Ratio Calculator Online

How to Use the Ratio Calculator Online

1. Enter the Ratio You Have: Type the two terms of your starting ratio into the A and B fields (for example, 12 and 8 to work with 12:8). Decimals, fractions like 1/2, and whole numbers all accept — the calculator normalises them before solving.
2. Pick a Mode: Choose Solve A:B = C:D to find a missing fourth term (leave one of the four boxes empty and the calculator cross-multiplies to fill it), Simplify to reduce A:B to lowest terms using the greatest common divisor, or Scale to multiply A:B by a factor for enlarging or shrinking a recipe, mix, or layout.
3. Add the Third Term (Solve Mode Only): Enter the known value into either C or D and leave the other blank. The unknown can sit in any of the four slots — the solver handles A, B, C, or D as the missing term.
4. Calculate and Read the Result: Click Calculate. You get the solved or simplified ratio, the equivalent fraction, the decimal value, and the percentage — all in one pass. Everything runs in your browser; nothing is uploaded.

Why Use a Ratio Calculator?

A ratio compares two (or more) quantities and shows how many times one contains the other. Ratios show up everywhere — recipes, concrete mixes, financial leverage, screen dimensions, map scales, odds, and chemistry stoichiometry. Doing the arithmetic by hand is fine for small whole numbers, but as soon as decimals, three-part mixes, or large numbers enter the picture, a calculator saves both time and mental-math mistakes. Common use cases:

• Scaling recipes — Halving a batch that calls for a 2:3 flour-to-sugar ratio is easy; tripling a 7:11 sourdough hydration ratio for a larger loaf is not. Punch in the new total and read the per-ingredient amounts.
• Mixing concrete, mortar, or fertiliser — A standard general-purpose concrete mix is 1:2:3 (cement : sand : aggregate) by volume; if you need 12 cubic feet of mix, the calculator splits that into 2, 4, and 6 cubic feet of each component without arithmetic. The same logic applies to 10-10-10 fertiliser blends and 3:1 paint thinner.
• Aspect ratios for video, design, and print — Resize a 1920×1080 frame to a target width while preserving 16:9, or convert a 3:2 DSLR photo to fit a 4:5 Instagram crop. For dimension-locked aspect work, our Aspect Ratio Calculator is the dedicated tool.
• Financial ratios — Debt-to-equity (D/E = total debt ÷ shareholders' equity), price-to-earnings, current ratio, and gear ratios all reduce to "simplify A:B and compare." A company with $200M debt and $100M equity has a D/E of 2.0 (or 2:1) — exactly what this calculator returns.
• Map and model scales — Map scales like 1:24,000 (USGS topographic) or model-train scales like HO (1:87) and N (1:160) need quick conversions between real-world and on-page distances.
• Chemistry and lab dilutions — A 1:5 dilution means 1 part solute to 5 parts solvent (6 parts total). Mixing 50 mL of a 1:10 stock into a final 1:100 working solution is a proportion solve with one unknown.

Common Ratios Reference Table

The table below collects the most-asked everyday ratios. Use the calculator to convert any of these to a custom scale.

Domain	Common ratio	What it means
Video (widescreen TV / YouTube / HDTV)	16:9	1920×1080, 1280×720, 3840×2160 (4K UHD), 7680×4320 (8K UHD)
Video (cinematic / ultrawide)	21:9	Often 2560×1080 or 3440×1440 — DCI standard is 2.39:1, slightly wider
Video (legacy SD TV)	4:3	640×480, 800×600, 1024×768 — pre-2009 broadcast standard
Social (Instagram square)	1:1	1080×1080 — feed posts, profile thumbnails
Social (Instagram portrait)	4:5	1080×1350 — the tallest crop the feed will display without cropping
Social (Reels / TikTok / Stories)	9:16	1080×1920 — vertical full-screen mobile
Photo (DSLR / mirrorless full-frame)	3:2	6000×4000, 24×36 mm sensor heritage from 35 mm film
Photo (Micro Four Thirds / older P&S)	4:3	Most smartphone main-sensor stills default to this
Photo (medium format square)	1:1	6×6 Hasselblad heritage
Print (US letter portrait)	8.5:11 ≈ 17:22	Common North American document size
Print (A-series ISO 216)	1:√2 ≈ 1:1.414	A4, A3, A5 — halving the long side yields the next size
Concrete (general purpose)	1:2:3	1 part cement : 2 parts sand : 3 parts aggregate, w/c ≈ 0.5
Mortar (Type N)	1:1:6	1 cement : 1 lime : 6 sand for general masonry
Cocktail (classic margarita)	3:2:1	3 tequila : 2 lime : 1 triple sec

