Why two modes?
Simplifying and solving are distinct tasks that get conflated in most online tools. Splitting them keeps each form minimal and labels exactly which term is unknown, so there is no ambiguity about what the calculator is computing.
Ratio Calculator
Simplify a ratio or solve a proportion. The formula shows alongside the answer.
Ratios compare two quantities — flour to water in a recipe, parts of paint in a mix, students to teachers, map scale to real distance. The two modes below cover the everyday ratio questions: reducing a ratio to its lowest whole-number terms, and finding the missing value in a proportion where three of the four terms are known. Every calculation runs in your browser and the formula is shown underneath so you can verify by hand.
Reduce a ratio to its lowest terms and show the decimal
10 : 15 simplified
2 : 3
10 : 15 = 2 : 3 · 10 ÷ 15 = 0.666667
How to use
Pick the question type
Tabs across the top: "Simplify a:b" reduces a ratio to lowest terms, "Solve a:b = c:?" finds the missing fourth term of a proportion. Pick the one that matches your question.
Fill in the numbers
The result and the formula update as you type. There is no submit button.
Read the answer
The big tinted value is the answer. The mono-spaced line under it shows exactly how the answer was computed, including the decimal form of the ratio.
Worked examples
| Question | Inputs | Answer |
|---|---|---|
| Simplify 10:15 | 10, 15 | 2 : 3 |
| Simplify 8:4 | 8, 4 | 2 : 1 |
| Solve 1:2 = 3:? | 1, 2, 3 | 6 |
| Solve 2:3 = 10:? | 2, 3, 10 | 15 |
Frequently asked questions
- How do I simplify a ratio by hand?
- Find the greatest common divisor (GCD) of both terms, then divide each term by it. For 10:15 the GCD is 5, so 10 ÷ 5 : 15 ÷ 5 = 2:3. The calculator uses the Euclidean algorithm to do exactly this.
- How do I solve a proportion?
- A proportion a:b = c:x is solved by cross-multiplication: a · x = b · c, so x = (b · c) ÷ a. For 1:2 = 3:x, x = (2 × 3) ÷ 1 = 6.
- What is the decimal form of a ratio?
- It's simply the first term divided by the second. The ratio 2:3 equals 2 ÷ 3 ≈ 0.6667. The simplify mode shows this decimal beside the reduced ratio.
- Why does simplifying with a zero second term show a dash?
- A ratio compared against zero (a:0) has no finite reduced form because reducing requires dividing by the GCD, and the decimal form would divide by zero. The calculator surfaces a dash rather than Infinity or NaN.
- Can I enter decimals like 1.5?
- Yes. In simplify mode, decimal terms are scaled up to whole numbers before reducing — 1.5:2 becomes 3:4. The proportion solver accepts any finite number directly.
- Does the calculator store my data?
- No. Every computation happens in your browser; nothing is sent to a server.
About
How reduction works
Ratios are reduced with the Euclidean algorithm for the greatest common divisor, the same method taught in school and used throughout computer science. Decimal inputs are first scaled by the smallest power of ten that makes both terms integers, so the result is always a clean whole-number ratio.
Rounding behaviour
Decimal results display with up to six decimal places, with trailing zeros trimmed. The raw IEEE 754 double is used for the underlying computation, so the displayed digits are exactly what JavaScript would produce for the same operation.
Sources & references
Authoritative references behind the math, constants, and tables on this page. Verified by Buğra Sözeri on the dates shown and re-checked at every deploy.
- ECMAScript Language Specification — Numbers — Specifies JavaScript's double-precision arithmetic that drives every result in the widget(as of )
- Euclidean algorithm — greatest common divisor — The GCD method used to reduce ratios to lowest terms(as of )
- Proportionality (mathematics) — Definition of proportions and cross-multiplication that drives the proportion solver(as of )