This calculator simplifies the ratio between two numbers to the smallest possible whole numbers.
Our Ratio Calculator allows you to compute, simplify, and scale ratios in seconds. Whether you’re a chef adjusting recipes, an engineer mixing solutions, a student tackling math problems, or a financial analyst comparing metrics, this tool delivers fast, accurate results without manual errors.
A ratio expresses the relative magnitude of two or more quantities. It shows how many times one value contains or is contained within another. Ratios can be written as a:b, a to b, or as fractions a/b. They appear in everyday contexts—from map scales (1:50 000) to ingredient proportions (2:1 sugar to flour).
Ratios provide insight into relative relationships. In finance, debt-to-equity ratios gauge solvency; in chemistry, reagent proportions ensure correct reactions; in cooking, flavor balance depends on proper ingredient ratios.
3/5).3:5).60% for 3/5).You can convert 3:5 → 3/5 = 0.6 = 60%. Our calculator handles all conversions seamlessly.
Follow these steps:
Simplification divides each term by their greatest common divisor (GCD). For 24:36:48, GCD = 12, yielding 2:3:4.
Our calculator finds the GCD instantly, even for large integers or mixed units.
Supports negative values (e.g., -2:4 simplifies to -1:2) and decimals (e.g., 1.5:2.5 → 3:5).
Input: 45 : 120
Output: 3 : 8
Scale a ratio when you know one part or the total sum. For ratio 2:5 and total 21 units, scale factor = 21 ÷ (2+5) = 3 → parts = 2×3=6, 5×3=15.
If one part must equal a given value: for ratio 3:7, set first part = 15 → scale = 15÷3 = 5 → second part = 7×5 = 35.
For multi-part ratios with simultaneous targets (e.g., first part = X and total = Y), solve linear equations to find unique scale factor matching both constraints.
Original recipe ratio sugar:flour:butter = 1:2:1. To make 800 g total, scale = 800÷(1+2+1)=200 → 200 g sugar, 400 g flour, 200 g butter.
Upload CSV with ratio sets and targets; receive batch-scaled results in downloadable CSV or JSON.
Verify if two ratios form a valid proportion. Input A:B and C:D → checks A/B = C/D within numerical tolerance.
Evaluates A×D ≟ B×C to confirm equality. Highlights near-matches for floating-point inputs.
Given three terms (A: B = C: D and one missing), solve for the fourth (e.g., A=4, B=5, C=8 → find D = (B×C)/A = 10).
Debt-to-equity ratio: debt = ₹120 000, ratio target = 0.6 → equity = debt÷0.6 = ₹200 000.
Displays messages for invalid inputs (zero denominators, negative total constraints) and suggests corrections.
Scale recipes accurately for any serving size without trial-and-error. Convert batch sizes, maintain flavor balance, and avoid waste.
Mix reagents in precise proportions. For volumetric analysis, maintain ratio tolerances within ±0.1% for critical assays.
Dilute medications by weight-to-volume ratios (e.g., mg:mL) to ensure safe, consistent dosing.
Combine materials (cement:sand:aggregate = 1:3:5) for concrete, scaling quantities for projects of any size.
Compare financial metrics: P/E ratios, current ratios, and leverage ratios. Normalize data across companies with different scales.
Teach ratio concepts with step-by-step examples. Generate practice problems and automatic answer keys for students.
Create pie charts or bar graphs showing ratio proportions. Export data directly to charting tools via CSV.
Multiply successive ratios: if A:B = 2:3 and B:C = 4:5, then A:C = 2×4 : 3×5 = 8:15 after simplifying if necessary.
Solve multi-step relationships in supply chains or scaling currency conversions across multiple pairs sequentially.
Given ratio A:B:C, find the mean proportional B = √(A×C) when A, B, C are in continued proportion (A:B = B:C).
Convert rates to ratios (e.g., 60 km/h → 1 km : 1/60 h). Inverse proportions help solve work-rate problems (A completes job in x days, B in y; together in xy/(x+y) days).
For multi-variable optimization, build ratio matrices and solve via linear algebra for resource allocation or portfolio balancing.
Access our Ratio Calculator programmatically through REST API:
POST /api/ratio
{
"values": [a, b, c, ...],
"mode": "simplify" | "scale" | "proportion",
"target": { "total": n } | { "partIndex": i, "value": v }
}Response returns simplified ratios, scaled values, or missing-term solutions as JSON.
Install via npm:
npm install @Easy Converters/ratio-calculatorUsage:
import { simplify, scale } from '@Easy Converters/ratio-calculator';
const simple = simplify([24, 36, 48]); // [2, 3, 4]
const scaled = scale([1, 2], { total: 30 }); // [10, 20]Upload CSV with ratio columns and targets; receive processed file with all computations and validation flags.
Download Excel template with built-in formulas and macros: =SIMPLE_RATIO(A2:C2), =SCALE_RATIO(A2:C2, 100), etc.
WordPress shortcode, Moodle module, and LMS widget to embed ratio tools in educational platforms effortlessly.
A: Yes—input decimals; the tool multiplies by powers of ten to convert to integers before simplifying and then presents fractional form.
A: Zero values are allowed only if other parts are nonzero; negative values simplify and scale like positive, maintaining sign.
A: Units are descriptive only; the tool focuses on numerical relationships. Display units manually alongside results.
A: Proportion checks use a tolerance of 1e–9 by default; configurable in advanced settings.
A: Yes—specify partIndex and value in scale mode to fix one part and derive others accordingly.
When scaling to a total, always confirm that scaled parts sum exactly to the target. The calculator rounds intelligently to avoid off-by-one errors.
Export detailed reports showing GCD calculation, scale factors, and rounding rules used for transparency in reports or exams.
