Ratio Calculator | Simplify & Solve
Simplify ratios, find equivalent ratios, and solve ratio problems.
Reduce a ratio to its simplest form.
All calculations run live in your browser. Simplification uses the Euclidean GCD algorithm.
What Is the Ratio Calculator | Simplify & Solve?
A ratio compares two or more quantities. This calculator handles four types of ratio problems: simplifying a ratio to lowest terms, finding equivalent ratios by scaling, solving a proportion (A:B = C:D) for a missing value, and working with three-way ratios including splitting a total amount. All calculations include step-by-step solutions.
- ›Simplify: reduce any ratio to its lowest terms using the GCD
- ›Equivalent: multiply both parts by a scale factor
- ›Solve: enter any 3 of 4 values in A:B=C:D, solve for the fourth
- ›3-Way: simplify and optionally split a total in a given 3-part ratio
Formula
Four Modes
Simplify
a : b → (a/GCD) : (b/GCD)
Equivalent
a : b × k = ak : bk
Solve A:B=C:D
D = (B × C) / A
3-Way Ratio
a : b : c → simplified + split
- ›Simplification uses GCD (Euclidean algorithm): GCD(a,b) divides both terms
- ›Cross-multiplication solves proportions: A/B = C/D ↔ AD = BC
- ›3-way: find GCD(GCD(a,b), c) to simplify all three terms simultaneously
How to Use
- 1Select a mode tab: Simplify, Equivalent, Solve A:B=C:D, or 3-Way Ratio
- 2In Simplify mode: enter two numbers A and B, the calculator reduces A:B
- 3In Equivalent mode: enter the base ratio A:B and a scale factor
- 4In Solve mode: enter any three values; leave one blank to solve for it
- 5In 3-Way mode: enter all three parts; optionally enter a total to split
- 6Click Calculate or press Enter, step-by-step solution is shown below
Example Calculation
Simplify the ratio 36 : 48:
36 / 12 = 3
48 / 12 = 4
Simplified: 3 : 4
As decimal: 0.75
36 is 42.86% of total (36+48=84)
Proportion example
If 3 apples cost $2.40, how much do 7 apples cost?
Proportion: 3 : 2.40 = 7 : D
D = (2.40 × 7) / 3 = 16.80 / 3 = $5.60
Understanding Ratio | Simplify & Solve
Common Ratios Reference
| Ratio | Simplified | Decimal | Application |
|---|---|---|---|
| 16:9 | 16:9 | 1.778 | Widescreen video |
| 4:3 | 4:3 | 1.333 | Traditional TV/monitor |
| 1:1.618 | — | 0.618 | Golden ratio |
| 3:2 | 3:2 | 1.5 | DSLR photo sensor |
| 1:1 | 1:1 | 1 | Square format |
| 22:7 | 22:7 | 3.143 | π approximation |
Frequently Asked Questions
What is a ratio?
A ratio expresses the relative sizes of two or more values. It can be written as a:b, a/b, or "a to b." Ratios are dimensionless, they compare quantities of the same unit.
- ›2:3 means "2 parts to 3 parts", if you have 5 total, split 2 and 3
- ›Ratios are equivalent when one is a scalar multiple of the other: 2:3 = 4:6 = 6:9
- ›A ratio a:b is in simplest form when GCD(a,b) = 1
- ›Ratios can compare more than two quantities: a:b:c is a three-way ratio
How do you simplify a ratio?
Simplifying (reducing) a ratio means expressing it with the smallest possible integers while keeping the same proportion.
- ›Find GCD(a, b) using the Euclidean algorithm
- ›Divide both a and b by the GCD
- ›Example: 24:36 → GCD=12 → 2:3
- ›For decimal inputs, multiply by a power of 10 first: 1.5:2.5 → 15:25 → 3:5
What is a proportion?
Proportions are one of the most useful tools in everyday mathematics, they underlie scaling recipes, map reading, unit conversion, and many word problems.
- ›Cross-multiplication property: A/B = C/D ↔ AD = BC
- ›Solve for D: D = (B × C) / A
- ›Solve for A: A = (B × C) / D
- ›Proportions are the foundation of percentage calculations and scale factors
How do I split an amount in a given ratio?
Splitting an amount in a ratio is a common task in finance, cooking, and resource allocation.
- ›Ratio 2:3 splitting $50: Part A = 50 × 2/5 = $20, Part B = 50 × 3/5 = $30
- ›Sum of parts (denominator) = 2 + 3 = 5
- ›Each part gets (its_ratio_value / total_parts) × total_amount
- ›3-way: 1:2:3 splitting 120 → 20 : 40 : 60
What is an equivalent ratio?
Equivalent ratios represent the same relationship at a different scale. They are useful in scaling recipes, maps, and technical drawings.
- ›Multiply or divide both parts by the same non-zero number
- ›2:3 × 5 = 10:15, a 5× scaled equivalent
- ›All equivalent ratios reduce to the same simplest form
- ›Example: a map scale of 1:50000 means 1 cm = 500 m
Can I use ratios with decimals or fractions?
Ratios are not limited to integers. This calculator accepts any positive decimal value and simplifies using an integer-scaled GCD approach.
- ›1.5 : 2.5 → scaled to 15:25 → GCD=5 → 3:5
- ›0.25 : 0.75 → 25:75 → GCD=25 → 1:3
- ›Very large or very small decimals use scientific notation in the output
- ›Enter fractions as decimals: ¾ = 0.75, ⅓ ≈ 0.333
What real-world problems use ratios?
Ratios are fundamental to quantitative reasoning across virtually every field.
- ›Cooking: scale a recipe for 4 to serve 10, multiply all ingredients by 10/4
- ›Maps: 1:50000 means every 1 cm on the map = 50,000 cm (500 m) in reality
- ›Finance: debt-to-equity ratio = total liabilities / shareholder equity
- ›Photography: 16:9 widescreen, 4:3 traditional, 1:1 square
- ›Chemistry: mixing 2 parts resin to 1 part hardener (2:1 mix)