Proportion Calculator

Enter any three values to solve a proportion for x. You get the exact fraction, the decimal, every cross multiplication step, a ratio table and a graph, all free and with no signup.

a:b

Solve a Proportion

Enter any three values and leave one box empty. Get the exact answer, the unit rate, and the steps, with a table and graph where applicable.

Direct Inverse

a/b a:b

Direct: the ratio stays constant. Inverse: the nonzero product stays constant.

Proportion values a, b, c and d

First numerator (a) a

: ×

First denominator (b) b

=

Second numerator (c) c

: ×

Second denominator (d) d

Add units optional, for word problems

Unit for a and c Unit for b and d

Type whole numbers, decimals, negatives, fractions like 3/4, mixed numbers like 1 1/2, decimal commas like 2,5 or percents like 25%. Fill all four boxes to check whether a proportion is true.

Calculate Clear

Missing value · c

x = 9

3/4 = 9/12

Unit rate

≈1.3333

Each 1 of a matches approximately 1.3333 of b.

Reverse rate

0.75

Each 1 of b matches 0.75 of a.

Scale factor

×3

The second ratio is the first one multiplied by 3.

Simplest ratio

3 : 4

Both ratios reduce to the same simplest form.

34=x12

3 × 12 = 36=4 × 9 = 36

a and d multiply together. b and c multiply together.

Step by step solution

1. Write the proportion with x in place of the missing value: 3/4 = x/12.
2. Cross multiply. In every true proportion, a × d equals b × c, so 3 × 12 = 4 × x.
3. Multiply the two known values on the other diagonal: 3 × 12 = 36. Now the equation reads 4 × x = 36.
4. Divide both sides by 4 to get x by itself: x = 36 ÷ 4 = 9.
5. Check the answer. 3 × 12 = 36 and 4 × 9 = 36. Both cross products match, so the answer is correct.

Ratio table

Every row has the same ratio. Your values are highlighted.

Top value	Bottom value
1	4/3
3	4
6	8
9	12
12	16
15	20
30	40

Every row has the same ratio. Your values are highlighted.

Graph: a straight line through 0

(3, 4) (9, 12). Across: a and c (top). Up: b and d (bottom).

Copy answer Copy steps Share link

Decimal places 2 4 6 8 10

Try a real example

Scale a recipe Read a map scale Resize a 16:9 image Use a mixed number Workers and days Speed and time Check two ratios

Table of Contents

1. What Is a Proportion Calculator?
2. How to Use the Proportion Calculator
3. The Proportion Formula and Cross Multiplication
4. Worked Examples You Can Try
5. Direct vs Inverse Proportion: How to Tell Them Apart
6. Features of Our Proportion Calculator
7. Why Choose This Proportion Calculator Over Others?
8. Who Should Use This Calculator?
9. Common Mistakes When Solving Proportions
10. How We Make Sure Every Answer Is Right
11. What Users Say
12. Frequently Asked Questions
13. Start Solving

What Is a Proportion Calculator?

A proportion calculator is a free online tool that finds the missing value in a proportion. You type three known values, leave one box empty, and the calculator returns the fourth value that makes both ratios equal.

A proportion is simply a statement that two ratios are equal. You can write it as a/b = c/d or as a:b = c:d. For example, 3/4 = 9/12 is a proportion, because both ratios simplify to 3/4.

Our tool goes further than a basic solver. It also:

• Checks whether two ratios form a true proportion when you fill all four boxes.
• Solves inverse proportions, where one value goes up while the other goes down.
• Shows the unit rate, the scale factor, a ratio table and a graph for every answer.
• Keeps fractions exact, so 1/3 stays 1/3 instead of turning into a rounded 0.33.

In short, it gives you the answer, the method and the meaning behind the numbers, all in one place.

How to Use the Proportion Calculator

Using the calculator takes about ten seconds. Here is exactly what to do.

1. Pick the type of proportion. Choose Direct when both values grow together, like cups of flour and cookies. Choose Inverse when one value shrinks as the other grows, like workers and days.
2. Enter any three values. Type them into the boxes for a, b, c and d. Then leave the fourth box empty or type x.
3. Add units if you want. Open “Add units” and type labels such as cups and cookies. The answer then reads “x = 5 cups” instead of a bare number.
4. Press Calculate. The page smoothly scrolls to your answer.
5. Read the steps. Every result includes five numbered steps, a color coded cross multiplication diagram, a ratio table and a graph.

Want to check your homework instead? Just fill all four boxes. The calculator tells you whether the proportion is true. If it is not, it even tells you which value would make it true.

What You Can Type Into the Boxes

The calculator understands numbers the way you write them on paper:

You type	The calculator reads it as
12	Whole number 12
2.5 or 2,5	Decimal 2.5
3/4	Fraction three quarters
1 1/2	Mixed number one and a half
25%	Percent, equal to 1/4
1,000	One thousand
x, ? or an empty box	The unknown value

The Proportion Formula and Cross Multiplication

Every direct proportion follows one simple rule, called the cross product property. If a/b = c/d, then a × d = b × c.

