Ratio Calculator

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Calculate simplified ratios, solve missing proportion values by cross-multiplication, and scale ratios to any target total. Works with both two part and three part ratios and shows the step by step working so you can verify every result.

How to Use

01

Choose a calculation mode: Simplify, Solve Proportion, or Scale to Total.

02

Enter the ratio parts A and B. Add Part C for three part ratios.

03

For proportions, enter the known value and select which side to solve. For scaling, enter the target total.

04

Click Calculate to see instant results with full working shown.

How the Ratio Calculator Works

A ratio compares two or more quantities by division. This calculator handles three tasks. Simplify divides all parts by their greatest common divisor (GCD), found with the Euclidean algorithm, reducing 12:8 to 3:2. Solve Proportion uses cross-multiplication: given A:B = C:?, the answer is (B × C) ÷ A. Scale to Total distributes a number across parts proportionally, so scaling 3:2 to 100 yields 60 and 40. All three modes accept an optional third part for three way ratios, with a percentage breakdown table for the three part case.

Step by Step Example

  1. Simplify 15:10. GCD(15, 10) = 5. Simplified ratio = 3:2.
  2. Decimal form: 15 ÷ 10 = 1.5. Percentage split: 60% to 40%.
  3. Solve proportion 3:2 = 9:? Missing = (2 × 9) ÷ 3 = 6. Answer: 9:6.
  4. Scale 3:2 to total 500. Part A = 500 × 3/5 = 300, Part B = 500 × 2/5 = 200.
  5. Three part simplify: 6:4:2. GCD = 2. Simplified = 3:2:1.
  6. Three part scale: 3:2:1 to total 120. A = 60, B = 40, C = 20.

When to Use This Calculator

  • Reducing a recipe or mixture ratio to its simplest form before scaling
  • Checking whether two ratios are equivalent by solving for the unknown value
  • Splitting a budget, ingredient quantity, or mixture into proportional parts
  • Mixing paint, concrete, or chemicals in a specified ratio to a known total volume
  • Converting a ratio to a percentage split for charts, reports, or presentations
  • Solving ratio and proportion questions in maths coursework or standardised tests

Important Note

All input values must be positive numbers greater than zero. For the proportion solver, Part A of the base ratio must be non-zero to avoid division by zero. Results use standard floating point arithmetic, so for ratios with many decimal places the GCD is approximated by scaling to integers. Verify precision independently for critical applications.

Simplifying vs Keeping the Original Ratio

Simplified ratios are easier to read, communicate, and compare at a glance
Lowest terms form reduces arithmetic errors in subsequent calculations
Standard form makes it straightforward to verify equivalence between ratios
Simplifying a recipe ratio too far may make measuring small fractions impractical
Simplification removes the original quantity context, which can matter in documentation

Key Features

Ratio Simplification

Reduces any ratio to lowest terms using the Euclidean GCD algorithm, with decimal and percentage forms for two part ratios.

Proportion Solver

Finds the missing value in equivalent ratios by cross-multiplication, solving for either side of the equation.

Scale to Total

Distributes a target number across ratio parts proportionally, showing each part's share and percentage.

Three Part Ratio Support

Handles three part ratios in simplify and scale modes with a full percentage breakdown table.

Step by Step Working

Displays the arithmetic behind every result so you can follow the logic or use it in coursework.