Ratio Calculator - Simplify & Solve Ratios

✂️ Simplify a Ratio

Enter a ratio to reduce it to its simplest form.

First Value

Second Value

Third (opt.)

Try:

Solve a Proportion

Enter 3 values - leave the unknown as blank (x). Find the missing value in a proportion.

Form: a/b = c/d Leave any ONE field blank to solve for it.

Try:

Missing Value (x)

Scale a Ratio

Scale a ratio up or down by a factor, or convert to a target value.

Original Ratio A

Original Ratio B

Scale Factor

🍕 Split an Amount by Ratio

Divide a total amount according to a ratio. Perfect for splitting bills, profits, or ingredients.

Total Amount

Ratio (colon-separated, e.g. 2:3 or 1:2:3)

Ratio Formulas

Simplifying a Ratio

Divide all parts by their Greatest Common Divisor (GCD).

Simplified ratio = (a÷GCD) : (b÷GCD)

Example: 12:18
GCD(12,18) = 6
= (12÷6):(18÷6) = 2:3

Solving a Proportion

Use cross multiplication: if a/b = c/d, then a×d = b×c.

a/b = c/d Cross multiply a×d = b×c

Solve for x:
3/4 = x/8 3×8 = 4×x 24 = 4x x = 6
3/x = 9/12 3×12 = x×9 36 = 9x x = 4

Scaling a Ratio

Scale up: a:b × n = (a×n):(b×n)
Scale down: a:b ÷ n = (a÷n):(b÷n)

Example: 3:4 scaled by factor 3
= (3×3):(4×3) = 9:12

Splitting an Amount

Given total T and ratio a:b:c

Share of a = T × a/(a+b+c)
Share of b = T × b/(a+b+c)
Share of c = T × c/(a+b+c)

Example: $1200 split 2:3
Total parts = 2+3 = 5
Part A = 1200 × 2/5 = $480
Part B = 1200 × 3/5 = $720

Ratio vs Fraction vs Percentage

Ratio 2:3 means:
Fraction: 2/3 (A is 2/3 of B)
A is 40% of total (2 out of 5 parts)
B is 60% of total (3 out of 5 parts)

Ratio a:b a/(a+b) and b/(a+b) as fractions of total

Frequently Asked Questions

A ratio compares two or more quantities. For example, 3:2 means for every 3 of the first quantity there are 2 of the second. Ratios can be simplified (like fractions) by dividing all parts by their GCD. Ratios describe a relationship - they can be scaled up or down and still represent the same relationship. 3:2 = 6:4 = 15:10 = 0.3:0.2 - all describe the same proportion.

Find the GCD (Greatest Common Divisor) of all parts and divide each part by it. Example: 12:18. GCD(12,18)=6. 12÷6=2, 18÷6=3. Simplified: 2:3. Three-part example: 4:6:10. GCD(4,6,10)=2. Simplified: 2:3:5. A ratio is fully simplified when no further common factor exists among all parts. The simplest form is unique - there is exactly one simplest equivalent ratio for any ratio.

A proportion states two ratios are equal: a:b = c:d, or a/b = c/d. To find a missing value, use cross multiplication: a×d = b×c. Example: 3/4 = x/8 → 3×8 = 4×x → 24 = 4x → x = 6. Example: 5/x = 15/12 → 5×12 = x×15 → 60 = 15x → x = 4. Any of the four positions can be the unknown - rearrange the cross-multiplication equation to isolate the unknown.

Add all ratio parts to get total parts. Each share = (ratio part ÷ total parts) × total amount. Example: split ₹5,000 in ratio 2:3:5. Total parts = 2+3+5 = 10. Share A = (2÷10) × 5,000 = ₹1,000. Share B = (3÷10) × 5,000 = ₹1,500. Share C = (5÷10) × 5,000 = ₹2,500. Verify: ₹1,000 + ₹1,500 + ₹2,500 = ₹5,000 ✓

A ratio a:b compares two quantities to each other. A fraction a/(a+b) shows what part of the whole a represents. Example: ratio 2:3. A is 2/3 of B. But A is 2/5 (40%) of the total (A+B=5). In contrast, the fraction 2/5 directly states '2 out of every 5.' To convert a ratio share to a percentage of the whole: part ÷ (sum of all parts) × 100. In ratio 2:3:5, the first part represents 2÷10 = 20% of the whole.

Equivalent ratios represent the same relationship between quantities. 1:2, 2:4, 3:6, 50:100 are all equivalent. To check if two ratios are equivalent: simplify both to lowest terms. If identical, they're equivalent. Another method: cross multiply - a:b and c:d are equivalent if a×d = b×c. Example: 4:6 and 6:9. Cross: 4×9=36 = 6×6=36 ✓ Equivalent. Creating equivalent ratios: multiply (or divide) all parts by the same number.

