Ratio Calculator
Enter a ratio and one known value — the tool solves the rest.
How to use
- Enter the ratio a : b.
- Fill in exactly one known value: a, b, or the total.
- Click Calculate to see the full breakdown.
Free online math tool.
What Is a Ratio Calculator?
A ratio expresses how two quantities relate — 3:4, 16:9, 1:2 — and ratio problems almost always reduce to one unknown: if the ratio is 3:4 and one side equals 21, what is the other? This calculator solves for the missing piece. Enter your ratio a : b, then supply exactly one known value — the actual value of a, the actual value of b, or the total (a + b) — and it calculates everything else, letting you scale recipes, resize images, mix materials, and split amounts proportionally without setting up proportions by hand.
Ratios preserve shape while changing size, which is why they run so much of the physical and digital world: screen aspect ratios, photographic enlargements, gear ratios, map scales, concrete mixes, and the golden ratio in design. Scaling a ratio means multiplying or dividing both sides by the same number — 3:4 and 6:8 and 75:100 are the same relationship at three different sizes.
How to Use the Ratio Calculator
- Enter the two parts of your ratio: a in the first box, b in the second (for example 3 and 4).
- Fill in exactly one known value: the real value corresponding to a, the real value corresponding to b, or the total of both parts combined.
- Click Calculate to see the completed values and the scaled ratio.
A Worked Example
Suppose a photo has a 3:2 aspect ratio and you want the width to be 1200 pixels. Enter a = 3, b = 2, and the known value of a = 1200. The scale factor is 1200 ÷ 3 = 400, so b = 2 × 400 = 800 pixels, and the total is 2000. Splitting money works identically: $500 divided in the ratio 2:3 means the total represents 5 parts, each part is $100, and the shares are $200 and $300. The calculator performs exactly this factor-finding step — every ratio problem is one such multiplication.
Tips for Ratio Problems
- Reduce the ratio first if it helps you think: 12:16 is 3:4, and the smaller numbers are easier to sanity-check (the calculator scales either form identically).
- Keep units consistent within each side — a ratio of lengths only works if both known values for that side use the same unit.
- For three-part ratios (like 1:2:3 cement mixes), solve in two steps: combine two parts and apply the calculator twice, or scale using the same factor logic — each part multiplies by total ÷ sum of parts.
What is the difference between a ratio and a fraction?
A fraction compares a part to a whole (3/4 of a pizza), while a ratio compares part to part (3 parts cheese to 4 parts sauce). They interconvert: the ratio 3:4 means the first quantity is 3/(3+4) = 3/7 of the total. Confusing the two is the most common ratio error — if a problem says "3 to 4," the fraction of the total is sevenths, not quarters.
Why can I only enter one known value?
Because a ratio plus one anchor determines everything — that is the mathematical structure of the problem. Two anchors would either agree (redundant) or contradict each other (no valid ratio). Entering exactly one value lets the calculator find the single scale factor that the whole solution hangs on.
How do I use this for aspect ratios like 16:9?
Enter a = 16 and b = 9, then enter the dimension you know: a screen 1920 pixels wide gives a = 1920 and returns b = 1080. It works in reverse for cropping: to fit a 16:9 frame inside a photo of known height, enter the height as b and read off the width to crop to.
Can ratios include decimals?
Yes. Ratios like 1.5:1 are common (photo prints, financial ratios). If decimals bother you, multiply both sides by whatever clears them — 1.5:1 = 15:10 = 3:2 — and the proportions are identical. The calculator handles decimal inputs and decimal known values directly, so either form works.