# Why not use Double or Float to represent currency?

## Why not use Double or Float to represent currency?

### Question

I've always been told *never* to represent money with `double`

or `float`

types, and this time I pose the question to you: why?

I'm sure there is a very good reason, I simply do not know what it is.

### Accepted Answer

Because floats and doubles cannot accurately represent the base 10 multiples that we use for money. This issue isn't just for Java, it's for any programming language that uses base 2 floating-point types.

In base 10, you can write 10.25 as 1025 * 10^{-2} (an integer times a power of 10). IEEE-754 floating-point numbers are different, but a very simple way to think about them is to multiply by a power of two instead. For instance, you could be looking at 164 * 2^{-4} (an integer times a power of two), which is also equal to 10.25. That's not how the numbers are represented in memory, but the math implications are the same.

Even in base 10, this notation cannot accurately represent most simple fractions. For instance, you can't represent 1/3: the decimal representation is repeating (0.3333...), so there is no finite integer that you can multiply by a power of 10 to get 1/3. You could settle on a long sequence of 3's and a small exponent, like 333333333 * 10^{-10}, but it is not accurate: if you multiply that by 3, you won't get 1.

However, for the purpose of counting money, at least for countries whose money is valued within an order of magnitude of the US dollar, usually all you need is to be able to store multiples of 10^{-2}, so it doesn't really matter that 1/3 can't be represented.

The problem with floats and doubles is that the *vast majority* of money-like numbers don't have an exact representation as an integer times a power of 2. In fact, the only multiples of 0.01 between 0 and 1 (which are significant when dealing with money because they're integer cents) that can be represented exactly as an IEEE-754 binary floating-point number are 0, 0.25, 0.5, 0.75 and 1. All the others are off by a small amount. As an analogy to the 0.333333 example, if you take the floating-point value for 0.1 and you multiply it by 10, you won't get 1.

Representing money as a `double`

or `float`

will probably look good at first as the software rounds off the tiny errors, but as you perform more additions, subtractions, multiplications and divisions on inexact numbers, errors will compound and you'll end up with values that are visibly not accurate. This makes floats and doubles inadequate for dealing with money, where perfect accuracy for multiples of base 10 powers is required.

A solution that works in just about any language is to use integers instead, and count cents. For instance, 1025 would be $10.25. Several languages also have built-in types to deal with money. Among others, Java has the `BigDecimal`

class, and C# has the `decimal`

type.

Read more... Read less...

**From Bloch, J., Effective Java, 2nd ed, Item 48:**

The

`float`

and`double`

types are particularly ill-suited for monetary calculations because it is impossible to represent 0.1 (or any other negative power of ten) as a`float`

or`double`

exactly.For example, suppose you have $1.03 and you spend 42c. How much money do you have left?

`System.out.println(1.03 - .42);`

prints out

`0.6100000000000001`

.The right way to solve this problem is to use

`BigDecimal`

,`int`

or`long`

for monetary calculations.

Though `BigDecimal`

has some caveats (please see currently accepted answer).

This is not a matter of accuracy, nor is it a matter of precision. It is a matter of meeting the expectations of humans who use base 10 for calculations instead of base 2. For example, using doubles for financial calculations does not produce answers that are "wrong" in a mathematical sense, but it can produce answers that are not what is expected in a financial sense.

Even if you round off your results at the last minute before output, you can still occasionally get a result using doubles that does not match expectations.

Using a calculator, or calculating results by hand, 1.40 * 165 = 231 exactly. However, internally using doubles, on my compiler / operating system environment, it is stored as a binary number close to 230.99999... so if you truncate the number, you get 230 instead of 231. You may reason that rounding instead of truncating would have given the desired result of 231. That is true, but rounding always involves truncation. Whatever rounding technique you use, there are still boundary conditions like this one that will round down when you expect it to round up. They are rare enough that they often will not be found through casual testing or observation. You may have to write some code to search for examples that illustrate outcomes that do not behave as expected.

Assume you want to round something to the nearest penny. So you take your final result, multiply by 100, add 0.5, truncate, then divide the result by 100 to get back to pennies. If the internal number you stored was 3.46499999.... instead of 3.465, you are going to get 3.46 instead 3.47 when you round the number to the nearest penny. But your base 10 calculations may have indicated that the answer should be 3.465 exactly, which clearly should round up to 3.47, not down to 3.46. These kinds of things happen occasionally in real life when you use doubles for financial calculations. It is rare, so it often goes unnoticed as an issue, but it happens.

If you use base 10 for your internal calculations instead of doubles, the answers are always exactly what is expected by humans, assuming no other bugs in your code.

I'm troubled by some of these responses. I think doubles and floats have a place in financial calculations. Certainly, when adding and subtracting non-fractional monetary amounts there will be no loss of precision when using integer classes or BigDecimal classes. But when performing more complex operations, you often end up with results that go out several or many decimal places, no matter how you store the numbers. The issue is how you present the result.

If your result is on the borderline between being rounded up and rounded down, and that last penny really matters, you should be probably be telling the viewer that the answer is nearly in the middle - by displaying more decimal places.

The problem with doubles, and more so with floats, is when they are used to combine large numbers and small numbers. In java,

```
System.out.println(1000000.0f + 1.2f - 1000000.0f);
```

results in

```
1.1875
```

Floats and doubles are approximate. If you create a BigDecimal and pass a float into the constructor you see what the float actually equals:

```
groovy:000> new BigDecimal(1.0F)
===> 1
groovy:000> new BigDecimal(1.01F)
===> 1.0099999904632568359375
```

this probably isn't how you want to represent $1.01.

The problem is that the IEEE spec doesn't have a way to exactly represent all fractions, some of them end up as repeating fractions so you end up with approximation errors. Since accountants like things to come out exactly to the penny, and customers will be annoyed if they pay their bill and after the payment is processed they owe .01 and they get charged a fee or can't close their account, it's better to use exact types like decimal (in C#) or java.math.BigDecimal in Java.

It's not that the error isn't controllable if you round: see this article by Peter Lawrey. It's just easier not to have to round in the first place. Most applications that handle money don't call for a lot of math, the operations consist of adding things or allocating amounts to different buckets. Introducing floating point and rounding just complicates things.

I'll risk being downvoted, but I think the unsuitability of floating point numbers for currency calculations is overrated. As long as you make sure you do the cent-rounding correctly and have enough significant digits to work with in order to counter the binary-decimal representation mismatch explained by zneak, there will be no problem.

People calculating with currency in Excel have always used double precision floats (there is no currency type in Excel) and I have yet to see anyone complaining about rounding errors.

Of course, you have to stay within reason; e.g. a simple webshop would probably never experience any problem with double precision floats, but if you do e.g. accounting or anything else that requires adding a large (unrestricted) amount of numbers, you wouldn't want to touch floating point numbers with a ten foot pole.