In other words, the two diagonal products are always equal. Mathematicians call a and d the extremes and b and c the means. So you will also hear this rule as “the product of the means equals the product of the extremes.”

Here is how the calculator uses that rule to find each missing value:

Missing value	Formula	Example
a	a = (b × c) ÷ d	x/8 = 3/4, so x = 24 ÷ 4 = 6
b	b = (a × d) ÷ c	6/x = 3/4, so x = 24 ÷ 3 = 8
c	c = (a × d) ÷ b	6/8 = x/4, so x = 24 ÷ 8 = 3
d	d = (b × c) ÷ a	6/8 = 3/x, so x = 24 ÷ 6 = 4

Why Cross Multiplication Works

Cross multiplication is not a magic trick. Start with a/b = c/d and multiply both sides by b and by d. The b cancels on the left and the d cancels on the right. As a result, you get a × d = b × c.

That is also why b and d can never be 0. Dividing by zero has no answer, so a proportion with a zero denominator does not exist. Our calculator catches this mistake and tells you which box to fix.

The Inverse Proportion Formula

Inverse proportions follow a different rule. Instead of equal ratios, they have equal products: a × b = c × d. This shared product is called the constant, k.

For example, 6 workers finish a job in 10 days, so k = 6 × 10 = 60 worker days. With 4 workers, the job takes 60 ÷ 4 = 15 days. Fewer workers means more days, which is exactly what you expect.

Worked Examples You Can Try

The fastest way to learn proportions is to see them in real life. Each example below matches one of the buttons inside the calculator, so you can load it with a single tap.

Example 1: Scale a Recipe

Two cups of flour make 12 cookies. How many cups do you need for 30 cookies?

Set it up as 2/12 = x/30. Then cross multiply: 2 × 30 = 12 × x, so 60 = 12x. Finally, divide by 12 to get x = 5 cups. The unit rate tells you the same story another way: each cup makes 6 cookies.

Example 2: Read a Map Scale

On a map, 1 inch equals 50 miles. How far apart are two towns that sit 3.5 inches apart?

Write 1/50 = 3.5/x. Cross multiply to get x = 50 × 3.5 = 175 miles.

Example 3: Resize a 16:9 Image

A video is 1920 pixels wide in a 16:9 format. How tall is it?

Write 16/9 = 1920/x. Then x = (9 × 1920) ÷ 16 = 1080 pixels. That is exactly why full HD screens measure 1920 by 1080.

Example 4: Work With a Mixed Number

One and a half cups of rice serve 4 people. How much rice serves 10?

Write 1 1/2 / 4 = x/10. The calculator returns x = 3.75 cups, and it also shows the exact fraction 15/4 and the mixed number 3 3/4. That way, you can measure with whichever cups you own.

Example 5: Solve an Inverse Proportion

A trip takes 3 hours at 60 mph. How long does it take at 90 mph?

Speed and time move in opposite directions, so switch the calculator to Inverse. Then 60 × 3 = 90 × x, which gives 180 = 90x and x = 2 hours.

Example 6: Solve a Percent Proportion

What number is 45% of 80? Percent problems are proportions in disguise. The percent proportion reads amount ÷ base = percent ÷ 100.

So write x/80 = 45/100. Cross multiply to get 100x = 3600, and therefore x = 36. This is the same method that the OpenStax Prealgebra textbook teaches for percent proportions.

Example 7: Check Two Ratios

Do 5/15 and 3/9 form a proportion? Fill all four boxes and press Calculate. The cross products are 5 × 9 = 45 and 15 × 3 = 45. They match, so yes, it is a true proportion. Both ratios simplify to 1/3.

Direct vs Inverse Proportion: How to Tell Them Apart

Picking the right type is the most important decision you make. Get it wrong, and the math still works, but the answer makes no sense.

Question	Direct proportion	Inverse proportion
What happens when one value doubles?	The other value doubles too	The other value halves
Equation	y = kx	y = k/x, or x × y = k
What stays the same?	The ratio y ÷ x	The product x × y
Graph	A straight line through 0	A curve that never touches the axes
Everyday examples	Recipes, map scales, unit prices, currency exchange	Workers and days, speed and travel time, pressure and volume

Here is a quick test. Ask yourself, “If I get more of the first thing, do I get more or less of the second?” More and more means direct. More and less means inverse.

These ideas line up with Common Core standard 7.RP.A.2, which asks students to recognize proportional relationships in tables, graphs and equations. That is why our calculator shows all three for every answer.

Features of Our Proportion Calculator

We built every feature to solve a real problem we saw students and teachers struggle with.