Ratio Types — What the Calculator Solves

Type	Form	Example	When to use
Part-to-part	a : b	2 girls : 3 boys in a class	Comparing two subgroups of the same whole
Part-to-whole	a : (a+b) or a/(a+b)	2 : 5 (girls out of 5 students) — equivalent to 40%	Expressing one part as a fraction or percentage of the total
Equivalent ratios	a:b = c:d	2:3 = 4:6 = 8:12	Showing two ratios scale identically; the basis of proportion
Simplified (lowest terms)	a:b with GCD(a,b) = 1	12:8 → 3:2	Reducing to canonical form so two ratios can be compared at a glance
Three-part (and higher)	a : b : c	1:2:3 concrete, 1:1:6 mortar, 10:10:10 NPK	Mixes with more than two components — recipes, alloys, fertilisers
Scaled	k·a : k·b	3:2 × 4 = 12:8	Enlarging or shrinking a mix while preserving proportions

Frequently Asked Questions

How do I simplify a ratio by hand?

Find the greatest common divisor (GCD) of both terms and divide each side by it. For 12:8, the factors of 12 are {1, 2, 3, 4, 6, 12} and the factors of 8 are {1, 2, 4, 8}; the largest shared factor is 4, so 12:8 = 3:2. For larger numbers the Euclidean algorithm is faster — repeatedly replace the larger number with the remainder when divided by the smaller until you hit zero; the last non-zero remainder is the GCD. The calculator does this automatically when you pick Simplify, so you can always cross-check your hand work.

How do I express a ratio as a percentage?

Convert the ratio to a part-to-whole fraction first, then multiply by 100. For the ratio 2:3 (read as "2 parts to 3 parts"), the total is 5, so the first part is 2/5 = 40% and the second is 3/5 = 60%. For 1:4, the first part is 1/5 = 20% and the second is 4/5 = 80%. If you have a part-to-part ratio like "win:loss = 3:1" and want win-rate, that's 3/(3+1) = 75%. The calculator returns both the decimal and percentage forms alongside the simplified ratio.

What is the difference between a ratio and a proportion?

A ratio compares two quantities (a:b). A proportion is a statement that two ratios are equal (a:b = c:d). Solving a proportion means finding the missing term so that the equality holds, using cross-multiplication: if a:b = c:d, then a × d = b × c. So "2:3" is a ratio; "2:3 = 8:12" is a proportion. Use Solve mode for proportions and Simplify mode for a standalone ratio.

How do I convert a decimal to a ratio?

Express the decimal as a fraction over a power of 10, then simplify. For example, 0.75 = 75/100 = 3/4 = 3:4. For 1.6 = 16/10 = 8:5. Repeating decimals need a different trick: 0.333… = 1/3 = 1:3. For irrational decimals like 1.414…, you can only approximate (1.414 ≈ 1414:1000 = 707:500, useful as a rational substitute for √2 in carpentry). The calculator accepts decimals in any input field and returns the simplified integer ratio.

How do three-part ratios like 1:2:3 work?

Three-part ratios extend the same logic to three (or more) components. A concrete mix of 1:2:3 means 1 part cement, 2 parts sand, 3 parts aggregate by volume — total 6 parts. If you need 12 ft³ of mix, each "part" is 12 ÷ 6 = 2 ft³, so you mix 2 ft³ cement + 4 ft³ sand + 6 ft³ aggregate. Same logic for recipes (3:2:1 margarita = 3 oz tequila + 2 oz lime + 1 oz triple sec, total 6 oz), fertiliser blends (10:10:10 NPK is balanced — 10% nitrogen, 10% phosphorus, 10% potassium by weight), and alloys (brass at ~70:30 copper-to-zinc).

Can ratios be negative?

In pure mathematics, ratios are typically defined for positive quantities (you can't have "−3 cups of flour"). In applied contexts — gear ratios with reverse direction, financial signed quantities, vector relationships — a negative sign is meaningful as a direction marker, but the magnitudes are still simplified using absolute values. The calculator treats both terms as positive magnitudes; if you need signed direction, track the sign separately.

What about aspect ratios — should I use this calculator or the aspect ratio one?

Use this Ratio Calculator when you just need the math: "Simplify 1920:1080" returns 16:9; "Solve 16:9 = ?:720" returns 1280. Use the dedicated Aspect Ratio Calculator when you want a dimensions-locked workflow — type a width and the height auto-updates to preserve the chosen aspect, with one-click 16:9 / 4:3 / 9:16 presets and pixel-snapping for image editing.

Why does my calculator return a non-integer ratio?

If you enter terms that don't share a clean integer relationship — say 7:π or 100:33 — the simplified form may itself be irrational or just close-to-irreducible (100:33 has GCD = 1, so it's already simplified). The calculator returns the simplest integer pair plus the decimal equivalent (3.03:1 in this case) so you can choose whichever form your downstream use needs.