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Math formula

How to calculate proportion

A proportion solves a missing value when two ratios describe the same relationship.

See the formulaOpen calculator
Direct answer
Formula
a / b = c / d

Use the table below to match each symbol with the right input. Keep units consistent before you start.

Proportion formula
Start here when you only need the equation and variable names.
Formula
a / b = c / d

A proportion solves a missing value when two ratios describe the same relationship.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
aFirst numeratorTop value in the first ratio.Depends on inputs
bFirst denominatorBottom value in the first ratio.Depends on inputs
cSecond numeratorTop value in the second ratio.Depends on inputs
dSecond denominatorBottom value in the second ratio.Depends on inputs
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Works for scaling recipes, drawings, rates, and similar triangles.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Write the two ratios as fractions.
  2. 2Cross multiply.
  3. 3Solve for the missing value.
  4. 4Check that both ratios reduce to the same value.
Examples
These sample numbers show the order of operations and units.
Find x in 3/5 = 9/x
a
3
b
5
c
9
d
x
  1. 1.3 / 5 = 9 / x
  2. 2.3x = 5 * 9
  3. 3.x = 15
Result
The missing value is 15.
Find x in x/12 = 5/8
a
x
b
12
c
5
d
8
  1. 1.x / 12 = 5 / 8
  2. 2.8x = 12 * 5
  3. 3.x = 7.5
Result
The missing value is 7.5.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Putting the wrong value in the numerator or denominator of the proportion formula.
  • Skipping signs, order, or sorting rules that change the result.
  • Rounding before the last step.
  • Assuming a formula applies when the needed input is zero or missing.
Open the Ratio Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open Ratio Calculator
FAQs
Short answers for common formula questions.
Can I calculate Proportion by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my Proportion result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the Ratio Calculator better than hand math?

Open the Ratio Calculator to check several scenarios or skip the hand arithmetic.