Proportion Calculator
Free Proportion Calculator for fractions. Enter values to get step-by-step solutions with formulas and graphs. See charts, tables, and visual results.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Formula
A/B = C/D → D = B × C / A
A proportion states that two ratios are equal. Cross-multiplying A/B = C/D gives A × D = B × C; dividing both sides by A isolates the unknown term D = (B × C) / A.
Worked Examples
Example 1: Medication dosage scaling
Problem:A medication is dosed at 5 mg per 10 kg of body weight. How much should a 42 kg patient receive?
Solution:Set up 5:10 = D:42, i.e. 5/10 = D/42. Cross-multiply: 10 × D = 5 × 42 = 210, so D = 21.
Result:Dose = 21 mg
Example 2: Currency-style unit conversion
Problem:If 8 kilometers equal 5 miles, how many miles equal 60 kilometers?
Solution:Set up 8/5 = 60/D. Cross-multiply: 8 × D = 5 × 60 = 300, so D = 300/8 = 37.5.
Result:60 km ≈ 37.5 miles
Frequently Asked Questions
What is a proportion in mathematics?
A proportion is a statement that two ratios are equal, written A/B = C/D (or A:B = C:D). It asserts that the relationship between A and B is exactly the same as the relationship between C and D, even if the actual numbers are different sizes. Solving a proportion means finding the one unknown value that keeps that equality true.
How do I know which value in a word problem is the unknown?
Set up the proportion so that corresponding quantities line up in the same position on each side — for example, (recipe amount of ingredient 1) / (recipe amount of ingredient 2) = (your amount of ingredient 1) / (your amount of ingredient 2). Whichever quantity you don't yet know becomes D, and the calculator solves for it once the other three are entered correctly.
What is the difference between a direct proportion and an inverse proportion?
In a direct proportion, both quantities increase or decrease together at the same rate (more workers, more output in the same time). In an inverse proportion, one quantity increases as the other decreases (more workers, less time to finish a fixed job) — inverse proportions are written A×B = C×D rather than A/B = C/D. Proportion Calculator solves the standard direct-proportion form.
How are proportions used to convert units?
Unit conversion is a direct application of proportions: if 1 mile = 1.60934 km, then 1/1.60934 = X miles/Y km for any distance Y. Setting up the known conversion factor as A:B and the value you want to convert as C lets you solve for its equivalent D in the new unit.
How do proportions relate to similar triangles and scale drawings?
Similar triangles (and any similar figures) have corresponding sides that are proportional — if triangle sides a, b, c are similar to sides A, B, C, then a/A = b/B = c/C. Architects and engineers use exactly this proportion logic to convert measurements between a scale drawing and the full-size structure.
What happens if I enter a zero for the first value (A)?
Because the proportion is solved as D = B×C/A, a value of zero for A would require dividing by zero, which is undefined — the calculator will not return a result in that case. In practice, A represents a nonzero reference quantity (like a known recipe amount or map scale unit), so this restriction rarely affects real problems.
Where do proportions show up in daily life outside of math class?
Nurses use proportions to scale medication dosages by patient weight, cooks use them to resize recipes, photographers use them to keep aspect ratios consistent when resizing images, and financial analysts use them to scale a small sample's results up to a full population estimate.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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