Simplify ratios, scale them up or down, and solve A:B = C:D for the missing term. Useful for cooking conversions, business splits, scale models and any proportional reasoning.
Simplified ratio
2 : 3
Original: 24 : 36 (divided by 12)
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Ratios are everywhere in everyday Indian life - cooking (rice:water = 1:2 for steamed basmati, 1:1.5 for pressure cooker), business partnerships (profit share in say 3:2:1 ratio for three partners), aspect ratios (16:9 for widescreen TVs, 3:2 for DSLR photos, 4:3 for legacy displays), financial ratios (debt-to-equity, current ratio, P/E), map scales (1:50,000 for topographic maps), gear ratios in vehicles, concrete mixes (1:2:4 for cement:sand:aggregate in M15 grade), and statistics (sex ratio, dependency ratio). This calculator handles three operations: simplification (reducing to lowest terms), scaling (multiplying through by a factor), and solving (finding a missing term in A:B = C:D proportions).
Class 5-10 mathematics introduces ratios early because they're a building block for fractions, percentages, proportions, similar triangles, and probability. JEE/NEET aspirants use ratios in mole concept (chemistry), specific heat and density problems (physics), and combination/permutation problems. The cross-multiplication shortcut (A/B = C/D → AD = BC) is one of the most-used algebraic moves in school math. This calculator gives instant answers plus the formula so you can build intuition for ratio reasoning.
Pick mode: simplify, scale, or solve missing term.
Enter the parts of the ratio.
Read the simplified or scaled result.
Simplification divides every part by their greatest common divisor. Scaling multiplies every part by the same factor to match a known new value. Solving uses cross-multiplication: A/B = C/D means A × D = B × C.
Simplified: divide all parts by GCD Scaled: A : B → k·A : k·B Solve: A/B = C/D → A·D = B·C
Simplification: a ratio A:B is in simplest form when GCD(A, B) = 1. The calculator divides both terms by their greatest common divisor. Example: 12:18 has GCD 6, so simplified ratio is 2:3. For three-part ratios like 6:9:15, divide all three by GCD(6, 9, 15) = 3, giving 2:3:5. Multi-part ratios work similarly. Decimals can be eliminated by multiplying through - 1.5:2.5 = 15:25 = 3:5.
Scaling: given a ratio A:B and a known new value C for term A, solve for the new value of B. If A:B = 3:5 and you scale A to 12 (factor of 4), B becomes 5 × 4 = 20. Used in cooking (recipe for 4 scaled to serve 6), business (profit share when total profit changes), drawings (scaling architectural drawings from 1:100 to 1:50), and unit conversions.
Solving for missing term: cross-multiplication. A/B = C/D implies A × D = B × C. So if 3/4 = x/20, then 3 × 20 = 4x → x = 15. This is the foundation of proportion-based problem-solving and underlies similar triangles, percentages, currency conversion, and rate-time-distance problems. Cross-multiplication works for any 2-term ratio comparison.
Total parts: 5+3+2 = 10. Each part: 3,00,000 / 10 = ₹30,000. Distribution: ₹1,50,000 (partner A), ₹90,000 (partner B), ₹60,000 (partner C). Common in startup co-founder splits and family business divisions.
Total parts: 1+2+4 = 7. Per part: 2/7 = 0.286 m³. Cement: 0.286 m³ × 1440 kg/m³ density = 412 kg ≈ 8.2 bags. Sand: 0.572 m³ ≈ 6.4 ft³. Aggregate: 1.143 m³ ≈ 40 ft³.
Original ratio: 4032:3024 = 4:3. Target: 6:4 = 3:2. Different aspect - will require cropping (either top/bottom strip or sides) to print exactly 6×4 without distortion.
Same idea, different notation. 3:4 means 3 parts to 4 parts; 3/4 means 3 quarters of a whole. Mathematically interchangeable.
Yes. 6:8 = 3:4 (divide both by 2). The simplest form has no common factors greater than 1.
If splitting ₹1000 in 2:3, total parts = 5. Each part = 1000/5 = ₹200. Distribute: 2×200 = ₹400 and 3×200 = ₹600.
A ratio with one term equal to 1, like 1:8 (one teacher per 8 students). Convert any ratio to unit form by dividing both terms by the smaller.
Recipes often scale by ratio. Rice:water = 1:2 means 1 cup rice needs 2 cups water. Doubling rice (2 cups) needs 4 cups water.
Yes - 1.5:1 is valid. But for cleaner results, multiply through to eliminate decimals: 1.5:1 = 3:2.
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Ratio Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.
