Ratio Calculator
What is a ratio?
A ratio is a mathematical relationship between two numbers that expresses how many times the first number contains the second. For example, the ratio between cars in the street and people in them would be 1:5 (1 to 5) if each car can fit 5 people in it and they are loaded to the maximum. If there are just 2 persons in each car, the ratio would be 1:2. The ratio can also be between things in a container, area, or subgroups in larger groups. For example, if you have 10 fruits and 3 of them are apples and 7 are oranges, the ratio between apples and oranges is 3:7.
There are more complex ratios where you might have more than two numbers in a single notation, like if you have 3 apples, 5 oranges and 2 bananas, the ratio between them is 3:5:2. Numbers in a ratio can be integers (whole numbers) or fractions and when the two quantities are measured in the same unit, the ratio output from our ratio calculator is a dimensionless number. If the units are different, then it is called a rate, e.g. in productivity calculations, if it takes 1 person 11 days to complete a given project, the daily productivity rate is 1:11 (he or she can complete 1/11-th of the work in a day), while the monthly productivity, assuming 22 working days a month, is 2:1 (he or she can complete 2 projects in 1 month).
Ratios can be visually represented using lengths or areas, and rarely - as volumes. An example is below:
ratio visualization
When visualizing, it is best to use thin lines or bars, as these are the least misleading. Wide bars may trigger subconscious comparison between their areas instead, which would be misleading to the extent to which the ratio of areas does not correspond to the ratio of lengths.
Ratios are often used in business metrics, accounting and investment decision-making to calculate things like profit margin, markup, ROI, return on assets, and conversion rate among many others.
How to solve ratios?
Ratio equations usually involve two ratios on both sides of an equation, with three numbers from the ratios given and the forth being solved for. Solving ratio equations is all about finding which number, multiplied by the one number given on the side of the missing number, would result in the same relationship as the one on the other side of the equation.
Other than using our ratio calculator, you can use simple equation rules: multiplying or dividing both sides of the equation in order to leave the missing variable alone on one side of the equation. For example, solving x:2 = 8:4 for x would be equivalent to solving x / 2 = 8 / 4, requiring us to multiplying both sides by 2, to get to x = 8/4 x 2 = 2 x 2 = 4.
In our ratio solver / calculator, just leave the part of the ratio you are solving for empty, then press "Calculate" to get what numbers needs to be there to balance the equation.
Multiplication, division, and reduction of ratios
If you multiply each member of a ratio by the same number, the ratio remains the same. For example, the ratio 1:3, when multiplied by 4, becomes 4:12, and in it the proportions between the quantities remain the same. Using the same logic, if you divide each quantity in a ratio by the same number, the number remains the same.
Reducing a ratio is done the same way as with fractions - you need to find the smallest integer that preserves the ratio, which is the greatest common divisor. If a ratio is given as 4:12, the GCD of 4 and 12 is 4, so we divide each side by 4 to get 1:4, which is the most convenient form of the ratio to use.
Odds as ratios
Odds, or probabilities of events occurring or not occurring, are expressed as ratios. The ratios must usually add up to 1 or 100%, for example 0.3:0.7 or 30:70, but most often they are presented in a from convenient for apprehension. In this case that would be 3:7 (30/10 and 70/10, and 0.3 x 10 , 0.7 x 10). They are often used in gambling and other games of chance, for example the chance for you to win the US Powerball lottery jackpot (2018 rules) are 1 in 292,201,338, or 1:292,201,338, as can be seen on our lottery number generator page.
Aspect ratio calculation
Ratios are also often used when one needs to calculate the aspect ratio of an image or video, for scaling maps or models, as well as in sizing cooking recipes. For example, some old TV sets had an aspect ratio of 4:6 (width by height), while others had a ratio of 2.35:1. New LCD, OLED, and other TVs and screens usually have a ratio of 16:9, which is in fact a compromise between the two.
Models of cars and buildings are often made in ratios of 1:20 to 1:40, while for maps the scaling is often much higher, for example 1:1,000,000 which means that 1 cm on the map would be 1,000,000 cm in real life (10 kilometers).
Ratios in geometry
Other than maps, ratios are very common in geometry. One of the most famous ratios in the world is denoted by the Greek letter π (pi) and is the ratio between the diameter of a circle and its circumference. It even has its own day of celebration: March 14 (3.14.YYYY)! It is used in the calculation of the area and circumference of circles and ovals, as well as the volume of spheres and spherical bodies. Similarly, trigonometric functions are also ratios: the sine, cosine and tangent function are simply expressions of the ratios between two sides of a triangle, relative to a specified angle.
