⚖️ Ratio Calculator
Simplify any ratio to its lowest terms, solve proportions for a missing value using cross multiplication, scale a ratio up or down by any factor, or split any total amount into exact shares by ratio - with complete step-by-step solutions for every calculation.
✂️ Simplify a Ratio
Enter a ratio to reduce it to its simplest form.
🔍 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.
📐 Scale a Ratio
Scale a ratio up or down by a factor, or convert to a target value.
🍕 Split an Amount by Ratio
Divide a total amount according to a ratio. Perfect for splitting bills, profits, or ingredients.
📐 Ratio Formulas
Simplifying a Ratio
Divide all parts by their Greatest Common Divisor (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.
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 down: a:b ÷ n = (a÷n):(b÷n)
Example: 3:4 scaled by factor 3
= (3×3):(4×3) = 9:12
Splitting an Amount
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
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
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
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).