What is the difference between `Math.Floor()`

and `Math.Truncate()`

in C#?

### views:

9906### answers:

3`Math.Floor`

rounds down, `Math.Ceiling`

rounds up, and `Math.Truncate`

rounds towards zero. Thus, `Math.Truncate`

is like `Math.Floor`

for positive numbers, and like `Math.Ceiling`

for negative numbers. Here's the reference.

For completeness, `Math.Round`

rounds to the nearest integer. If the number is exactly midway between two integers, then it rounds towards the even one. Reference.

See also: Pax Diablo's answer. Highly recommended!

Some examples:

```
Round(1.5) = 2
Round(2.5) = 2
Round(1.5, MidpointRounding.AwayFromZero) = 2
Round(2.5, MidpointRounding.AwayFromZero) = 3
Round(1.55, 1) = 1.6
Round(1.65, 1) = 1.6
Round(1.55, 1, MidpointRounding.AwayFromZero) = 1.6
Round(1.65, 1, MidpointRounding.AwayFromZero) = 1.7
Truncate(2.10) = 2
Truncate(2.00) = 2
Truncate(1.90) = 1
Truncate(1.80) = 1
```

Follow these links for the MSDN descriptions of:

`Math.Floor`

, which rounds down towards negative infinity.`Math.Ceiling`

, which rounds up towards positive infinity.`Math.Truncate`

, which rounds up or down towards zero.`Math.Round`

, which rounds to the nearest integer or specified number of decimal places. You can specify the behavior if it's exactly equidistant between two possibilities, such as rounding so that the final digit is even ("`Round(2.5,MidpointRounding.ToEven)`

" becoming 2) or so that it's further away from zero ("`Round(2.5,MidpointRounding.AwayFromZero)`

" becoming 3).

The following diagram and table may help:

```
-3 -2 -1 0 1 2
+--|------+---------+----|----+--|------+----|--|-+
a b c d e
a=-2.7 b=-0.5 c=0.3 d=1.5 e=2.8
====== ====== ===== ===== =====
Floor -3 -1 0 1 2
Ceiling -2 0 1 2 3
Truncate -2 0 0 1 2
Round (ToEven) -3 0 0 2 3
Round (AwayFromZero) -3 -1 0 2 3
```

Note that `Round`

is a lot more powerful than it seems, simply because it can round to a specific number of decimal places. All the others round to zero decimals always. For example:

```
n = 3.145;
a = System.Math.Round (n, 2, MidpointRounding.ToEven); // 3.14
b = System.Math.Round (n, 2, MidpointRounding.AwayFromZero); // 3.15
```

With the other functions, you have to use multiply/divide trickery to achieve the same effect:

```
c = System.Math.Truncate (n * 100) / 100; // 3.14
d = System.Math.Ceiling (n * 100) / 100; // 3.15
```