Ratio Calculator
Last updated: 27 June 2026
Reviewed by Gavin Meiring, Lead research and primary author · Doctoral Candidate (Corporate Governance) · Research and drafting assisted by AI
a : b = c : d → solve for d
- The golden ratio (approximately 1:1.618) appears in the Parthenon, Leonardo da Vinci's work, and nautilus shells. Whether it was deliberately used in art or just perceived retrospectively is debated.
- Aspect ratios of screens: 4:3 was the TV standard until HD. 16:9 is standard HD. Cinematic widescreen is 2.39:1. Phone screens are often 19.5:9 or 20:9.
- Maps use ratio scales like 1:50,000 — meaning 1cm on the map = 50,000cm (500m) in reality. The Ordnance Survey Landranger maps beloved by UK walkers are at this scale.
Ratio Calculator
A ratio calculator simplifies ratios, scales them up or down, and solves for a missing value in a proportion. It is used by students, cooks, engineers, architects, and anyone who needs to maintain or compare proportional relationships between quantities.
How to Use the Ratio Calculator
- Enter the two values of a ratio in the A and B fields (e.g., 4 and 6).
- Click Simplify to reduce the ratio to its lowest form.
- To scale the ratio, enter a multiplier or a target value for one part and the calculator finds the other.
- To solve a proportion (A:B = C:D), enter three known values and leave the fourth blank, then click Solve.
- Switch to the equivalent ratios mode to see a table of multiples for easy reference.
The Formula
To simplify a ratio A:B, find the Greatest Common Factor (GCF) of A and B, then divide both by it. Simplified ratio = (A divided by GCF) : (B divided by GCF). To solve a proportion where A:B = C:D and D is unknown: D = (B multiplied by C) divided by A. This is called cross-multiplication. To scale a ratio by factor k: multiply both parts by k to get (A times k) : (B times k).
Real-World Example
A recipe uses flour and sugar in a ratio of 3:1. You need to scale it up to use 750 g of flour. First, simplify: 3:1 is already in simplest form. Find the scale factor: 750 divided by 3 = 250. Sugar needed = 1 multiplied by 250 = 250 g. Now scale a second scenario: a paint mix requires red to white in ratio 2:5. You have 300 ml of red. White needed = (5 multiplied by 300) divided by 2 = 750 ml. Total paint = 300 plus 750 = 1,050 ml.
Ratios in Maps, Scale Drawings, and Finance
In cartography, a map scale of 1:50,000 means 1 cm on the map equals 50,000 cm (500 m) in reality. Architects use scale ratios such as 1:100 to represent buildings in drawings. In finance, key ratios such as the price-to-earnings (P/E) ratio compare one financial metric to another, summarising company value in a single number. Debt-to-equity ratios express financial gearing. Understanding whether a ratio is expressed as A:B, A to B, or A/B (a fraction) is important because they are the same relationship written differently.
Frequently Asked Questions
What is the difference between a ratio and a fraction? A ratio compares two or more quantities that do not have to add to a whole. A fraction represents a part of a whole. The ratio 3:5 means for every 3 of one thing there are 5 of another; as a fraction, 3 out of 8 total parts is 3/8. Both representations are useful depending on context.
How do I convert a ratio to a percentage? Convert the ratio to a fraction of the total, then multiply by 100. If the ratio is 3:7, the total parts are 10. The first quantity is 3/10 = 30 percent. The second is 7/10 = 70 percent.
What is a proportion and how is it different from a ratio? A ratio is a comparison of two quantities. A proportion is a statement that two ratios are equal: A:B = C:D. Proportions are used to scale recipes, convert units, and solve similar triangle problems in geometry.
Can ratios involve more than two numbers? Yes. A ratio can compare three or more quantities: concrete might be mixed in a ratio of cement to sand to gravel of 1:2:3. When working with multi-part ratios, the same principles apply; find the GCF of all parts to simplify, or find the scale factor to adjust each part proportionally.
A three part ratio in the mixer
Ratios with three parts are common in construction, and the arithmetic is the same as for two parts.
A concrete mix of 1:2:3 by volume means one part cement, two parts sand and three parts aggregate. The parts add to six.
Suppose you want 1.5 cubic metres of mixed concrete. One cubic metre is 1,000 litres, so the total is 1,500 litres. Each part takes 1,500 divided by 6, which is 250 litres.
| material | parts | share of the total | cubic metres | litres |
|---|---|---|---|---|
| cement | 1 | 1/6 = 0.166667 | 0.2500 | 250.00 |
| sand | 2 | 2/6 = 0.333333 | 0.5000 | 500.00 |
| aggregate | 3 | 3/6 = 0.500000 | 0.7500 | 750.00 |
The cement share is 16.6667 percent of the mix by volume, and it stays at that figure however much concrete you order. A two cubic metre pour takes 333.33 litres of cement. A ten cubic metre pour takes 1,666.67 litres.
