the aspect ratio. A 1920 by 1080 image is 1920:1080, which simplifies to 16:9, so resizing to a width of 1200 gives 1200 × 1080 / 1920 = 675 pixels of height. Any height other than 675 stretches or squashes the picture. The same setup works in reverse if you know the target height and need the width.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
Related Calculators
🧮Surface Area to Volume Ratio Calculator
Calculate surface area to volume ratio with inputs, formulas, and instant results.
🧮Annulus Area Calculator
Calculate annulus area with inputs, formulas, and instant results.
🧮Area Calculator
Calculate area with inputs, formulas, and instant results.
🧮Area of a Rectangle Calculator
Calculate the area, perimeter, and diagonal of a rectangle. Find missing sides from known area. Convert between metric and imperial area units.
🧮Area of Crescent Calculator
Calculate area of crescent with inputs, formulas, and instant results.
🧮Center of Mass Calculator
Calculate center of mass with inputs, formulas, and instant results.
🧮Centroid Calculator
Calculate centroid with inputs, formulas, and instant results.
🧮Chord Length Calculator
Calculate chord length with inputs, formulas, and instant results.