While the metric system handles decimals in a straightforward way, for imperial measurements like feet and inches, converting from a decimal into a usable measurement isn’t always easy.
Whether you’re looking to convert a decimal value in feet to feet and inches, or inches as a decimal to fraction inches, you’ll need to think a little about how decimals work and what you’re looking for. Luckily, though, once you’ve understood the basics, you will be able to make the conversions easily, and there are always online calculators if you don’t want to go through the math.
Decimal Measures – What They Mean
Thinking about the meaning of a decimal number is the key to working out how to convert most decimals to whatever you’re looking for. A decimal is basically just a fraction of 1, in whatever unit you’re working in. So, for instance, 0.5 is really just another way of saying a half, 0.25 is just another way of saying a quarter, and 0.3333 is just another way of saying a third.
Converting decimals really revolves around this fact. If you have a proportion as a decimal, and you want a percent value, for instance, remember that you want a percentage — a fraction of 100 — when you have a fraction of 1. So to convert you just multiply by 100. In the same way, to convert decimal feet to inches, you have a fraction of 1 where you want a fraction of 12.
Decimal Feet to Inches Conversion
Say you’re given a value in feet but with decimals instead of inches, such as 12.25 feet. It might not be immediately obvious what the value in feet and inches is, but you can use the lessons of the last section to work out what to do. The 12 is fine, because that is a whole number of feet, but what about the 0.25 leftover?
To find the value in inches, note that this is 0.25 of a foot, but there are 12 inches in a foot — so you simply multiply this value by 12 to get 3 inches, giving 12 feet, 3 inches in total.
Often, you can see a shortcut that makes the decimal to inches conversion easier. In this case you might have recognized that 0.25 is a quarter, and a quarter of a foot is 3 inches, thus giving you the answer in a simpler way. However, the method above always works even if you can’t see an easier way.
Decimal to Fractional Inches
If you have fractions of an inch, the process is quite similar, but with the key difference that you have to choose how accurate a measure you want.
For a fractional inch value like 4.656 inches, you do the same thing with the whole numbers — you know you have 4 full inches so you can ignore that for now. For the 0.656, choose a denominator for your fraction and then do the same calculation as before, multiplying this value by your decimal.
For 0.656, the best option is 1/32 of an inch, so you can multiply this value by 32 to find the fraction. Here, 0.656 × 32 = 20.99, so the result is about 21/32 of an inch, and in total, 4.656 inches is 4 and 21/32 inches. Of course, this value was chosen to be close to a whole value, but in practice you may need to do some guesswork and either round up or round down as appropriate to balance accuracy with usability.
Of course, if you don’t want to go through the calculation yourself, there are many online calculators you can use to convert decimal feet to inches, decimal inches to fractional inches and more (see Resources).
When you’re working with fractions of an inch, you usually need to choose a denominator, but remember that too much accuracy isn’t always helpful, so you’re better off sticking with 8, 16, 32 or 64 as your denominator.
About the Author
Lee Johnson is a freelance writer and science enthusiast, with a passion for distilling complex concepts into simple, digestible language. He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. He was also a science blogger for Elements Behavioral Health's blog network for five years. He studied physics at the Open University and graduated in 2018.