For high-precision requirements (pharmaceutical, aerospace), enable fraction-only mode to avoid decimal rounding entirely.
Save common ratio patterns (e.g., 1:3:5 mixing oil:paint:thinner) as presets for quick reusability.
Pay attention to warning flags for division by zero, large integers causing overflow, or proportions near tolerance limits.
The Ratio Calculator streamlines all proportional tasks—from simple simplifications to complex multi-variable scaling—ensuring precision, speed, and reliability. Empower your recipes, experiments, designs, and analyses with this versatile tool. Try it now to eliminate guesswork and elevate your proportional reasoning!
Ratios underpin many higher-level mathematical concepts, from series convergence to analytic geometry. Understanding how ratios behave when variables change is essential for proofs, optimizations, and numerical methods.
In calculus, the ratio test determines if an infinite series converges by comparing successive term magnitudes. For series ∑aₙ:
ρ = limₙ→∞ |aₙ₊₁ / aₙ|
Our calculator can approximate ρ for large n by inputting symbolic expressions or numeric terms, aiding both coursework and research.
For ∑(1/2)ⁿ, ratio between terms is constant:
ρ = (1/2) / 1 = 0.5 < 1 ⇒ converges
Apply ratio test to power series, factorials, or combinations—where term ratios simplify complex expressions.
When aₙ involves oscillatory factors (e.g., (-1)ⁿ), examine absolute values or use alternating series tests for full analysis.
Ratios measure relative frequencies, odds, and rates in data analysis. They appear in contingency tables, risk assessments, and model evaluation metrics.
In medical statistics, the odds ratio compares the odds of an event occurring between two groups, while the risk ratio (relative risk) compares probabilities:
Our Ratio Calculator can process 2×2 contingency table inputs to output OR, RR, and their confidence intervals, streamlining epidemiological studies.
Treatment group: 30 successes, 70 failures; control: 20 successes, 80 failures:
OR > 1 indicates higher odds with treatment; RR > 1 indicates higher risk or benefit. Context determines which ratio is appropriate.
Compute CI around OR and RR using log transformations and standard error estimates for robust statistical inference.
Financial analysts rely on ratios to evaluate company performance, leverage, liquidity, and valuation metrics.
Input financial statement line items into our calculator to get instant ratio analyses and trend visualizations for multi-period comparisons.
Company A: Share price ₹500, EPS ₹25 → P/E = 500 ÷ 25 = 20. A lower P/E may indicate undervaluation or lower growth expectations.
Compare computed ratios against industry averages; our tool includes built-in benchmarks for tech, healthcare, manufacturing, and finance.
Build custom ratios by combining metrics, such as EV/EBITDA (Enterprise Value ÷ Earnings before Interest, Taxes, Depreciation & Amortization) for deep valuation analysis.
In visual media, aspect ratios define canvas shapes—from classic 4:3 paintings to cinematic 2.39:1 widescreen films. Choosing the appropriate ratio affects composition, viewer focus, and technical delivery.
Input width and height to simplify to standard formats (e.g., 1920×1080 → 16:9). Use scale mode to resize designs without distortion by locking one dimension and computing the other.
For web and mobile, use ratio-based padding and container scaling (via CSS aspect-ratio property) to maintain design consistency across devices.
The golden ratio (≈1.618:1) appears in nature and architecture. Use our tool to generate grids, frames, and typography scales based on φ for harmonious compositions.
Crop images to common print sizes (5×7, 8×10, 11×14) by ratio simplification, ensuring minimal cropping of key subjects.
Precise ratios ensure correct mixing, gear ratios, and system balances in mechanical and chemical engineering.
Given driver and driven gear teeth counts, compute ratio and resulting rotational speed:
Ratio = Driven teeth ÷ Driver teeth; RPM₂ = RPM₁ × Driver teeth ÷ Driven teeth
Our calculator outputs speed, torque multipliers, and common gear train combinations for drivetrain design.
For formulations, enter component concentrations (e.g., resin:hardener:solvent = 5:1:10) to scale batch sizes and ensure reaction stoichiometry.
Calculate composite material proportions (fiber:matrix) by weight or volume for aerospace, automotive, and sporting goods manufacturing.
Include tolerance ranges when mixing—our tool flags if scaled parts exceed acceptable manufacturing variances.
Biologists and pharmacists use ratios for dilutions, dosages, and population studies.
For laboratory protocols, compute volumes for stock and working solutions:
C₁V₁ = C₂V₂ (Concentration × Volume before = after)
Input any three variables to solve for the fourth—critical for assay preparations.
Physicians use weight-based dosing (mg/kg) to determine patient-specific medication volumes; our calculator includes BMI and renal function adjustments.
Compute prevalence, incidence, and mortality ratios in population health studies, with built-in demographic filters (age, gender, region).
Mendelian inheritance predicts offspring genotype ratios (3:1, 1:1, 9:3:3:1). Our tool models Punnett squares and probabilities for complex crosses.
Support for localized numeral systems: Arabic-Indic digits, Chinese numerals, and Hindi devanagari digits. Toggle digit sets to display ratios in regional scripts.
In RTL languages, ensure colon separators (:) align correctly and scale inputs mirror appropriately in form fields.
Maintain unit labels next to values (“kg:g”, “km:m”) and translate ratio descriptors (e.g., “to” vs. “करके”) based on locale preferences.
For forex, compare currency pairs (USD/EUR, JPY/GBP) with bid-ask ratio displays and historical scaling charts integrated via exchange rate APIs.
Compute rates per time unit (e.g., units/hour, transactions/minute). Our real-time mode ingests streaming data and outputs live ratio metrics for dashboards.