Ratio and Proportion Calculator (Solve A:B = C:D, Scale a Ratio)

Find the one missing term of the proportion A:B = C:D, or scale the ratio A:B up or down. Fill in the fields for the calculation you want.

First term A

Second term B

First term C

Second term D

Enlarge by (× k)

Reduce to 1/k (÷ k)

[Solve a proportion] Fill in three of A to D and leave only the term you want to find blank. [Scale a ratio] Enter the original ratio in A and B, and fill in only one of the two scale factors (leave C and D blank).

Result

Enter the terms of the ratio in the fields on the left and press "Calculate". The result will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formula
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter any three of the four terms of the proportion \(A:B=C:D\), and the missing one (for example, the \(x\) in 3:4 = 600:\(x\)) is found on the spot
The answer is also shown in the forms "1 : n" and "m : 1", and as the percentage the first term makes up of the whole
Scale a ratio up or down just by entering the scale factor (for example, 3:4 enlarged 5 times is 15:20, and 250:280 reduced to 1/2.5 is 100:112)
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

A combination where the term you divide by is 0 cannot be calculated (it would be division by 0). Negative numbers can be entered, but ratios are normally used with positive numbers.

What is this calculation used for?

Scaling a recipe for more people

If a recipe uses 3 cups of rice for 4 people, then for 6 people the proportion 4:3 = 6:\(x\) gives \(x = 3 \times 6 \div 4 = 4.5\) cups.
In practice you multiply every ingredient by the same factor (\(6 \div 4 = 1.5\)), which is exactly enlarging a ratio. It is the ratio calculation people use most in everyday cooking.

Finding real distances from a map scale (hiking and safety)

On a 1:24,000 topographic map, a trail that measures 5 inches on the map is \(5 \times 24{,}000 = 120{,}000\) inches in real life, which is 10,000 feet (about 1.9 miles).
Map scale is one of the most common uses of ratios, whether you are planning a hike or estimating the distance to an evacuation shelter.

Working with screen and video aspect ratios (16:9)

Most TV and computer screens have a width-to-height ratio of 16:9. For a screen 1920 pixels wide, 16:9 = 1920:\(x\) gives a height of \(x = 9 \times 1920 \div 16 = 1080\) pixels (Full HD).
Video editors and slide makers use this to find the right height once the width is set.

Diluting drinks, cleaners and garden sprays

For a drink concentrate mixed "1 part concentrate to 4 parts water", 2 fl oz of concentrate needs 1:4 = 2:\(x\), so \(x = 4 \times 2 \div 1 = 8\) fl oz of water.
The same calculation is used for garden sprays and disinfectants, where getting the mix too strong or too weak matters for safety (always follow the dilution on the product label).

Converting currency (travel and shopping)

Suppose 1 US dollar = 0.90 euros. Something that costs 45 euros is then 1:0.90 = \(x\):45, so \(x = 1 \times 45 \div 0.90 = 50\) dollars.
An exchange rate is a proportion where the amount per 1 is known. It helps you estimate prices when you travel or shop from overseas stores (your actual payment may include extra fees).

Working out scale model sizes

A 1:48 scale model of an airplane that is 40 feet long is \(40 \times 12 = 480\) inches \(\div 48 = 10\) inches long.
Every measurement is reduced by the same scale factor. This kind of reduction is the basis of model building and architectural drawings.

Formula

Property of proportions (product of the extremes = product of the means)

Standard notation (the usual math form)

\(A\) \(\times\) \(D\) \(=\) \(B\) \(\times\) \(C\)

In words (symbols replaced with words)

① \(A\): outer term \(\times\) ② \(D\): outer term \(=\) ③ \(B\): inner term \(\times\) ④ \(C\): inner term

The formula in words

① In the proportion \(A:B=C:D\), take the outer term \(A\): outer term ,

② multiply it by the other outer term \(D\): outer term (the product of the extremes).

③ This always equals the inner term \(B\): inner term

④ times the other inner term \(C\): inner term (the product of the means).

