Ratio Calculator: Solve Proportions & Simplify Ratios (A:B = C:D)
Free ratio calculator and proportion solver. Solve for the missing value in A:B = C:D using cross-multiplication. Simplify ratios to lowest terms with GCD. Compare proportions visually. Aspect ratio scaling (16:9, 4:3). Step-by-step logic trace. Trusted by students and educators.
What This Ratio Calculator Does & Who It's For
Calculator Purpose & Ideal Users
- What You'll Get:In Solve/Scale: the missing value, simplified ratios, fractional form, and a Logic Trace showing A ร D = B ร C and variable isolation. In Simplify: GCD and reduced ratio. In Scale (four values): visual bar showing which ratio is larger or if they are equal. All calculations run locally; no sign-up.
- Ideal Users:Students & math: Learn proportions, cross-multiplication, and ratio simplification. Teachers: Demonstrate the proportion formula with transparent steps. Designers & video: Aspect ratio scaling (16:9, 4:3). Cooks: Recipe scaling. Anyone: Quick proportion calculator and ratio simplifier for homework, design, or everyday math.
- Scope & Limits:Real numbers only. Division by zero returns Invalid. Non-integer ratios show numeric form in Simplify (GCD applies only to integers). All data stays in your browser.
This ratio calculator and proportion solver handles three use cases: Solve for X (enter three of A, B, C, D to find the fourth), Simplify (reduce A:B to lowest terms using the Euclidean GCD), and Scale (compare two ratios with a proportional bar). It is built with mathematical rigor and step-by-step transparency, so you can verify every result.
Ratio and Proportion: Definitions and the Cross-Multiplication Formula
A ratio compares two quantities (e.g. A:B or A/B). A proportion states two ratios are equal: A:B = C:D. The fundamental rule is cross-multiplication:
A ร D = B ร C
To solve for the unknown: if D is missing, D = (B ร C) / A; if C is missing, C = (A ร D) / B; if B is missing, B = (A ร D) / C; if A is missing, A = (B ร C) / D. This proportion calculator applies these formulas when exactly three of the four values are entered.How to Simplify a Ratio to Lowest Terms
To simplify a ratio A:B, find the Greatest Common Divisor (GCD) of A and B using the Euclidean algorithm, then divide both parts. Example: 8:12 โ GCD(8,12) = 4 โ (8รท4):(12รท4) = 2:3. In Simplify mode, enter A and B; the tool displays the GCD and the reduced ratio. For decimals, a numeric equivalent is shown. This is useful for simplifying fractions, aspect ratios, and recipe scales.
Aspect Ratio Scaling: 16:9, 4:3, 1:1, and Golden Ratio
Common aspect ratios include 16:9 (widescreen video), 4:3 (standard), 1:1 (square), and the Golden ratio (ฯ โ 1.618:1). Use the presets to fill A and B, then enter C (or D) to find the matching dimension. Example: 4:3 preset with C=400 gives D=300, so 4:3 = 400:300. This supports image resizing, video formatting, and layout design.
Ratio Calculator FAQ
? What is the formula for solving proportions?
For A:B = C:D, use cross-multiplication:
A ร D = B ร C
Solve for the unknown (e.g. D = (B ร C) / A). This calculator applies that formula automatically when you enter three values.? How do I simplify a ratio to lowest terms?
Divide both parts by their GCD. Example: 8:12 โ GCD = 4 โ 2:3. Use Simplify mode: enter only A and B; the tool displays the GCD and reduced ratio.
? What is the difference between Solve and Scale mode?
Both solve for the missing value when three are filled. Scale mode additionally lets you fill all four to compare the ratios and see a visual bar (which is larger or if they are equal).
? Can I use this for aspect ratios like 16:9?
Yes. Use presets (16:9, 4:3, 1:1, Golden ratio) to fill A and B, then enter C or D to scale. Example: 4:3 preset with C=400 gives D=300.
? Does the calculator show steps?
Yes. The Logic Trace shows the cross-multiplication and variable isolation. Results are displayed in the dashboard with simplified ratio and fractional form.
? Is this ratio calculator free?
Yes. Free to use, no sign-up. All calculations run locally in your browser.