Proportions Calculator

Proportion solver

Solve the missing value

Enter any three positive values in A/B = C/D. Leave the value you want to find blank.

Proportion solver

Set up A over B equals C over D

The blank field is the unknown. All three known values must be positive.

Missing value

A = 6

Completed proportion: 6 / 10 = 3 / 5

How the answer is found

Solution by cross multiplication

Write the proportionx / 10 = 3 / 5
Cross multiplyx × 5 = 10 × 3
Isolate the unknownx = (10 × 3) ÷ 5 = 6

Left ratio · A ÷ B: 0.6
Right ratio · C ÷ D: 0.6
Equality check: Both sides match

Proportion solving guide

Solve A/B = C/D with one missing value

A proportion says that two ratios are equal. Enter three positive values, leave one position blank, and use equal cross products to recover the missing value without losing track of which quantities correspond.

Step-by-step guide · Proportion solving guide

Use the proportions calculator in three steps

Proportion: A/B = C/D
Cross products: A×D = B×C
Answer check: A÷B and C÷D must match

Place corresponding values in matching positions
Read the form as A/B = C/D. Values that describe the same kind of quantity belong in the same numerator or denominator position on both sides.
Enter three values and leave one box blank
The blank box is the unknown. Do not enter x or a question mark; leaving exactly one box empty tells the calculator which term to solve.
Solve, then compare both quotients
Select Solve proportion. The result identifies the missing position, shows the cross multiplication and division, then reports A÷B and C÷D as a direct check.

Solve A/B = C/D with one missing value: A proportion says that two ratios are equal. Enter three positive values, leave one position blank, and use equal cross products to recover the missing value without losing track of which quantities correspond.

Use the proportions calculator in three steps

Place corresponding values in matching positions
Read the form as A/B = C/D. Values that describe the same kind of quantity belong in the same numerator or denominator position on both sides.
Enter three values and leave one box blank
The blank box is the unknown. Do not enter x or a question mark; leaving exactly one box empty tells the calculator which term to solve.
Solve, then compare both quotients
Select Solve proportion. The result identifies the missing position, shows the cross multiplication and division, then reports A÷B and C÷D as a direct check.

Cross multiplication turns four positions into one short equation

For A/B = C/D, multiply across the diagonals to obtain A×D = B×C. If 4/5 = 6/D, then 4D = 5×6 = 30, so D = 30÷4 = 7.5. Substitution confirms 4÷5 = 0.8 and 6÷7.5 = 0.8.

Cross multiplication is an equation step, not a new kind of ratio. If you need to express one ratio as a percentage rather than solve an equality, use the percentage calculator. Use the fraction calculator to compare or combine fractions, and the algebra calculator when the equation is not a proportion.

The blank position determines the isolation formula

Blank A

From A×D = B×C, divide by D: A = (B×C)÷D.

Blank B

Divide both sides by C: B = (A×D)÷C.

Blank C

Divide both sides by B: C = (A×D)÷B.

Blank D

Divide both sides by A: D = (B×C)÷A.

A trail map shows why corresponding units matter

Build two map-to-ground ratios
Suppose 7.5 centimeters on a map represents 3 kilometers on the ground and a trail measures 18 centimeters. Preserve map/ground order: 7.5/3 = 18/x.
Solve the missing ground distance
Equal cross products give 7.5x = 3×18 = 54. Divide by 7.5 to get x = 7.2 kilometers.
Verify the constant scale
The two quotients are 7.5÷3 = 2.5 and 18÷7.2 = 2.5. Matching values confirm the completed numeric proportion.

Avoid the common proportion setup mistakes

Leave exactly one field blank. Four filled fields provide no unknown; two blank fields do not provide enough information for a unique solution.
Keep corresponding units in matching positions, or convert first. Reversing only one ratio changes the meaning of the equation.
Use positive values within this calculator's stated scope. A zero denominator is undefined, and zero or negative terms are rejected rather than silently interpreted.
Round measured results only after solving and checking the proportion. Extra displayed digits do not improve the precision of a ruler, recipe measure, or source estimate.

