Ratio & Proportion Calculator

About the Ratio & Proportion Calculator

Enter a ratio such as 12:18, 1.5 : 2.25, 1/2 : 3/4 or 4:6:10 to get its simplest whole-number form with each step — clearing decimals or fractions, then dividing by the greatest common factor. You also see the ratio as a fraction, a decimal and a percentage, each part’s share of the whole, and the unit forms 1 : n and n : 1.

The other modes solve a proportion A : B = C : D for any missing term by cross-multiplication, scale a ratio up or down, divide an amount in a ratio (with rounded shares that still add up to the total), solve direct and inverse variation problems, and split a length in the golden ratio or check how close two lengths are to it. The arithmetic uses exact fractions, so 1/3 stays 1/3 until the final answer.

Common uses

• Scaling a recipe or a concrete or paint mix to a new quantity.
• Checking aspect ratios of screens, photos and videos.
• Splitting money, profit or costs between people in an agreed ratio.
• Map and model scales, and homework on ratio, proportion and variation.

How ratios are simplified

A ratio is in simplest form when its terms are whole numbers with no common factor other than 1.

• Whole numbers: divide every term by their greatest common factor (GCF): 12 : 18 → ÷ 6 → 2 : 3.
• Decimals: multiply every term by 10, 100, 1000… to make them whole, then divide by the GCF: 1.5 : 2.25 → × 100 → 150 : 225 → ÷ 75 → 2 : 3.
• Fractions: multiply every term by the lowest common multiple of the denominators: 1/2 : 3/4 → × 4 → 2 : 3.
• Three or more terms work the same way: 4 : 6 : 10 → ÷ 2 → 2 : 3 : 5.

Proportions and cross-multiplication

Two equal ratios form a proportion: a : b = c : d, which means a/b = c/d. Multiplying both sides by b and d gives a × d = b × c — the cross products are equal. To find a missing term, multiply the two known terms that are diagonal to each other and divide by the third: in 3 : 4 = x : 20, x = 3 × 20 ÷ 4 = 15.

Dividing an amount in a ratio

Add the terms to get the number of parts, divide the amount by it to find one part, then multiply. For 1,200 in 2 : 3 : 5 there are 10 parts of 120, so the shares are 240, 360 and 600.

Rounded shares may no longer add up: 100 in 1 : 1 : 1 is 33.33 each, only 99.99 in total. The tool uses the largest remainder method — round every share down, then give the leftover units to the shares with the largest remainders — so the rounded shares add up to the amount (rounded to the same number of decimal places), and it marks the shares it adjusted.

Direct and inverse variation

In direct variation, y = kx: doubling x doubles y, and y ÷ x is always k. Example: 4 kg cost 300, so k = 75 per kg and 7 kg cost 525.

In inverse variation, y = k ÷ x: doubling x halves y, and x × y is always k. Example: 5 workers take 12 days, so k = 60 worker-days and 6 workers take 10 days, assuming everyone works at the same rate.

The golden ratio

Two lengths a > b are in the golden ratio when a ÷ b = (a + b) ÷ a. The value of this ratio is φ = (1 + √5) ÷ 2 ≈ 1.6180339887. Because 1 ÷ φ = φ − 1 ≈ 0.618 and φ² = φ + 1 ≈ 2.618, splitting a whole in the golden ratio gives parts of about 61.8% and 38.2% of it. φ is the ratio of a regular pentagon’s diagonal to its side, and the limit of the ratios of consecutive Fibonacci numbers (8/5, 13/8, 21/13, …).

Limitations

• Ratios can have up to 10 terms, and each term up to 30 digits.
• Terms must be zero or more in Simplify, Scale and Divide amount; Proportion and Variation also accept negative numbers.
• Shares can be rounded to 2, 1 or 0 decimal places, or kept as exact fractions.
• Golden-ratio results use φ to 60 decimal places — far more than any measurement needs.

Privacy

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