Mathematics calculator

Ratio Calculator

Solve the missing fourth value in the proportion a : b = c : d using cross multiplication.

Calculator inputs

Enter your values

Equivalent ratios
Value a cannot be zero.
Calculated output

Result summary

Your result will appear here

Complete the required fields and select the calculate button.

Table of Contents

1

What is Ratio?

This ratio calculator solves a proportion in the form A:B = C:D when D is unknown. It preserves the relationship between the first pair and the second pair. Proportions appear in recipes, maps, scale drawings, prices, mixtures, unit rates, and many other everyday comparisons.

The positions matter. The page treats A and C as corresponding first terms and B and D as corresponding second terms, then calculates D = B × C ÷ A. A cannot be zero because it becomes the divisor in that rearranged equation.

2

How to Use This Calculator

  1. Write the relationship as A:B = C:D and identify the missing fourth term.
  2. Enter the known values A, B, and C in the same order as the proportion.
  3. Select Calculate to find D.
  4. Check that A/B and C/D agree, provided the denominators used in that comparison are nonzero.

Keep units in corresponding positions. If A is kilograms and B is dollars, then C should also be kilograms and D will be dollars. Convert unlike units before entering them when the comparison requires a shared scale.

3

Formula Used

A : B = C : D

Writing the ratios as fractions gives A/B = C/D. Cross multiplication gives A × D = B × C, so D = (B × C) ÷ A. This page specifically solves for D. Its calculation requires A ≠ 0.

4

Variables Explained

PositionRole in the proportion
AThe first term of the known ratio and the divisor in the solved formula; it cannot be zero.
BThe second term of the known ratio.
CThe first term of the scaled ratio, corresponding to A.
DThe unknown second term returned by the page, corresponding to B.
Scale factorC ÷ A; multiplying B by this factor produces D.
5

Worked Example

Suppose 4 notebooks cost 7 dollars and you want the proportional cost for 20 notebooks. Enter A = 4, B = 7, and C = 20. The scale factor is 20 ÷ 4 = 5.

Multiply the matching second term by that factor: D = 7 × 5 = 35. Cross multiplication confirms the result because 4 × 35 = 140 and 7 × 20 = 140. Under a constant-price assumption, 20 notebooks cost 35 dollars.

6

Why Use This Calculator?

The returned number is the value of D that makes the entered proportion true. It inherits the type of quantity and unit used for B. A result of 35 in the example means 35 dollars, not 35 notebooks, because B occupied the cost position.

A correct mathematical proportion does not prove the real-world relationship is proportional. Bulk discounts, fixed fees, changing concentrations, measurement error, or nonlinear behavior can break the assumption. Confirm that a constant ratio is reasonable before applying the answer beyond the given values.

The scale-factor view is often easier than memorizing cross multiplication. Moving from A to C multiplies by C/A, so moving from B to D must use that same factor. It also helps reveal unreasonable entries: if C is five times A, D should be five times B. A result moving in the opposite direction signals misplaced terms or a sign issue.

Ratios may be written with a colon, as fractions, or in words such as “four to seven.” Convert them into a consistent order before typing. When measurements were rounded, report D with precision that reflects those measurements rather than a long string of calculator digits. Labeling every value before entry makes this check much easier.

7

Common Mistakes

  • Putting corresponding quantities in different positions, such as items:dollars on one side and dollars:items on the other.
  • Entering zero for A, which makes the solved formula undefined.
  • Mixing centimetres and metres, or other unlike units, without converting first.
  • Using a proportion where the relationship includes a fixed charge or does not scale linearly.
  • Rounding A, B, or C too early and carrying that error into D.
8

Frequently Asked Questions

Which value does this calculator solve for?

It solves for D in A:B = C:D. Arrange your known values in those three positions before entering them.

Why can A not be zero?

The rearranged formula divides B times C by A. Division by zero is undefined, so a zero in that position cannot produce D.

Can B or C be zero?

Yes. If either B or C is zero while A is nonzero, the returned D is zero and the cross-products still agree.

Do all four quantities need the same unit?

No, but corresponding positions do. A and C should measure the same kind of quantity, while B and D should measure their shared kind.

How can I check the answer?

Compare the cross-products A times D and B times C. Equal products confirm the numerical proportion, allowing for any rounding.

Can I use negative numbers?

The arithmetic permits them, and they are useful in abstract problems. Decide separately whether a negative ratio makes sense for the real quantity being modeled.

When is a proportion a poor model?

Avoid assuming proportionality when there are fixed fees, thresholds, discounts, curved growth, or other effects that change the ratio as the quantity changes.

9

Sources & References