Important limitations

This solver accepts positive finite terms only. Entering zero, a negative value, more than one blank, or no blank is rejected. Keep corresponding units in the same numerator or denominator position and round real measurements only at the end.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

Proportion solving guide

Solve A/B = C/D with one missing value

Step-by-step guide · Proportion solving guide

Use the proportions calculator in three steps

Proportion: A/B = C/D
Cross products: A×D = B×C
Answer check: A÷B and C÷D must match

Place corresponding values in matching positions
Read the form as A/B = C/D. Values that describe the same kind of quantity belong in the same numerator or denominator position on both sides.
Enter three values and leave one box blank
The blank box is the unknown. Do not enter x or a question mark; leaving exactly one box empty tells the calculator which term to solve.
Solve, then compare both quotients
Select Solve proportion. The result identifies the missing position, shows the cross multiplication and division, then reports A÷B and C÷D as a direct check.

Use the proportions calculator in three steps

Place corresponding values in matching positions
Read the form as A/B = C/D. Values that describe the same kind of quantity belong in the same numerator or denominator position on both sides.
Enter three values and leave one box blank
The blank box is the unknown. Do not enter x or a question mark; leaving exactly one box empty tells the calculator which term to solve.
Solve, then compare both quotients
Select Solve proportion. The result identifies the missing position, shows the cross multiplication and division, then reports A÷B and C÷D as a direct check.

Cross multiplication turns four positions into one short equation

For A/B = C/D, multiply across the diagonals to obtain A×D = B×C. If 4/5 = 6/D, then 4D = 5×6 = 30, so D = 30÷4 = 7.5. Substitution confirms 4÷5 = 0.8 and 6÷7.5 = 0.8.

The blank position determines the isolation formula

Blank A

From A×D = B×C, divide by D: A = (B×C)÷D.

Blank B

Divide both sides by C: B = (A×D)÷C.

Blank C

Divide both sides by B: C = (A×D)÷B.

Blank D

Divide both sides by A: D = (B×C)÷A.

A trail map shows why corresponding units matter

Build two map-to-ground ratios
Suppose 7.5 centimeters on a map represents 3 kilometers on the ground and a trail measures 18 centimeters. Preserve map/ground order: 7.5/3 = 18/x.
Solve the missing ground distance
Equal cross products give 7.5x = 3×18 = 54. Divide by 7.5 to get x = 7.2 kilometers.
Verify the constant scale
The two quotients are 7.5÷3 = 2.5 and 18÷7.2 = 2.5. Matching values confirm the completed numeric proportion.

Avoid the common proportion setup mistakes

Leave exactly one field blank. Four filled fields provide no unknown; two blank fields do not provide enough information for a unique solution.
Keep corresponding units in matching positions, or convert first. Reversing only one ratio changes the meaning of the equation.
Use positive values within this calculator's stated scope. A zero denominator is undefined, and zero or negative terms are rejected rather than silently interpreted.
Round measured results only after solving and checking the proportion. Extra displayed digits do not improve the precision of a ruler, recipe measure, or source estimate.

Set up A over B equals C over D

Solution by cross multiplication

Place corresponding values in matching positions

Enter three values and leave one box blank

Solve, then compare both quotients

Use the proportions calculator in three steps

Cross multiplication turns four positions into one short equation

The blank position determines the isolation formula

Blank A

Blank B

Blank C

Blank D

A trail map shows why corresponding units matter

Avoid the common proportion setup mistakes

Important limitations

Set up A over B equals C over D

Solution by cross multiplication

Place corresponding values in matching positions

Enter three values and leave one box blank

Solve, then compare both quotients

Use the proportions calculator in three steps

Cross multiplication turns four positions into one short equation

The blank position determines the isolation formula

Blank A

Blank B

Blank C

Blank D

A trail map shows why corresponding units matter

Avoid the common proportion setup mistakes