Quick example

Checking with the proportion 3:4 = 600:800 (both products are 2400)

outer term (3) \(\times\) outer term (800) \(=\) inner term (4) \(\times\) inner term (600)

\(3 \times 800 = 2400\)

\(4 \times 600 = 2400\)

Key idea

Why is this true? \(A:B=C:D\) says that the two ratios are equal. Written as fractions, that is \(\dfrac{A}{B} = \dfrac{C}{D}\). Multiply both sides by \(B \times D\) and you get \(A \times D = B \times C\). This is the "cross multiplication" you may know from school. This one equation is the starting point for finding any missing term of a proportion.

Finding the missing term (when \(D\) is missing)

Standard notation (the usual math form)

\(D\) \(=\) \(B\) \(\times\) \(C\) \(\div\) \(A\)

In words (symbols replaced with words)

④ \(D\): missing outer term \(=\) ① \(B\): inner term \(\times\) ② \(C\): inner term \(\div\) ③ \(A\): outer term

The formula in words

① Multiply the inner term \(B\): inner term

② by the other inner term \(C\): inner term to get the product of the means,

③ then divide it by the known outer term \(A\): outer term

④ and you get the \(D\): missing outer term

Quick example

The \(x\) (that is, \(D\)) in 3:4 = 600:\(x\) is

\(D\): missing outer term \(=\) inner term (4) \(\times\) inner term (600) \(\div\) outer term (3)

\(D = 4 \times 600 \div 3 = 2400 \div 3 = 800\)

Key idea

The idea is the same whichever term is missing. Write "product of the extremes = product of the means", then divide the product on the other side by the term that is paired with the missing one. There are four cases: \(A = B \times C \div D\), \(B = A \times D \div C\), \(C = A \times D \div B\) and \(D = B \times C \div A\). If the term you divide by is 0, it cannot be calculated, because that would be division by 0.

Enlarging a ratio (multiplying by \(k\))

Standard notation (the usual math form)

\(a'\) \(=\) \(a\) \(\times\) \(k\)

\(b'\) \(=\) \(b\) \(\times\) \(k\)

In words (symbols replaced with words)

③ \(a'\): new first term \(=\) ① \(a\): original first term \(\times\) ② \(k\): scale factor

\(b'\): new second term \(=\) \(b\): original second term \(\times\) \(k\): scale factor

The formula in words

① Take the \(a\): original first term

② multiply it by the \(k\): scale factor (multiply the second term \(b\) by it too),

③ and you get the \(a'\): new first term of the enlarged ratio \(a' : b'\).

Quick example

Enlarging 3:4 five times (the answer is 15:20)

new first term (15) \(=\) original first term (3) \(\times\) scale factor (5)

\(3 \times 5 = 15\)

\(4 \times 5 = 20\)

Key idea

Multiplying both terms of a ratio by the same number (not 0) gives an equivalent ratio: the relationship stays the same. For both 3:4 and 15:20, the value of the ratio (first ÷ second) is 0.75. Scaling a recipe up for more people or turning a model's measurements into full-size ones is exactly this kind of enlargement.

Reducing a ratio (to \(1/k\))

Standard notation (the usual math form)

\(a'\) \(=\) \(a\) \(\div\) \(k\)

\(b'\) \(=\) \(b\) \(\div\) \(k\)

In words (symbols replaced with words)

③ \(a'\): new first term \(=\) ① \(a\): original first term \(\div\) ② \(k\): scale factor

\(b'\): new second term \(=\) \(b\): original second term \(\div\) \(k\): scale factor

The formula in words

① Take the \(a\): original first term

② divide it by the \(k\): scale factor (divide the second term \(b\) by it too),

③ and you get the \(a'\): new first term of the ratio \(a' : b'\) reduced to \(1/k\).

Quick example

Reducing 250:280 to 1/2.5 (the answer is 100:112)

new first term (100) \(=\) original first term (250) \(\div\) scale factor (2.5)

\(250 \div 2.5 = 100\)

\(280 \div 2.5 = 112\)

Key idea

Dividing by \(k\) is the same as multiplying by \(1/k\), so a reduced ratio is also equivalent to the original ratio. If the division does not come out even, you get a ratio of decimals (for example, 7:9 reduced to 1/3 is 2.33…:3). When you need a ratio of whole numbers, use a rounded, approximate ratio. Keep in mind that a rounded ratio is not exactly equal to the original one.

