# Rounding Methods Calculator

## Calculator Use

Round numbers and decimals using the halfway value rules of your selected rounding method. Includes round half up and round half down methods as well as ceiling and floor rounding.

## Rounding Methods

There are several methods for rounding numbers. The method you use depends on why you are rounding numbers and the usual rounding conventions for the types of numbers you're working with.

The typical rounding methods are:

- Round Half Up
- Round Half Down
- Round Half Toward Zero
- Round Half Away from Zero
- Round Half Even (Bankers' Rules)
- Round Half Odd
- Round Half Random
- Round All Up (Ceiling)
- Round All Down (Floor)

Rounding up and rounding down are fairly straightforward unless you are dealing with numbers that lie exactly half way between the numbers you're rounding to. For example, financial calculations can result in figures like $24.765. Would you round the 5 up to 77 cents, or down to 76 cents?

Or when calculating the area of a circle, you might need to round the value of pi (3.1415926535898...) to a specific decimal place before your calculation.

### Example of Rounding

Say you have a set of measurements accurate to two decimal places, but you need numbers accurate to one decimal place. You must round the decimal in the hundredths place to the tenths place.

Do you drop all of the digits to the right of the tenths place so all values become 1.1? No, because 1.1 is not a fair representation of the data set. Instead you round each number to the value it is closest to.

Take the first data point: do you round 1.11 down to 1.1 or up to 1.2? The first step is to evaluate whether 1.11 is closer in value to 1.1 or 1.2. It's closer to 1.1, so you round 1.11 down to 1.1.

What about 1.18 -- is it closer to 1.1 or 1.2? Since it is closer in value to 1.2 you'd round up to 1.2.

You can see that 1.15 is exactly half way between 1.1 and 1.2. Every number below 1.15 is closer to 1.1 so you should round down. And every number above 1.15 is closer to 1.2 so you should round up. But what about 1.15?

**1.1**

**1.15**

**1.2**

The rounding methods explained below have been devised to handle the halfway point and, in theory, minimize accumulated rounding errors. In real-world situations the rounding method selected depends on the application of the math as well as programming languages involved. The Rounding Calculator at CalculatorSoup uses the common method Round Half Away From Zero.

## Types of Rounding

The following explanations show how to round the halfway value decimal 1.15 to the 1 in the tenths place.
*x* is the number being rounded.

### Round Half Up

Round halfway values up toward positive infinity.

*x*< 5 round down*x*>= 5 round up

For positive numbers:

- 1.149 rounds to 1.1
- 1.150 rounds to 1.2 up
- 1.151 rounds to 1.2

For negative numbers:

- -1.149 rounds to -1.1
- -1.150 rounds to -1.1 up
- -1.151 rounds to -1.2

### Round Half Down

Round halfway values down toward negative infinity.

*x*<= 5 round down*x*> 5 round up

For positive numbers:

- 1.149 rounds to 1.1
- 1.150 rounds to 1.1 down
- 1.151 rounds to 1.2

For negative numbers:

- -1.149 rounds to -1.1
- -1.150 rounds to -1.2 down, more negative
- -1.151 rounds to -1.2

### Round Half Toward Zero

Round halfway values *toward* zero. This rounding rule acts symmetrically around 0.

- For positive numbers,
*x*<= 5 round down, toward zero - For negative numbers,
*x*>= 5 round up, toward zero

For positive numbers:

- 1.149 rounds to 1.1
- 1.150 rounds to 1.1 down, toward 0
- 1.151 rounds to 1.2

For negative numbers:

- -1.149 rounds to -1.1
- -1.150 rounds to -1.1 up, toward 0
- -1.151 rounds to -1.2

### Round Half Away From Zero

Round halfway values *away* from zero. This rounding rule acts symmetrically around 0.

- For positive numbers,
*x*>= 5 round up, away from zero - For negative numbers,
*x*>= 5 round down, away from zero

For positive numbers:

- 1.149 rounds to 1.1
- 1.150 rounds to 1.2 up, away from 0
- 1.151 rounds to 1.2

For negative numbers:

- -1.149 rounds to -1.1
- -1.150 rounds to -1.2 down, away from 0
- -1.151 rounds to -1.2

### Round Half Even (Bankers' Rules)

Round halfway values to the closest *even* value.

Note that 1.150 will round up to the even value 1.2 and 1.250 will round down to the even value 1.2

*x*< 5 round toward zero*x*= 5 round to the nearest even (non-odd) value*x*> 5 round away from zero

For positive numbers:

- 1.149 rounds to 1.1 and 1.249 rounds to 1.2
- 1.150 rounds to 1.2 and 1.250 rounds to 1.2 closest even value
- 1.151 rounds to 1.2 and 1.251 rounds to 1.3

For negative numbers:

- -1.149 rounds to -1.1 and -1.249 rounds to -1.2
- -1.150 rounds to -1.2 and -1.250 rounds to -1.2 closest even value
- -1.151 rounds to -1.2 and -1.251 rounds to -1.3

### Round Half Odd

Round halfway values to the closest *odd* value.

Note that 1.150 will round down to the odd value 1.1 and 1.250 will round up to the odd value 1.3

*x*< 5 round toward zero*x*= 5 round to the nearest odd (non-even) value*x*> 5 round away from zero

For positive numbers:

- 1.149 rounds to 1.1 and 1.249 rounds to 1.2
- 1.150 rounds to 1.1 and 1.250 rounds to 1.3 closest odd value
- 1.151 rounds to 1.2 and 1.251 rounds to 1.3

For negative numbers:

- -1.149 rounds to -1.1 and -1.249 rounds to -1.2
- -1.150 rounds to -1.1 and -1.250 rounds to -1.3 closest odd value
- -1.151 rounds to -1.2 and -1.251 rounds to -1.3

### Round Half Random

Round halfway values according to the randomly chosen method of either Round Half Up or Round Half Down.

### Round All Up (Ceiling)

Round all values up. 1.150 rounds to 2 and -1.150 rounds to -1.

- 1.7 rounds to 2
- 1.5 rounds to 2
- 1.3 rounds to 2
- -1.3 rounds to -1
- -1.5 rounds to -1
- -1.7 rounds to -1

### Round All Down (Floor)

Round all values down. 1.150 rounds to 1 and -1.150 rounds to -2.

- 1.7 rounds to 1
- 1.5 rounds to 1
- 1.3 rounds to 1
- -1.3 rounds to -2
- -1.5 rounds to -2
- -1.7 rounds to -2

## Further Reading

Wikipedia contributors, "Rounding," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Rounding (accessed February 15, 2022).

ThoughtCo.com: Simple Rules for Rounding Numbers Correctly

MathPlayground: How to Round Whole Numbers

Math.com: Estimating and Rounding Decimals