Proportion Calculator

What a proportion is

A proportion is an equation that says two ratios are equal. Written as fractions, it looks like A/B = C/D: “A is to B as C is to D.” The statement 4/10 = 6/15 is a proportion because both fractions equal 0.4.

Every true proportion has the same property: its cross products are equal. Multiply each numerator by the denominator on the opposite side and you get the same number both times, here 4 × 15 = 10 × 6 = 60. That single rule is how you solve for a missing term and how you test whether four numbers really form a proportion.

How to use the proportion calculator

1. Pick the unknown in the Solve for menu: A, B, C or D. The box for that term disappears, so you can’t fill it by mistake.
2. Enter the other three numbers. Decimals and negatives are fine. Denominators (B and D) can’t be 0.
3. Read the answer and the working: the proportion written out, the cross-multiplication, the one-step equation and a check that both ratios match.

To test a proportion instead, choose Check: is A/B = C/D true? and enter all four numbers. The calculator compares A × D with B × C exactly and, if they differ, tells you which value of D would make the proportion true.

Answers that end within six decimal places are shown exactly. When the answer repeats forever, as with 10/3, the proportion calculator rounds it to six places and also gives the exact fraction and the repeating pattern.

Solving a proportion by hand with cross-multiplication

Suppose 9 out of every 12 tiles in a box are white, and you want to know how many of 20 tiles would be white at the same rate. Write it as 9/12 = x/20.

1. Cross-multiply: 9 × 20 = 12 × x, so 180 = 12x.
2. Divide both sides by the number next to x: x = 180 ÷ 12 = 15.
3. Check: 9 ÷ 12 = 0.75 and 15 ÷ 20 = 0.75. The ratios match.

The unknown can sit anywhere. In x/6 = 14/21, the cross products are 21x and 6 × 14 = 84, so x = 84 ÷ 21 = 4. A quick rule covers all four positions: multiply the two numbers on the full diagonal, then divide by the number that shares a diagonal with x.

When the numbers are friendly

Sometimes a scale factor is easier than cross-multiplying. In 3/5 = 12/x, the numerator went from 3 to 12, a factor of 4, so the denominator must also be multiplied by 4: x = 20. Cross-multiplication gives the same answer (3x = 60) and works when the factor isn’t obvious.

Quick checks: is it a proportion?

These cross products were worked out with the calculator’s Check option.

Equal cross products mean equal ratios. Comparing decimals such as 3/7 ≈ 0.4286 and 9/20 = 0.45 also works, but rounding can hide a small difference, which is why the calculator compares the cross products exactly.

Real-life uses of proportions

Recipes and mixing

A pancake recipe that uses 3 eggs for 16 pancakes needs 3/16 = x/40 eggs for 40 pancakes: x = 120 ÷ 16 = 7.5, so use 7 or 8 eggs depending on size. The same setup scales paint tints, garden fertilizer and cleaning solutions.

Map and model scales

If 1 inch on a trail map represents 2.5 miles, a 3.4-inch route is 1/2.5 = 3.4/x, so x = 8.5 miles. For scale models, the full-size object sits in the denominator and the model in the numerator, consistently on both sides.

Resizing images without distortion

A 1500 × 1000 photo that must be 900 pixels wide keeps its shape when 1500/1000 = 900/x, which gives a height of 600 pixels. This is the “proportion calculator image” problem designers solve daily.

Fuel range and unit prices

If a car went 280 miles on 8 gallons, then 280/8 = x/13 says 13 gallons should take it about 455 miles. Prices work the same way: if 5 pounds cost $7.25, then 12 pounds at that rate cost (7.25 × 12) ÷ 5 = $17.40.

Shadows and similar triangles

At the same time of day, a 6-foot person casting a 4-foot shadow and a tree casting an 18-foot shadow form a proportion: 6/4 = x/18, so the tree is 27 feet tall. Similar triangles in geometry rely on exactly this idea.

Common mistakes

• Mismatched positions. If the first ratio is eggs/pancakes, the second must also be eggs/pancakes. Writing eggs/pancakes = pancakes/eggs gives a wrong answer that still looks reasonable.
• Mixed units. Convert everything to the same unit first. Inches on one side and feet on the other breaks the proportion.
• Inverse relationships. If 4 painters take 6 days, 8 painters don’t take 12 days. More workers means less time, so this is an inverse proportion (4 × 6 = 8 × x), not A/B = C/D.
• Adding instead of multiplying. 2/3 and 4/5 are not equal just because you added 2 to each term. Equal ratios come from multiplying or dividing both terms by the same number.

Proportions, ratios and fractions

A proportion is built from ratios, and each ratio is a fraction. The ratio calculator simplifies ratios such as 18 : 24 to 3 : 4, the fraction calculator works with the fractions themselves, and the decimal calculator handles exact decimal arithmetic. Percent problems are proportions too: “15 is what percent of 60?” is 15/60 = x/100, which the percentage calculator answers directly.

• Cross products: A × D and B × C in A/B = C/D. They are equal exactly when the proportion is true.
• Means and extremes: older names for the inner terms (B and C) and outer terms (A and D) of A : B = C : D.
• Constant of proportionality: the fixed ratio k in y = kx shared by every pair in a proportional relationship.