Ratio Calculator
Simplify ratios, solve for missing values, scale ratios, and split quantities — all with step-by-step working
How to Use This Ratio Calculator
- Select one of four modes: Simplify Ratio, Solve for Missing Value, Scale a Ratio, or Split a Quantity.
- Fill in the required input fields for your chosen mode. Each mode displays only the relevant fields.
- Press the Calculate button to instantly compute the result with a full step-by-step breakdown.
- Review the result, simplified form, and percentage breakdown shown in the result panel.
- Use the Clear button to reset all fields and run a new calculation at any time.
Key Features
Simplify to Lowest Terms
Automatically finds the GCD and reduces any ratio — including 3-part ratios — to its simplest equivalent form.
Solve Missing Values
Leave any one value blank in A:B = C:D and the calculator uses cross-multiplication to find the unknown instantly.
Scale Any Ratio
Multiply both parts of a ratio by any factor to generate an equivalent scaled ratio — useful for recipes, maps, and models.
Split Quantities by Ratio
Divide any total into 2 or 3 parts according to a given ratio, with each share shown as a value and as a percentage.
Percentage Breakdown
Every result includes the percentage each part represents of the whole, making ratios easy to interpret visually.
Step-by-Step Working
Every calculation shows the formula applied and each arithmetic step so you can follow and verify the logic.
Formulas and How Each Mode Works
All four calculator modes use well-established mathematical rules. Here is a clear explanation of each formula applied.
GCD = Greatest Common Divisor of all parts
Simplified A = A ÷ GCD
Simplified B = B ÷ GCD
Simplified C = C ÷ GCD (if provided)
Percentage of A = A / (A+B+C) × 100
Cross-multiplication: A × D = B × C
Missing A = (B × C) ÷ D
Missing B = (A × D) ÷ C
Missing C = (A × D) ÷ B
Missing D = (B × C) ÷ A
Scaled A = A × Factor
Scaled B = B × Factor
The ratio relationship A:B remains unchanged — only the magnitude increases.
Sum of parts = A + B + C
Share A = Total × A ÷ Sum
Share B = Total × B ÷ Sum
Share C = Total × C ÷ Sum (if provided)
All simplification uses the Euclidean algorithm to find the GCD, which works by repeatedly applying GCD(a,b) = GCD(b, a mod b) until the remainder is zero. This guarantees the smallest whole-number ratio every time.
Practical Examples
🇮🇳 Priya — Paint Mixing, Kolkata, India
Scenario: Priya is mixing wall paint. The formula calls for red, white, and blue in the ratio 6:9:3. She wants the simplest form to measure accurately with a small cup.
Calculation: GCD(6,9,3) = 3. Simplified ratio = 6÷3 : 9÷3 : 3÷3 = 2 : 3 : 1
✓ Simplified: 2 : 3 : 1🇮🇳 Ramesh — Profit Sharing, Hyderabad, India
Scenario: Ramesh and his two partners invested in a business in the ratio 5:3:2. The total profit for the year is ₹2,40,000. How much does each partner receive?
Calculation: Sum = 10. Ramesh = 2,40,000 × 5/10 = ₹1,20,000. Partner 2 = ₹72,000. Partner 3 = ₹48,000.
✓ ₹1,20,000 : ₹72,000 : ₹48,000🇺🇸 Emily — Recipe Scaling, New York, USA
Scenario: Emily's cookie recipe uses flour and sugar in a 3:1 ratio. She wants to scale up by a factor of 6 for a school bake sale.
Calculation: Scaled ratio = 3×6 : 1×6 = 18 : 6. That's 18 cups flour to 6 cups sugar.
✓ Scaled: 18 : 6🇮🇳 Arjun — Exam Problem, Chennai, India
Scenario: Arjun's maths exam asks: "If 4 : 7 = 12 : ?, find the missing value."
Calculation: Cross-multiply: missing D = (7 × 12) ÷ 4 = 84 ÷ 4 = 21. So 4:7 = 12:21.
✓ Missing value = 21What Is a Ratio Calculator?