• Solve for any position. The unknown can sit in a, b, c or d. You never have to rearrange the problem first.
• Exact fraction math. The calculator works with whole number fractions behind the scenes, so it never suffers from the rounding errors that make many calculators show 0.30000000000000004.
• Repeating decimals, shown honestly. An answer like 2/7 appears as the exact fraction, as 0.285714 with a line over the repeating digits, and as a rounded value.
• Direct and inverse modes. One switch changes the whole method, the steps, the table and the graph.
• Units for word problems. Add labels like miles and hours, and they appear in your answer, your unit rate and your table.
• Unit rate, scale factor and simplest ratio. You get the numbers that teachers ask for next, without extra work.
• Ratio table and graph. See your answer on a straight line through 0, or on an inverse curve.
• Five clear steps. Each solution explains what to do and why, in plain words.
• Proportion checker. Fill all four boxes to test any proportion, and see the value that would make it true.
• Copy and share. Copy the answer, copy all steps for your notes, or share a link that opens with your numbers already filled in.
• Private history. Your recent calculations stay in your own browser, so you can return to them anytime.
• Works everywhere. The tool runs on phones, tablets and computers, with keyboard and screen reader support.

Why Choose This Proportion Calculator Over Others?

Most proportion calculators stop at a single number. However, a bare number rarely helps when you need to show your work, check a recipe or explain the answer to someone else. Here is how our tool compares with what you usually find.

What you need	Typical proportion calculator	Our proportion calculator
Unknown in any of the four boxes	Sometimes	Always
Fractions and mixed numbers	Rarely	Yes, with exact answers
Inverse proportions	Usually a separate tool	Built in, one switch
Units in the answer	No	Yes
Step by step working	Sometimes	Always, five steps
Unit rate and scale factor	No	Yes
Ratio table and graph	No	Yes
Check if a proportion is true	Rarely	Yes, plus the fix
Sign up required	Sometimes	Never

In other words, you get a calculator, a tutor and a checker in one tool. Better still, it costs nothing.

Who Should Use This Calculator?

Proportions show up in more places than most people expect. So, our calculator helps a wide range of people.

• Middle school students learning ratios and proportional relationships in grades 6 and 7 can check homework and study the steps.
• High school and college students can solve geometry problems with similar triangles, chemistry ratios and percent problems.
• Teachers and tutors can project the tool in class, use the ratio table and graph to explain concepts, and share prefilled links with students.
• Parents can help with homework even if they last solved a proportion years ago.
• Home cooks and bakers can scale recipes up or down without guessing.
• Designers, photographers and video editors can resize images and screens without stretching them.
• Travelers and drivers can read map scales and estimate travel times.
• Small business owners can scale costs, prices and ingredient orders.

One honest note: if you work with medication doses or other high stakes numbers, use the calculator to check your math, and then confirm the result with a qualified professional.

Common Mistakes When Solving Proportions

While building and testing this calculator, we kept seeing the same mistakes. Avoid these six, and your answers will be right far more often.

1. Mixing up the order. If you put cups over cookies on one side, you must put cups over cookies on the other side too.
2. Mixing units. Never put inches on one side and feet on the other. Convert first, because 1 foot equals 12 inches.
3. Using direct when the problem is inverse. More workers finish faster, so time goes down. That is an inverse proportion.
4. Rounding too early. Keep fractions exact until the very end. For example, rounding 1/3 to 0.33 in the middle of a problem shifts your final answer.
5. Forgetting to check. Plug your answer back in and compare the cross products. If they match, you are done.
6. Putting zero in a denominator. A ratio like 5/0 has no value, so it cannot be part of a proportion.

How We Make Sure Every Answer Is Right

You should never have to trust a calculator blindly. That is why we show our work and publish our methods.

• Exact arithmetic. The calculator uses exact fraction math, not floating point shortcuts, so answers like 1/3 and 2/7 stay precise.
• Built on recognized standards. Our definitions follow the Common Core standards for ratios and proportional relationships.
• Tested before launch. We checked the solver against hand worked problems and textbook examples, including tricky cases like zeros, negatives, decimals and mixed numbers.
• Every answer checks itself. The final step plugs the answer back in and confirms that both cross products match.
• Private by design. The calculator runs in your browser. We never see or store the numbers you type.
• No sign up, no limits. Use it as often as you like, for free.

Want the full details? Read How Our Calculators Work and our Editorial Policy. You can also learn who builds Proportion Calculator.

What Users Say

Proportion Calculator is brand new, and we want real feedback, not made up praise. So, instead of filling this space with fake reviews, we are asking you directly.

Did the calculator help with your homework, recipe or project? Did something confuse you? Tell us at proportioncalculator.marketing@gmail.com. With your permission, we will share genuine comments from our first users right here.

Frequently Asked Questions

Start Solving

Proportions do not have to feel hard. Scroll back up, type your three numbers, and let the calculator show you the answer and the reasoning behind it. Then try one of the examples and watch how the ratio table and graph change. Before long, you will spot proportions everywhere, from your kitchen to your next road trip.

Need to simplify a ratio, scale it, split a total or compare two ratios instead? Our ratio calculator handles all of that with the same exact math and step by step working.