Multiply or divide all parts of the ratio by the same factor. Example: scale 3:4 by factor 5 → 15:20. Scale 2:3:1 by 4 → 8:12:4. To reduce: scale by 1/factor. 15:20 ÷ 5 → 3:4. Scaling is how you find equivalent ratios useful for a specific context - like scaling a recipe from 4 servings to 10 (factor = 10÷4 = 2.5) or converting a map distance to real distance.

The golden ratio φ = (1+√5)÷2 ≈ 1.6180... is the unique ratio a:b where (a+b)/a = a/b = φ. Represented as 1:1.618 or approximately 5:8. Consecutive Fibonacci numbers (1,1,2,3,5,8,13,21,34...) approach φ - each pair 8:13, 13:21, 21:34 gets closer. Found in nature (sunflower seeds, nautilus shells, pine cones), classical architecture (Parthenon proportions), and art. Whether it is specifically 'more beautiful' than other ratios is debated - but it genuinely appears throughout natural growth patterns.

Ratio Calculator - Simplifying, Proportions, Scaling and Splitting Explained

Ratios are one of the most fundamental mathematical concepts - and one of the most frequently misapplied. Whether you're scaling a recipe, splitting a bill, solving a proportion in a maths exam, or checking if two ratios are equivalent, the underlying operations are straightforward once you understand them clearly.

The four ratio operations: (1) Simplify 12:18 divide both by GCD(12,18)=6 2:3. (2) Solve 3:4 = x:8 cross multiply x = (3×8)÷4 = 6. (3) Scale 3:4 by factor 5 15:20. (4) Split ₹1,200 in 2:3 shares: ₹480 and ₹720.

The Four Ratio Operations

Simplify and Proportion

Simplify: Divide all parts by GCD. 15:25:35 GCD=5 3:5:7.
A ratio is fully simplified when GCD of all parts = 1.
Proportion (a:b = c:d): Cross multiply: a×d = b×c. Unknown = (product of known three ÷ opposite). 3:4 = 9:x x = (4×9)÷3 = 12.
Works for all four positions - any one can be the unknown.

Scale and Split

Scale: Multiply (or divide) all parts by the same factor. 2:3 scaled ×4 = 8:12. Equivalent ratios - same relationship, different values.
Split amount: Add all parts (total parts). Each share = (part ÷ total parts) × total amount.
Example: ₹5,000 split 1:2:2. Total parts = 5. Shares: ₹1,000, ₹2,000, ₹2,000.

Ratios vs Fractions - The Key Distinction

Ratios and fractions are related but not identical:

A ratio a:b compares two quantities to each other - it describes a relationship.
A fraction a/(a+b) shows what part a is of the whole (a+b).
Example: ratio 2:3. The first quantity is 2/3 of the second quantity. But the first quantity is 2/5 (40%) of the total (2+3=5).
Scaling a ratio: multiply all parts by the same number. This produces equivalent ratios - different numbers, same relationship. 2:3 = 4:6 = 6:9 = 100:150.
Equivalent ratios simplify to the same lowest-terms ratio. To check equivalence: simplify both - if identical, they're equivalent.

Real-World Ratio Applications

Cooking and recipes: A recipe for 4 serves uses 300g flour and 200g butter - ratio 3:2. For 10 serves: scale by 10÷4 = 2.5 750g flour and 500g butter.
Map and scale drawing: A map at scale 1:50,000 means 1cm on paper = 50,000cm = 500m in reality. Measured 4cm on map 4 × 500m = 2km in reality.
Business profit sharing: Partners A, B, C contributed capital in ratio 3:5:2. On a profit of ₹2,00,000: A gets ₹60,000, B gets ₹1,00,000, C gets ₹40,000.
Photography aspect ratios: 16:9 (widescreen), 4:3 (traditional), 3:2 (DSLR). Scaling for different screen sizes while maintaining the same proportional dimensions.
Concrete mix: Standard mix is cement:sand:aggregate = 1:2:4 by volume. For 1 cubic metre: approximately 143kg cement, 286kg sand, and 571kg aggregate.

The Golden Ratio - φ ≈ 1.618

The golden ratio (φ = (1 + √5) ÷ 2 ≈ 1.6180339...) is the ratio a:b such that (a+b):a = a:b. It appears in nature (flower petals, shell spirals, leaf arrangements), art and architecture (the Parthenon, Leonardo da Vinci's compositions), and is often described as intrinsically aesthetically pleasing. In simplified ratio terms: 1:1.618. In whole number approximation: 5:8, 8:13, 13:21 (each consecutive pair from the Fibonacci sequence approaches φ).

How this calculator works, and where the numbers come from

The Ratio Calculator applies the standard formula for this calculation to the values you enter and updates the result as you type. The calculation itself happens in your browser, and the page explains the method so you can check any result by hand.

Please note: Results are provided for general information and are calculated from the values you enter.

Sources and further reading

Last reviewed: October 6, 2026 by the CalcQube Editorial Team. See our editorial policy for how we build and check calculators, or report an error.

⚖️ Ratio Calculator