Equivalent ratios and the share each part keeps
Multiplying every part by the same number gives an equivalent ratio. The proportions do not move.
| ratio | sum of parts | cement | sand | aggregate | cement share |
|---|---|---|---|---|---|
| 1:2:3 | 6 | 1 | 2 | 3 | 16.6667 percent |
| 2:4:6 | 12 | 2 | 4 | 6 | 16.6667 percent |
| 3:6:9 | 18 | 3 | 6 | 9 | 16.6667 percent |
| 4:8:12 | 24 | 4 | 8 | 12 | 16.6667 percent |
| 5:10:15 | 30 | 5 | 10 | 15 | 16.6667 percent |
The last column is the check. If the share changes when you scale, the scaling is wrong. This is the property that lets a builder write a mix as 1:2:3 and a supplier read it as 4:8:12 without either of them converting anything.
Reading a map scale
A map scale written as 1:50,000 is a ratio. One unit on the paper is 50,000 of the same unit on the ground.
| map distance | ground distance in cm | in metres | in kilometres |
|---|---|---|---|
| 1 cm | 50,000 | 500.00 | 0.5000 |
| 3.5 cm | 175,000 | 1,750.00 | 1.7500 |
| 7.4 cm | 370,000 | 3,700.00 | 3.7000 |
| 12 cm | 600,000 | 6,000.00 | 6.0000 |
The inverse is just as useful. A footpath 4.2 kilometres long measures 420,000 centimetres on the ground, so on a 1:50,000 sheet it runs 8.4 centimetres. That is the calculation to reach for when you are deciding whether a route fits on one page.
Converting the ratio to a fraction gives the same answer and is harder to get wrong. The fraction 1/50,000 multiplied by 420,000 centimetres is 8.4 centimetres.
Paper sizes and the ratio that fixes them
The ISO 216 series of paper sizes is defined by a single ratio, 1 to the square root of 2, which is 1 to 1.4142136. Halving a sheet along its long edge produces two sheets with the same ratio.
| size | dimensions | ratio of long to short side | area in square millimetres | nominal area |
|---|---|---|---|---|
| A0 | 841 by 1,189 mm | 1.413793 | 999,949 | 1,000,000 |
| A2 | 420 by 594 mm | 1.414286 | 249,480 | 250,000 |
| A4 | 210 by 297 mm | 1.414286 | 62,370 | 62,500 |
The gaps in the last two columns are not errors. The dimensions are rounded to whole millimetres for manufacture, so a printed A4 sheet measures 62,370 square millimetres against a nominal 62,500. The ratio survives the rounding to five decimal places, which is the whole point of the standard.
Three ways to solve one proportion
The proportion 3:4 = 12:x can be solved three ways, and all three give 16.
Cross multiplication multiplies the means and the extremes: x = (4 multiplied by 12) divided by 3, which is 48 divided by 3, which is 16.
The scale factor route asks how the known pair relates. The first part went from 3 to 12, a factor of 4, so the second part goes from 4 to 4 multiplied by 4, which is 16.
The fraction route writes the ratio as 3/4 and the answer as 12/16. Both equal 0.75. Checking that the two fractions match is the quickest way to catch a cross multiplication you have set up upside down.
Aspect ratios and screen dimensions
An aspect ratio is a ratio with the units dropped. The table below shows how the decimal value converts to pixel dimensions.
| ratio | as a decimal | height at 1,920 wide | height at 1,280 wide |
|---|---|---|---|
| 16:9 | 1.777778 | 1,080 | 720 |
| 4:3 | 1.333333 | 1,440 | 960 |
| 3:2 | 1.500000 | 1,280 | 853 |
| 21:9 | 2.333333 | 823 | 549 |
The 3:2 and 21:9 rows do not land on whole pixels. Any size you actually export has to be rounded, which is why a 21:9 display is usually quoted as 2,560 by 1,080 rather than as a clean multiple of nine.
What a price to earnings ratio compares
Financial ratios work the same way as any other ratio: one quantity divided by another, with the units dropped.
A share trading at 45.00 with earnings of 2.50 per share carries a price to earnings ratio of 45.00 divided by 2.50, which is 18.0. The same figure comes out of the company totals: a market value of 4,500,000,000 divided by earnings of 250,000,000 is also 18.0.
The ratio is a price per unit of earnings. Inverting it gives the earnings yield, which here is 1 divided by 18.0, or 5.5556 percent. That is the return the buyer gets if earnings stay flat and the price never moves.
Where the ratio calculator stops
Ratios compare quantities in the same unit. A ratio of 1:2 between litres and kilograms is not a ratio at all, because the units do not cancel.
Parts must also be non-negative for the simplification step to behave. A negative part is arithmetically valid but describes a comparison few people need, and the greatest common factor routine will happily return one.
Finally, a proportion needs three known values and one unknown. If two values are missing, the relationship is underdetermined and no arithmetic recovers it.
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