Math & General

Ratio Calculator

Simplify ratios, solve proportions, scale values, split amounts, compare ratios and find equivalent ratios — with full step-by-step working. Supports 2-part and 3-part ratios.

7 Calculation Types
Step-by-Step Working
2 & 3-Part Ratios
100% Free

Ratio Calculator — All Types

Select a calculation type, enter your values, and get the answer with complete step-by-step working

✨
Simplify
Reduce a:b
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Proportion
Solve a:b = c:?
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Scale Ratio
Multiply/divide
🍕
Split Amount
Divide a total
⚖️
Compare
Which is bigger?
🔗
Equivalent
Find equal ratios
🔺
3-Part Ratio
Simplify a:b:c
✨ Simplify: Reduce a:b to its simplest form
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Optional: Enter a total amount below to also split it in this 3-part ratio.
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    What Is a Ratio?

    Core concepts, types of ratios, and how they are used in everyday life

    Definition
    A Comparison Between Two or More Quantities

    A ratio is a way of comparing two or more quantities of the same kind. Written as A:B (read "A to B"), it shows how much of A there is for every B. For example, a ratio of 3:1 means there are 3 parts of the first quantity for every 1 part of the second.

    Ratios are dimensionless — a ratio of 2:3 apples to oranges is the same whether you have 2 and 3, or 200 and 300. This scale-independence is what makes ratios so powerful in recipes, maps, financial analysis, engineering drawings, paint mixing, and academic exam questions.

    Ratio vs. Fraction: A ratio A:B is closely related to the fraction A/B. The key difference is context — a fraction A/B means A out of A+B total parts, while the ratio A:B compares A to B directly. So a 1:3 ratio means 1 part in 4 total (fraction ¼), not 1 out of 3.
    Real-World Ratio Examples
    🍳
    Recipes & Cooking

    Flour to butter ratios in baking (2:1), concrete mix ratios (cement:sand:gravel = 1:2:3), paint mixing to match custom colours.

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    Maps & Scale Drawings

    A scale of 1:50,000 means 1 cm on the map = 50,000 cm (500 m) in real life. Engineers use scale ratios constantly in blueprints.

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    Finance & Business

    Price-to-earnings (P/E) ratio, debt-to-equity ratio, current ratio — all are used to evaluate the health and valuation of companies.

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    Chemistry & Medicine

    Drug dilutions, chemical solutions, and reagent mixtures are all specified as ratios. A 1:10 dilution means 1 part in 10 total.

    Ratio Formulas — Complete Reference

    All ratio operation rules with formulas and worked examples

    OperationFormula / MethodExampleResult
    SimplifyA:B → (A÷GCD) : (B÷GCD)12:18, GCD=62:3
    Proportion (find ?)A:B = C:? → ? = (B×C)÷A3:4 = 9:?12
    Scale up/down(A×k) : (B×k)2:3 × 510:15
    Split totalA share = Total × A/(A+B)1200 in 3:1900 : 300
    CompareConvert to decimal: A/B vs C/D3:4 vs 2:30.75 > 0.667
    Equivalent ratio(A×n) : (B×n) for n=1,2,3…2:3 → ×2,×3…4:6, 6:9…
    Ratio to %A% = 100×A/(A+B)3:175% : 25%
    3-Part simplifyGCD(A,B,C) then divide all6:9:152:3:5
    Quick tip — Proportion shortcut: In any proportion A:B = C:D, the cross-products are equal: A×D = B×C. This is called the "means-extremes" property and lets you find any missing value instantly.

    Frequently Asked Questions

    Common questions about ratios, proportions and how to use this calculator

    How do you simplify a ratio?
    Find the Greatest Common Divisor (GCD) of both numbers and divide each part by it. For example, to simplify 24:36: GCD(24,36) = 12. 24÷12 = 2, 36÷12 = 3. So 24:36 = 2:3. A ratio is fully simplified when its GCD is 1 (i.e. both numbers share no common factor other than 1).
    How do you solve a proportion (find the missing value)?
    Use cross-multiplication. If A:B = C:D (or A/B = C/D), then A×D = B×C. To find D: D = (B×C)÷A. Example: 3:4 = 9:? → ? = (4×9)÷3 = 36÷3 = 12. So 3:4 = 9:12. Always verify by checking if the two fractions are equal: 3/4 = 9/12 = 0.75 ✓
    How do you divide an amount in a given ratio?
    Add all the ratio parts to find the total number of shares. Divide the amount by total shares to find the value of one share. Multiply each part by the value of one share. Example: Split ₹1,200 in ratio 3:1. Total shares = 3+1 = 4. One share = 1200÷4 = 300. Part A = 3×300 = ₹900. Part B = 1×300 = ₹300. Check: 900+300 = 1200 ✓
    How do you compare two ratios?
    Convert each ratio to a decimal (divide the first part by the second) and compare. For 3:4 vs 2:3: 3÷4 = 0.75 and 2÷3 = 0.667. Since 0.75 > 0.667, the ratio 3:4 is greater. Alternatively, cross-multiply: 3×3 vs 2×4 = 9 vs 8, so 3:4 > 2:3.
    What are equivalent ratios?
    Equivalent ratios represent the same comparison scaled up or down. Multiply or divide both parts by the same non-zero number. For example, 2:3 is equivalent to 4:6 (×2), 6:9 (×3), 10:15 (×5), 1:1.5 (÷2). All equivalent ratios simplify to the same simplest form (2:3 in this case).
    How do you simplify a 3-part ratio like 6:9:15?
    Find the GCD of all three numbers. GCD(6,9) = 3, then GCD(3,15) = 3. So GCD(6,9,15) = 3. Divide each part: 6÷3 = 2, 9÷3 = 3, 15÷3 = 5. Simplified ratio = 2:3:5. The GCD of three numbers is the GCD of the GCD of the first two and the third number.
    Is this calculator private? Is any data stored?
    Yes, completely private. All calculations happen entirely in your browser using JavaScript — no number you enter is ever sent to a server. The page works fully offline once loaded. Your inputs disappear the moment you close or refresh the tab.