Ratio Calculator
Solve proportions (A:B = C:D) via cross-multiplication, find missing values, and scale ratios (shrink or enlarge) with GCD reduction.
Ratio Calculator
Solve proportions (A:B = C:D), find missing terms through cross-multiplication, and enlarge or shrink ratios with scale factors and greatest common divisor (GCD) simplification.
• Module 1 (Proportion): Enter any 3 of the 4 values (A, B, C, D) to solve for the missing term via cross-multiplication (A × D = B × C).
• Module 2 (Ratio Scaling): Enter ratio terms, choose Shrink or Enlarge, and provide a scale factor.
Proportion Inputs (A:B = C:D)
Please provide any three values below to calculate the fourth in the ratio A:B = C:D.
Awaiting Calculation
Provide any 3 values on the left (A, B, C, or D) to solve the 4th with step-by-step cross-multiplication.
Comprehensive Guide to Ratios, Proportions, and Scaling
Understanding proportional relationships, cross-multiplication, aspect ratio math, and GCD simplification.
1What is a Ratio?
A ratio is a mathematical comparison of two or more quantities indicating how many times one value is contained within another. In a ratio A : B, the first number A is the antecedent and the second number B is the consequent.
Ratios can be written in three common notations:
- Colon Notation: 3 : 4
- Fraction Notation: 3 / 4
- Word Notation: "3 to 4"
2Proportions and Cross-Multiplication
A proportion is an equation stating that two ratios are equal:
3Common Aspect Ratios & Scaling in Real Life
16:9 Widescreen
Standard for YouTube, HDTV, Full HD (1920×1080), 4K UHD (3840×2160).
4:3 Classic Display
Standard television broadcast, iPad displays, and vintage PC monitors (1024×768).
21:9 Ultrawide Cinema
Cinematic anamorphic format and gaming monitors (3440×1440).
4Step-by-Step Worked Example
Frequently Asked Questions
What is the difference between a ratio and a proportion?
A ratio compares two quantities (e.g., 3:4). A proportion is a statement that two ratios are equal to each other (e.g., 3:4 = 6:8).
How do you reduce or simplify a ratio to lowest terms?
Find the greatest common divisor (GCD) of both terms and divide both numbers by the GCD. For example, for 250:280, the GCD is 10, giving 25:28.
Can ratios contain decimals or fractions?
Yes. Decimal ratios (like 1.5 : 2.5) can be converted to integer ratios by multiplying both terms by 10 or 100 and simplifying (1.5 : 2.5 → 15 : 25 → 3 : 5).
How does cross-multiplication work when solving for an unknown variable?
Because A/B = C/D, multiplying both sides by (B × D) yields A × D = B × C. Dividing both sides by the known coefficient yields the exact value of the unknown variable.
Understanding Ratio Calculator & Formula
The Ratio Calculator on CalculatorScale.com is engineered to deliver instant, mathematically verified calculations conforming strictly to standard institutional equations. Whether planning long-term investments, managing household budgets, tracking clinical fitness targets, analyzing academic genetics, calculating veterinary dosages, or converting dimensional units, every calculation updates dynamically in real time without lag.
Every formula used in this tool adheres to certified international standards, including World Health Organization biometric metrics, veterinary clinical guidelines, NIST physical conversion constants, and standard biological equations. Results are computed entirely client-side inside your browser with complete data privacy, ensuring your sensitive numbers and statistics never leave your device.
Our calculators are 100% free with no registration, subscriptions, or paywalls required. You can toggle between imperial and metric units, customize input parameters, export calculation summaries, or embed this calculator directly into your own website or blog.
How to Use the Ratio Calculator
- 1 Module 1 (Proportion): Enter any 3 values among A, B, C, and D to solve for the 4th missing term via cross-multiplication.
- 2 Module 2 (Scaling): Enter ratio terms, choose Shrink (÷) or Enlarge (×), and specify the scale factor.
- 3 Select a Quick Ratio Preset (such as 16:9 widescreen or recipe scaling) for instant values.
- 4 Click "Calculate" to view the full proportion, decimal equivalent, and step-by-step cross-multiplication steps.
- 5 Use the "Copy" action to export the exact solution and simplified ratio.
Ratio Calculator — Frequently Asked Questions
Q1 How do you solve for an unknown term in a ratio (A:B = C:D)? ▾
Set up the fraction equivalence A/B = C/D and cross-multiply: A × D = B × C. Divide both sides by the known factor to isolate the unknown variable (e.g., D = (B × C) / A).
Q2 How do you simplify a ratio to its lowest integer form? ▾
Find the greatest common divisor (GCD) of both numbers and divide each number by the GCD. For example, in 600:800, GCD = 200, so 600/200 : 800/200 = 3:4.
Q3 What are common aspect ratios used in media and photography? ▾
Common aspect ratios include 16:9 (modern TVs, YouTube, standard smartphones), 4:3 (classic TV, iPads, photography), 21:9 (ultrawide cinema monitors), and 1:1 (square social media formats).
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