A ratio calculator is a tool that helps you work with ratios — mathematical expressions that compare two or more quantities. Ratios appear in nearly every practical domain: cooking, construction, finance, chemistry, photography, maps, and school mathematics. Instead of calculating GCDs or cross-multiplications by hand, a ratio calculator handles all the arithmetic instantly.
This tool goes beyond basic simplification. It solves proportions (finding missing values in equivalent ratios), scales ratios up or down by any factor, and splits any total amount into parts according to a given ratio. Each result includes a percentage breakdown so you can instantly see what share each part represents. Whether you are a student solving proportion problems, a business owner dividing profits, or a cook scaling a recipe, this calculator covers the full range of ratio operations in one place.
All calculations happen entirely in your browser. Nothing is sent to any server, there is no sign-up required, and results are available the moment you press Calculate. The step-by-step breakdown is designed so you can understand and verify every result, not just copy a number.
🇮🇳 Indian Languages
Hindi: अनुपात कैलकुलेटर — अनुपात को सरल करें, लापता मान खोजें, स्केल करें या मात्रा विभाजित करें।
Tamil: விகித கணிப்பான் — விகிதத்தை எளிமைப்படுத்தவும், காணாமல் போன மதிப்பைக் கண்டறியவும், அளவை பிரிக்கவும்.
Telugu: నిష్పత్తి కాల్క్యులేటర్ — నిష్పత్తిని సులభతరం చేయండి, తప్పిన విలువను కనుగొనండి, మొత్తాన్ని విభజించండి.
Bengali: অনুপাত ক্যালকুলেটর — অনুপাত সরল করুন, অনুপস্থিত মান খুঁজুন এবং পরিমাণ ভাগ করুন।
Marathi: गुणोत्तर कॅल्क्युलेटर — गुणोत्तर सरल करा, अज्ञात मूल्य शोधा, प्रमाण वाढवा किंवा रक्कम विभाजित करा.
Gujarati: ગુણોત્તર કેલ્ક્યુલેટર — ગુણોત્તરને સરળ બનાવો, ગુમ મૂલ્ય શોધો, સ્કેલ કરો અથવા જથ્થો વિભાજિત કરો.
Kannada: ಅನುಪಾತ ಕ್ಯಾಲ್ಕುಲೇಟರ್ — ಅನುಪಾತವನ್ನು ಸರಳಗೊಳಿಸಿ, ಕಾಣೆಯಾದ ಮೌಲ್ಯ ಕಂಡುಹಿಡಿಯಿರಿ, ಮೊತ್ತ ವಿಭಜಿಸಿ.
Malayalam: അനുപാത കാൽക്കുലേറ്റർ — അനുപാതം ലഘൂകരിക്കുക, കാണാത്ത മൂല്യം കണ്ടെത്തുക, അളവ് വിഭജിക്കുക.
🌍 International Languages
Spanish: Calculadora de razones — Simplifica razones, resuelve valores desconocidos y divide cantidades.
French: Calculatrice de ratio — Simplifiez les ratios, résolvez les valeurs manquantes et divisez les quantités.
German: Verhältnisrechner — Verhältnisse vereinfachen, fehlende Werte lösen und Mengen aufteilen.
Japanese: 比率計算機 — 比率を簡略化し、欠損値を解き、数量を分割します。
Arabic: حاسبة النسب — بسّط النسب، احسب القيم المفقودة، وقسّم الكميات بسهولة.
Portuguese: Calculadora de razões — Simplifique razões, resolva valores desconhecidos e divida quantidades.
Korean: 비율 계산기 — 비율을 단순화하고, 누락된 값을 구하고, 수량을 분할합니다.
📖 Want a deeper guide on ratios, proportions, and real-world applications?
Read Our Complete Guide to Ratios and Proportions →Frequently Asked Questions
Is this Ratio Calculator free to use?
What is a ratio?
How do you simplify a ratio?
How do you solve for a missing value in a ratio?
What does scaling a ratio mean?
How do you split a quantity using a ratio?
Can I use decimals in the ratio calculator?
What is the difference between a ratio and a proportion?
How do I convert a ratio to a percentage?
Can this calculator handle 3-part ratios?
Does the tool work on mobile devices?
What is GCD and why is it used in ratio simplification?
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