All ratio calculations rest on one fact - if you multiply both terms by the same number, or divide both by the same number other than 0, you get an equivalent ratio. To solve a proportion, work backward from "product of the extremes = product of the means". To enlarge or reduce a ratio, multiply (or divide) both terms by the same scale factor.

Symbols and terms

Symbols

\(A:B\)	A to B	A ratio. It shows how two amounts compare, written with a colon (:) between them. (Example - 3:4 is read "3 to 4")
\(A:B=C:D\)	A is to B as C is to D	A proportion. An equation that says the two ratios on the left and right are equal.
\(A \times D = B \times C\)	A times D equals B times C	Product of the extremes = product of the means. Every proportion has this property, and it is the starting point for finding a missing term.
\(k\)	k	The scale factor. The number that tells how many times you enlarge a ratio (or that you reduce it to \(1/k\)). (Example - for 2.5 times, \(k = 2.5\))
\(a'\)	a prime	A term of the ratio after enlarging or reducing. The small mark at the upper right (a prime) marks "the value after the change".

Terms

ratio	A comparison of two amounts written side by side, such as "3:4". It is useful because it captures just the relationship, whatever the total amount is.
proportion	An equation that says two ratios are equal. It is written \(A:B=C:D\), and the product of the extremes equals the product of the means.
means (inner terms)	In a proportion \(A:B=C:D\), the two inner terms (\(B\) and \(C\)). The product of the means equals the product of the extremes.
extremes (outer terms)	In a proportion \(A:B=C:D\), the two outer terms (\(A\) and \(D\)). The product of the extremes equals the product of the means.
value of the ratio	For a ratio \(A:B\), the number \(A \div B\). Two ratios with the same value are equivalent ratios. The \(m\) in the form "m : 1" on this page is exactly the value of the ratio.
equivalent ratio	Ratios that describe the same relationship. Multiplying both terms by the same number, or dividing both by the same number other than 0, gives an equivalent ratio. (Example - 3:4 and 15:20)
enlargement	Making something several times larger without changing its shape (its proportions). For a ratio, this is multiplying both terms by the same number.
reduction	Making something smaller by a fraction without changing its shape (its proportions). For a ratio, this is dividing both terms by the same number.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Ratios (Grade 6)	Knowing how to write a ratio such as "3:4" and read it as "3 to 4" Knowing that multiplying both terms by the same number, or dividing both by the same number other than 0, gives an equivalent ratio Being able to find the value of a ratio (first term ÷ second term)
Scale drawings (Grade 7)	Knowing that to change the size without changing the shape, you multiply every length by the same scale factor Knowing that "reduce to 1/2.5" is the same as "divide by 2.5"
Proportions (Grade 7)	Knowing that in a proportion \(A:B=C:D\), the product of the extremes equals the product of the means (\(A \times D = B \times C\)) Being able to call the unknown number \(x\) and write an equation
Multiplying and dividing decimals and fractions (Grades 5–6)	Being able to divide with decimals, as in \(250 \div 2.5\) Knowing that multiplication and division undo each other

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to check "product of the extremes = product of the means"

Outer term A	3
Inner term B	4
Inner term C	600
Outer term D	800
Product of the extremes A×D	=B1*B4
Product of the means B×C	=B2*B3

Table to find the missing term D of a proportion

Outer term A	3
Inner term B	4
Inner term C	600
Missing outer term D	=B2*B3/B1

Table to enlarge a ratio

Original first term	3
Original second term	4
Scale factor k	5
Enlarged first term	=B1*B3
Enlarged second term	=B2*B3

Table to reduce a ratio

Original first term	250
Original second term	280
Scale factor k	2.5
Reduced first term	=B1/B3
Reduced second term	=B2/B3

After pasting, the upper cells in column B are your inputs and the formula cells below them are calculated automatically.
In the first table, the product of the extremes (B5) and the product of the means (B6) are both 2400, which confirms the proportion holds.
The second table shows the missing term D = 800 in B4. The third table shows the enlarged ratio (15 and 20), and the fourth the reduced ratio (100 and 112).
Just replace the numbers in column B with your own.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to check "product of the extremes = product of the means"