Hex Calculator / Converter
Use this tool in hex calculator mode to perform algebraic operations with hex numbers (add, subtract, multiply and divide hexadecimals). Use it in hex converter mode to easily convert a hex number to a decimal number, or a decimal number to a hex one (decimal to hex and hex to decimal converter), or to convert hex to binary and binary to hex.
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Related calculators
Hex to Decimal Converter
Decimal to Hex Converter
Binary Calculator
What is a hex number?
A hex number, short for hexadecimal number, is a number expressed in the hexadecimal positional numeral system with a base of 16 which uses sixteen symbols: the numbers from 0 to 9 and the letters A,B,C,D,E, and F, to represent values from 0 to 15. Equivalently, small-case letters a through f can be used. For example, 10 in decimal is A in hex, 100 in decimal is 64 in hex, while 1,000 in decimal is 3E8 in hex. Hex numbers have signs, just like decimal ones, for example -1e is equal to -30 in decimal.
Hex numerals are used mostly in computing: computer system designers, software engineers and programmers as a convenient representation of the underlying binary systems. An ordinary person would encounter them every day when browsing the web since in website addresses (URLs) special characters are encoded as a hex numeral, e.g. %20 stands for "space" (blank). A lot of webpages also encode special characters in html in terms of their hexadecimal numerical character reference (ode), e.g. ’ is the Unicode for a single quotation mark (’).
Using our hex calculator, you can perform arithmetic operations (addition, subtraction, multiplication and division of hex numbers) as well as use it as a hex converter for hex to decimal, decimal to hex, hex to binary and binary to hex conversions.
Here is a table of some numbers represented in the decimal, hex and binary systems (base 10, base 2 and base 16).
Numbers in decimal, hex and binary
Decimal Hex Binary
0 0 0
1 1 1
2 2 10
3 3 11
5 5 101
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
50 32 110010
63 3F 111111
100 64 1100100
1000 3E8 1111101000
10000 2710 10011100010000
Converting to and from hex numerals
Converting numbers to and from hex does not change the number itself, it just changes its form. Using our hex converter above, you can do both types of conversions quickly and easily.
Hex to decimal
Each position in a hexadecimal numeral represents a power of 16 the same way each position in a decimal number represents a power of 10. For example, the number 20 in decimal is 2 · 101 + 0 · 100 = 20. The hex number 20 is then 2 · 161 + 0 · 160 = 32 in dec. Similarly, the number 1E is 1 · 16 + 14 · 1 = 30 in decimal.
The process of hex to decimal conversion is therefore to first take each position and convert it to decimal, e.g. 9 is 9, but B is converted to 11, then to multiply each position by 16 to the power of the position number, counting from right to left and starting at zero. If you need to calculate large exponents like 168 you might find our exponent calculator useful.
Decimal to hex
This process is a bit more complex as we are going from a higher base to a lower base. Let us say the number we want to convert from decimal to hex is X. Begin by finding the largest power of 16 ≤ X and denote it by E. Then determine how many times the power of 16 found above goes into X, denote it by Z1. Denote the remainder by Y1.
Repeat the above steps using Yn as a starting value until 16 is larger than the remaining value and assign the remainder to the 160 position, then assign each of the values Y1...n to its respective position and you will have your hex value.
Example dec to hex conversion: Convert 1000 in decimal to hex.
1.) Largest power E = 2 (162 = 256 ≤ 1000, 163 = 4,096 ≥ 1000)
2.) Z1 = 1000 / 162 = 3 (232 remainder); Y1 = 232
3.) Largest power E = 1 (161 = 16 ≤ 232, 162 = 256 ≥ 232)
4.) Z2 = 232 / 161 = 14 (8 remainder); Y2 = 8
5.) 8 < 16; Z3 = 8, end.
Combine Z1..n to get 3E8 (14 dec = E hex).
Hex to decimal and decimal to hex conversion follows the same principles, but with base 2 instead of base 10.
Algebraic operations with hexadecimal numbers
Using our tool in hex calculator mode you can perform the four basic arithmetic operations on hex numbers: addition, subtraction, multiplication and division. In order to do the hexadecimal calculations yourself most would prefer using a table for smaller numbers and a calculator for larger ones. Subtraction works the same way as any other number system, except when borrowing a number you need to borrow a group of 1610 instead of 1010 as you would with decimals.
Cite this calculator & page
If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "Hex Calculator", [online] Available at: https://www.gigacalculator.com/calculators/hexadecimal-calculator.php URL [Accessed Date: 30 Jul, 2019].
