Ratio Calculator - Solve Proportions & Simplify Ratios
Solve for a missing value in a proportion A:B = C:D, or simplify a ratio to its lowest terms. Perfect for recipes, maps, scale models, and everyday math.
Enter three values and leave the unknown as 'x' to solve a proportion, or enter two values to simplify a ratio to lowest terms.
Ratio Calculator - Solve Proportions & Simplify Ratios
Solve for a missing value in a proportion A:B = C:D, or simplify a ratio to its lowest terms. Perfect for recipes, maps, scale models, and everyday math.
Value A : Value B = Value C : Value D
About the Ratio Calculator
A ratio is a comparison of two quantities expressed as a fraction or with a colon — for example, 3:4 or 3/4. Ratios describe the relative sizes of two numbers and are fundamental to everyday mathematics: mixing paint colors, scaling recipes, reading maps, calculating odds, interpreting statistics, and designing proportional graphics all rely on ratios.
A proportion is a statement that two ratios are equal: A:B = C:D, or equivalently A/B = C/D. Proportions arise whenever you scale a ratio up or down. If a recipe calls for 2 cups of flour to make 12 cookies, and you want 30 cookies, the proportion 2:12 = x:30 gives x = 5 cups of flour. Cross-multiplying gives the general rule: when A/B = C/D, then A × D = B × C, so the unknown x can always be isolated as x = (known product) / (opposing known value).
This ratio calculator handles two tasks. The proportion solver takes any three of the four values A, B, C, D and solves for the fourth. Leave the unknown field empty or enter 'x'. The solver uses cross-multiplication: if x is in position A, then x = B × C / D; if x is in position B, then x = A × D / C; and so on.
The simplify mode reduces a ratio A:B to lowest terms by dividing both values by their greatest common divisor (GCD). The GCD is found using the Euclidean algorithm. For example, 18:24 simplifies to 3:4 because GCD(18, 24) = 6, and 18/6 = 3, 24/6 = 4.
Decimal ratios are also supported. For 1.5:2, multiply both by 10 to get 15:20, divide by GCD(15,20) = 5 to get 3:4. Scale factors in architecture, map reading, aspect ratios in photography (16:9), and gear ratios in engineering all require this kind of ratio simplification.
Understanding ratios is also foundational to understanding rates (a ratio with different units in numerator and denominator), unit prices (cost per item), slopes (rise over run), and trigonometric ratios (sine, cosine, tangent). Mastering the algebra of ratios and proportions is therefore an essential building block for all of applied mathematics.
Ratio Calculator Examples
Examples showing both proportion solving and ratio simplification.
| Problem | Answer | Application |
|---|---|---|
| 2 : 12 = x : 30 (proportion) | x = 5 | Recipe scaling: 2 cups of flour makes 12 cookies; 5 cups are needed for 30 cookies. Cross-multiply: x = 2×30/12 = 5. |
| 1 : 50000 = 4.5 : x (proportion) | x = 225000 | Map scale: a 1:50,000 map means 1 cm represents 50,000 cm (500 m). A map distance of 4.5 cm = 225,000 cm = 2.25 km real distance. |
| 16 : 9 = 1920 : x (proportion) | x = 1080 | Screen resolution: a 16:9 aspect ratio with width 1920 pixels gives height 1080 pixels (Full HD). |
| Simplify 18 : 24 | 3 : 4 | GCD(18, 24) = 6. Divide both by 6: 18/6 = 3, 24/6 = 4. The class of 18 boys to 24 girls simplifies to 3:4. |
How to Use the Ratio Calculator
- Select the calculation mode: 'Solve Proportion (A:B = C:D)' to find a missing value, or 'Simplify Ratio (A:B)' to reduce a ratio to lowest terms.
- For proportion mode, enter any three of the four values A, B, C, D. Leave the unknown field blank (it will be treated as x). All four fields are shown; fill three and leave one empty.
- For simplify mode, only fill in Value A and Value B. The calculator reduces A:B to its simplest form by dividing both by their GCD.
- Click Calculate. The result shows the solved value (proportion) or the simplified ratio, plus a verification check.
- Click Reset to clear all fields and start a new calculation.
Ratio Calculator FAQ
What is a ratio and how is it different from a fraction?
A ratio compares two quantities of the same type (e.g., 3 red marbles to 4 blue marbles = 3:4). A fraction represents a part of a whole (3/4 means 3 out of 4 equal parts). While both use the same numbers, they describe different relationships. A ratio can also be expressed as a fraction, so 3:4 = 3/4, but the interpretation depends on context.
How do I solve a proportion by cross-multiplication?
If A/B = C/D, then A × D = B × C (cross-multiply). To solve for any one unknown, isolate it algebraically. For example, if A/5 = 6/10, then A × 10 = 5 × 6 = 30, so A = 3. This works because multiplying both sides of the proportion by B × D eliminates the denominators.
How do I simplify a ratio to lowest terms?
Divide both parts of the ratio by their greatest common divisor (GCD). To find the GCD, use the Euclidean algorithm or list the factors of both numbers. For 36:48, GCD = 12, so 36:48 = 3:4. The simplified ratio has the same value but uses the smallest possible integers.
Can ratios involve decimals or fractions?
Yes. A ratio like 1.5:2 can be simplified by multiplying both sides by 10 to get 15:20, then dividing by GCD(15,20) = 5 to get 3:4. This calculator accepts decimal inputs and handles the conversion automatically.
What is the difference between a ratio and a rate?
A ratio compares quantities of the same unit (e.g., boys to girls, 3:5). A rate compares quantities of different units (e.g., speed as km/hr, price as $/kg). Rates are technically ratios, but the distinction matters when simplifying: you typically don't simplify mixed-unit rates the same way you simplify pure ratios.
How are proportions used in map reading and scale models?
A map scale of 1:50,000 means every 1 unit on the map equals 50,000 of the same unit in reality. To find a real distance, set up the proportion: 1/50000 = map_distance/real_distance and solve for real_distance. Scale models in architecture and engineering use identical logic: model length / scale = actual length.