Ratio Calculator

Fill in two boxes for a : b, click Calculate. This ratio calculator simplifies the ratio to lowest terms, shows its decimal value, and solves for a missing fourth term when you add one more number.

• First term (a) - the left side of the ratio. The page loads with 4.
• Second term (b) - the right side. It loads with 6, so the form starts on 4 : 6.
• Third term (c) - for solving a : b = c : d, the label's exact setup. Try 10.
• Fourth term (d) - optional; leave it out and the ratio calculator solves it for you.

With the preloaded 4 : 6 and c = 10, clicking Calculate returns four lines: the simplest form of your ratio (2 : 3), the missing fourth term d from a : b = c : d (15), and the decimal value of a : b ($4 \div 6 = 0.666667$, rounded to six places). Change any box and the ratio calculator re-solves on the spot.

This page is more than a static ratio calculator - it is also an AI tutor you can ask questions:

• Ask in plain words. “Simplify 18 : 24” or “Flour to water is 4 : 6 and I have 10 cups of flour - how much water?” The AI solves it step by step.
• Take a photo of your homework. No typing: the AI reads the ratio and works through it.
• Ask about the ideas, not just the number. “Why does dividing both terms keep the ratio the same?” The AI explains, and you can check every number against the ratio calculator above.
• Work backwards. Give a simplified ratio like 2 : 3 and ask what the original could have been - the ratio calculator scales both directions.
• Keep asking follow-ups. Every answer opens the next question, and the ratio calculator page keeps teaching.

A ratio compares two quantities by division. A recipe mixing 4 cups of flour with 6 cups of water has a flour-to-water ratio of 4 : 6 - read “4 to 6”, written 4 : 6, 4 to 6, or $\frac{4}{6}$. All three spellings say the same thing, and the ratio calculator on this page works on any of them once you type the two numbers.

Order matters. 4 : 6 says flour first; 6 : 4 says water first, and the two are different comparisons. Swap the terms and you swap the meaning - the most common way a ratio goes wrong before any arithmetic starts.

Ratios come in two flavors:

• Part-to-part - one part against another part, like 4 : 6 flour to water.
• Part-to-whole - one part against the total, like 4 : 10 flour to the whole 10-cup batter, which simplifies to 2 : 5.

The second flavor is where ratios meet fractions: a part-to-whole ratio 4 : 10 says the same thing as “4 out of every 10 cups is flour”. The ratio calculator handles the numbers either way - you just have to know which comparison you are making, and keep the terms in the order the sentence names them.

Simplifying a ratio means rewriting it with the smallest whole numbers that keep the same comparison - the same move as reducing a fraction.

$4 : 6 = 2 : 3$

1. Find the greatest common divisor (gcd) of the two terms. For 4 and 6, that is $\gcd(4, 6) = 2$.
2. Divide both terms by it: $4 \div 2 = 2$ and $6 \div 2 = 3$.
3. Stop when nothing but 1 divides both terms. The simplest form of 4 : 6 is 2 : 3.

The step works because dividing both terms by the same number leaves the division $a \div b$ unchanged. That single fact powers the whole page: two ratios are the same comparison exactly when they simplify to the same pair, so 4 : 6 and 2 : 3 are one ratio in two costumes. It is also why the ratio calculator's first two output lines report the simplest form before anything else - collapse every ratio to its smallest spelling and comparisons become easy.

And the move runs in reverse: divide both terms to shrink 4 : 6 down to 2 : 3, or multiply both terms to scale it back up - which is the next block.

An equivalent ratio is what you get by multiplying both terms of a ratio by the same number. The comparison never changes; only the size of the batches does.

$2 : 3 = 4 : 6 = 10 : 15$

Read the table downward: 2 : 3 scaled by 2 gives the form's default 4 : 6; scaled by 5 it gives 10 : 15. Simplifying runs the same ladder backwards - divide 10 : 15 by 5, or 4 : 6 by 2, and 2 : 3 is waiting at the bottom.

Set two equivalent ratios equal with a sentence like $2 : 3 = 10 : 15$ and you have written a proportion. That is the bridge from this page to proportion proper: one recipe written as 2 : 3 serves any crowd, because every row of the multiplication table is the same recipe at a different size. The ratio calculator checks any row you name - type its terms into the boxes and the simplest-form lines collapse it back to 2 : 3 every time.

A bread recipe uses 4 cups of flour to 6 cups of water - the ratio 4 : 6. Today you have 10 cups of flour. How much water keeps the ratio?

Set the equivalent ratios side by side with a missing fourth term:

$4 : 6 = 10 : d$

1. Cross-multiply: $a \cdot d = b \cdot c$, so $4 \cdot d = 6 \cdot 10$.
2. Simplify: $4d = 60$.
3. Divide both sides by 4: $d = 15$.

So 10 cups of flour needs 15 cups of water - the same 2 : 3 comparison, with both terms scaled by 5.

That is exactly the computation behind the ratio calculator's missing-term line: it forms $c \times b \div a = 10 \times 6 \div 4$ and prints 15. Type 4, 6, 10 into the three boxes and confirm - then change c to any flour amount you actually have, and the ratio calculator re-solves the water instantly.

Three slips cause most wrong ratio answers, and all three happen before the ratio calculator ever gets clicked:

1. Swapping the order of the terms. 4 : 6 is flour-to-water; 6 : 4 is water-to-flour. The ratio calculator simplifies whichever order you type - 6 : 4 comes back as 3 : 2, a different comparison. Read the sentence, then type the terms in the order it names.
2. Adding to both terms to “keep the ratio”. Ratios are preserved by multiplication, not addition. Adding the same number to both terms of 4 : 6 changes the comparison - only multiplying (or dividing) both terms by the same number keeps it. If your scaling move is a plus sign, the ratio calculator's simplest-form lines will quietly disagree with your answer.
3. Mixing units inside one ratio. 4 cups : 6 cups is a ratio; 4 cups : 6 tablespoons is a surprise. Convert to the same unit first, then type the numbers - the ratio calculator treats both boxes as plain numbers and cannot see the labels.

Check the setup against the sentence before you click - the ratio calculator will faithfully simplify a wrong pairing.