Ratio Calculator

A comprehensive equation solver that handles both linear and quadratic equations. It provides detailed solutions, including discriminant values, multiple roots, and even complex number solutions. The solver features live equation preview and handles all mathematical edge cases automatically.

How to Use

Step 1: Enter Your Ratio

• Input two numbers in the format A: B (e.g., 3:4, 5:2, 12:18)
• These represent the base ratio you want to work with

Step 2: Choose a Calculation Mode

• Find B: Use when you know the ratio and have a value for A, and want to find B
  • Example: Ratio 2:3, if A = 10, then B = 15
• Find A: Use when you know the ratio and have a value for B, and want to find A
  • Example: Ratio 4:5, if B = 20, then A = 16
• Simplify: Reduces any ratio to its simplest form
  • Example: 12:18 simplifies to 2:3

Step 3: Enter Known Value (for Find A/Find B modes only)

• Type the value you already know
• Skip this step if you’re just simplifying

Step 4: Calculate

• Click the “Calculate” button or press Enter
• View your results instantly

Step 5: Clear (optional)

• Click “Clear” to reset all fields and start over

Use Cases

• Recipe scaling (double or halve ingredients)
• Paint/concrete mixing ratios
• Aspect ratio calculations for images/videos
• Currency or unit conversions
• Map scale calculations

🔢 Equation Solver

Description

A comprehensive equation solver that handles both linear and quadratic equations. It provides detailed solutions, including discriminant values, multiple roots, and even complex number solutions. The solver features live equation preview and handles all mathematical edge cases automatically.

How to Use

Step 1: Select Equation Type

• Linear (ax + b = 0): For simple first-degree equations
• Quadratic (ax² + bx + c = 0): For second-degree equations

Step 2: Enter Coefficients

• Type values for a, b, and c (if quadratic)
• Watch the equation preview update in real-time
• Default values are provided (a=1, b=0, c=0)

Step 3: Solve

• Click the “Solve” button or press Enter
• View detailed solution breakdown

Step 4: Interpret Results

For Linear Equations:

• Single solution: x = [value]
• Special cases: infinite solutions or no solution

For Quadratic Equations:

• Discriminant value (Δ = b² – 4ac)
• If Δ > 0: Two different real solutions
• If Δ = 0: One repeated root
• If Δ < 0: Two complex solutions (with i)

Step 5: Clear (optional)

• Click “Clear” to reset coefficients to default values

Use Cases

• Algebra homework and practice
• Physics problems (motion, energy equations)
• Engineering calculations
• Financial modeling (break-even analysis)
• Geometry problems (area, perimeter equations)
• Finding roots and intercepts for graphing

Examples

Linear Example:

• Equation: 2x + 6 = 0
• Solution: x = -3

Quadratic Examples:

• 1x² – 5x + 6 = 0 → Two real roots: x₁ = 3, x₂ = 2
• 1x² – 4x + 4 = 0 → One repeated root: x = 2
• 1x² + 0x + 1 = 0 → Complex roots: x₁ = 0 + 1i, x₂ = 0 – 1i

Both calculators feature:

• ✅ Clean, modern interface
• ✅ Mobile responsive design
• ✅ Real-time validation
• ✅ Smooth animations
• ✅ Clear result displays
• ✅ Easy-to-use Clear button