Outer term A	3
Inner term B	4
Inner term C	600
Outer term D	800
Product of the extremes A×D	=B1*B4
Product of the means B×C	=B2*B3

Table to find the missing term D of a proportion

Outer term A	3
Inner term B	4
Inner term C	600
Missing outer term D	=B2*B3/B1

Table to enlarge a ratio

Original first term	3
Original second term	4
Scale factor k	5
Enlarged first term	=B1*B3
Enlarged second term	=B2*B3

Table to reduce a ratio

Original first term	250
Original second term	280
Scale factor k	2.5
Reduced first term	=B1/B3
Reduced second term	=B2/B3

The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.

How to calculate it in Python

# Find D in the proportion A:B = C:D (product of the means ÷ A)
ratio_a = 3
ratio_b = 4
ratio_c = 600

ratio_d = ratio_b * ratio_c / ratio_a
print(f"D = {ratio_d}")  # 800.0

# Enlarging or reducing a ratio (example: reduce 250:280 to 1/2.5)
left_term = 250
right_term = 280
scale_factor = 2.5

print(f"Reduced ratio = {left_term / scale_factor} : {right_term / scale_factor}")  # 100.0 : 112.0

Runs with the standard library only. "*" is multiplication and "/" is division. To enlarge instead, change "/ scale_factor" to "* scale_factor". Replace the numbers at the top with your own and run it.

How to write it in LaTeX and other math languages (copy and paste)

Property of proportions (product of the extremes = product of the means)

A × D = B × C

A \times D = B \times C

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>A</mi><mo>&#x00D7;</mo><mi>D</mi>
    <mo>=</mo>
    <mi>B</mi><mo>&#x00D7;</mo><mi>C</mi>
  </mrow>
</math>

A xx D = B xx C

a d == b c

a * d = b * c;  # D is reserved in Maple (the differential operator), so all variables are lowercase

A * D == B * C;

A×D=B×C

Finding the missing term (when \(D\) is missing)

D = B × C ÷ A

D = \dfrac{B \times C}{A}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>B</mi><mo>&#x00D7;</mo><mi>C</mi></mrow>
      <mi>A</mi>
    </mfrac>
  </mrow>
</math>

D = (B xx C)/A

b c / a

d := b * c / a;  # D is reserved in Maple (the differential operator), so all variables are lowercase

D = B * C / A;

D=(B×C)/A

Enlarging a ratio (multiplying by \(k\))

a′ = a × k,  b′ = b × k

a' = a \times k,\quad b' = b \times k

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msup><mi>a</mi><mo>&#x2032;</mo></msup>
    <mo>=</mo>
    <mi>a</mi><mo>&#x00D7;</mo><mi>k</mi>
    <mo>,</mo>
    <msup><mi>b</mi><mo>&#x2032;</mo></msup>
    <mo>=</mo>
    <mi>b</mi><mo>&#x00D7;</mo><mi>k</mi>
  </mrow>
</math>

a' = a xx k, b' = b xx k

{a k, b k}

aNew := a * k; bNew := b * k;

aNew = a * k; bNew = b * k;

a′=a×k, b′=b×k

Reducing a ratio (to \(1/k\))

a′ = a ÷ k,  b′ = b ÷ k

a' = \dfrac{a}{k},\quad b' = \dfrac{b}{k}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msup><mi>a</mi><mo>&#x2032;</mo></msup>
    <mo>=</mo>
    <mfrac><mi>a</mi><mi>k</mi></mfrac>
    <mo>,</mo>
    <msup><mi>b</mi><mo>&#x2032;</mo></msup>
    <mo>=</mo>
    <mfrac><mi>b</mi><mi>k</mi></mfrac>
  </mrow>
</math>

a' = a/k, b' = b/k

{a/k, b/k}

aNew := a / k; bNew := b / k;

aNew = a / k; bNew = b / k;

a′=a/k, b′=b/k

How to have ChatGPT do the calculation

You are a calculation assistant for ratios. Do the following calculations by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

1. Find D in the proportion 3:4 = 600:D, using "product of the extremes = product of the means" (A×D = B×C).
2. Reduce the ratio 250:280 to 1/2.5 and give the resulting ratio.

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula