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Proportions & ratios

Ratio Calculator

Solve proportions A:B = C:D, simplify ratios with GCD, compare visually. Cross-multiplication, aspect ratio presets.

By Jeff Beem

Updated

Proportion Intelligence Engine

Choose a mode to solve proportions, simplify a ratio, or scale A:B and C:D. Use presets for common aspect ratios and the golden ratio.

Formatting

Round to…
Sig figs
Comparison results
Fill exactly three fields to solve for the fourth.

How to Use This Calculator

Pick Solve, Simplify, or Scale. Solve/Scale: fill three fields β†’ get the fourth. Simplify: enter A and B β†’ get reduced ratio.

Workflow Tips

Solve for X

Fill three of A, B, C, D. The empty field (labeled x) shows the result in the dashboard and Logic Trace.

Simplify

Enter A and B only. The tool reduces to lowest terms using GCD and shows the fraction.

Scale

Three filled β†’ solves for fourth. All four filled β†’ compares ratios with a visual bar.

Presets

16:9, 4:3, 1:1, or Golden ratio fills A and B. Add C or D to scale (e.g. 4:3 + C=400 β†’ D=300).

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

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.
  • What You'll Get:
    In Solve/Scale: the missing value, simplified ratios, fractional form, and a Logic Trace showing A Γ— D = B Γ— 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.

How to Use This Calculator

Choose one of three modes at the top of the calculator. Solve finds the missing value when you fill three of A, B, C, and D. Simplify reduces A:B to lowest terms using the greatest common divisor. Scale works like Solve but also compares both ratios visually when all four values are filled. Common aspect-ratio presets (16:9, 4:3, 1:1, Golden ratio) auto-fill A and B so you can enter C or D to scale to a target dimension.
  • Solve Mode:
    Leave one of the four fields empty and fill the other three. The dashboard displays the solved value, the simplified ratio, and the fractional form. The Logic Trace shows the cross-multiplication step A Γ— D = B Γ— C and the isolation of the unknown.
  • Simplify Mode:
    Enter only A and B. The calculator divides both by their greatest common divisor and displays the reduced ratio alongside the GCD value.
  • Scale Mode:
    With three values filled, Scale works like Solve. With all four filled, it compares A:B and C:D with a proportional bar showing which ratio is larger or whether they are equal.
  • Presets:
    Select 16:9, 4:3, 1:1, or Golden ratio to populate A and B instantly. Then enter a target width or height in C or D to find the matching dimension for that aspect ratio.

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 Γ— D = B Γ— C
To solve for the unknown: if D is missing, D = (B Γ— C) / A; if C is missing, C = (A Γ— D) / B; if B is missing, B = (A Γ— D) / C; if A is missing, A = (B Γ— 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 β†’ GCD(8,12) = 4 β†’ (8Γ·4):(12Γ·4) = 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 (Ο† β‰ˆ 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 Γ— D = B Γ— C
Solve for the unknown (e.g. D = (B Γ— 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 β†’ GCD = 4 β†’ 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.

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.

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