Ratio Calculator

What is a Ratio Calculator?

A ratio calculator solves proportion problems of the form A : B = C : D. Given any three values, it finds the missing fourth value, simplifies a ratio to its lowest terms, and computes the scale factor between the two sides. Ratios compare quantities everywhere — flour to sugar in recipes, width to height on screens, map distance to real-world distance — and this tool handles the math instantly.

How to Use the Ratio Calculator

1. Enter three known values into fields A, B, C, and D.
2. Leave exactly one field blank—the calculator will solve for it.
3. Click Calculate to see the missing value, simplified ratio, and scale factor.

The Proportion Formula

A proportion states that two ratios are equal. The calculator is built on cross-multiplication:

A : B = C : D  →  A × D = B × C

• A — the first term of the first ratio
• B — the second term of the first ratio
• C — the first term of the second ratio
• D — the second term of the second ratio

Whichever term is missing is isolated algebraically: D = (B × C) ÷ A, C = (A × D) ÷ B, B = (A × D) ÷ C, or A = (B × C) ÷ D.

Worked Example: 3 : 4 = x : 20

If the second quantity in a 3 : 4 ratio must become 20, set A = 3, B = 4, D = 20, and leave C blank:

1. Cross-multiply: A × D = B × C, so 3 × 20 = 4 × x, which gives 4x = 60.
2. Divide both sides by 4: x = 60 ÷ 4 = 15.
3. Check: 15 : 20 simplifies to 3 : 4 (divide both by 5), so the proportion holds.

The calculator confirms this: Missing Value C = 15, Simplified Ratio 3 : 4, and Scale Factor 5.

Simplifying Ratios with the GCD

To simplify a ratio, divide both terms by their greatest common divisor (GCD), the largest number that divides both evenly. Take 48 : 64:

1. Find the GCD of 48 and 64 — it is 16.
2. Divide both terms by 16: 48 ÷ 16 = 3 and 64 ÷ 16 = 4.
3. The simplified ratio is 3 : 4.

Verify the GCD of any pair of numbers with our GCF calculator. Decimal ratios work the same way: multiply both terms of 1.5 : 2.5 by 10 to get 15 : 25, which reduces to 3 : 5.

Equivalent Ratios

Multiplying or dividing both terms by the same nonzero number produces an equivalent ratio — the underlying relationship stays the same.

Ratios with Three or More Terms

To divide an amount by a multi-term ratio, add the terms, divide the amount by that total, then multiply each term by the result. Splitting $1,000 in the ratio 2 : 3 : 5:

1. Total parts: 2 + 3 + 5 = 10.
2. Value per part: $1,000 ÷ 10 = $100.
3. Shares: 2 × $100 = $200, 3 × $100 = $300, and 5 × $100 = $500 — together they add back up to $1,000.

Ratio vs. Fraction: Part-to-Part and Part-to-Whole

A ratio usually compares part to part, while a fraction compares part to whole. If a jar holds 3 red marbles and 2 blue marbles, the ratio of red to blue is 3 : 2, but the fraction that are red is 3 out of 5 total, or 3/5 = 60%.

The same idea drives recipe scaling. If the ratio of flour to sugar is 3 : 2 and you use 600 g of flour, each part is 600 ÷ 3 = 200 g, so you need 2 × 200 = 400 g of sugar and the batch totals 1,000 g. Our fraction calculator and percentage calculator handle the part-to-whole conversions.

Common Aspect Ratios

An aspect ratio compares width to height; these standards dominate screens, photography, and video:

Map and Scale Ratios

A map scale of 1 : 24,000 means one unit on the map stands for 24,000 of the same units on the ground. One inch on the map equals 24,000 inches in reality, and since there are 12 inches in a foot, that is 24,000 ÷ 12 = 2,000 feet (about 0.38 miles); in metric terms, 1 cm equals 240 m. Two landmarks 3.5 inches apart on the map are 3.5 × 2,000 = 7,000 feet apart in the real world. To convert a measurement with the calculator, set A = 1, B = the scale denominator, C = the measured distance, and solve for D.

Frequently Asked Questions