# Rounding Calculator

Rounding a number involves replacing the number with an approximation of the number that results in a shorter, simpler, or more explicit representation of said number based on specific rounding definitions. For example, if rounding the number 2.7 to the nearest integer, 2.7 would be rounded to 3.

### Rounding Methods

There are various rounding definitions that can be used to round a number. The calculator defaults to rounding to the nearest integer, but settings can be changed to use other rounding modes and levels of precision. All the rounding modes the calculator is capable of are described below.

**Round half up:**

This rounding method is one of the more common rounding methods used. It means rounding values that are halfway between the chosen rounding precision up. For example, when rounding to the ones place:

5.50 | ⇒ | 6 |

5.51 | ⇒ | 6 |

5.49 | ⇒ | 5 |

When the value being rounded is negative, the definition is somewhat ambiguous. Some round -5.5 to -5, some round to -6. We agree here the "up" can be thought of as rounding values that are halfway towards the bigger or more positive value. For example, when rounding to the ones place:

-5.50 | ⇒ | -5 |

-5.51 | ⇒ | -6 |

-5.49 | ⇒ | -5 |

**Round half down:**

Rounding half down is similar to rounding half up, except that it means rounding values that are halfway between the chosen rounding precision down, rather than up. For example, when rounding to the ones place:

5.50 | ⇒ | 5 |

5.51 | ⇒ | 6 |

5.49 | ⇒ | 5 |

In the case of negative numbers, same as rounding half up, the definition is ambiguous. We agree here rounding half down can be thought of as rounding values that are halfway towards the smaller or more negative value. For example, when rounding to the ones place:

-5.50 | ⇒ | -6 |

-5.51 | ⇒ | -6 |

-5.49 | ⇒ | -5 |

**Round up (ceiling):**

Rounding up, sometimes referred to as "taking the ceiling" of a number means rounding up towards the nearest integer. For example, when rounding to the ones place, any non-integer value will be rounded up to the next highest integer, as shown below:

5.01 | ⇒ | 6 |

In the case of negative numbers, rounding up means rounding a non-integer negative number to its next closest, more positive integer. For example:

-5.01 | ⇒ | -5 |

-5.50 | ⇒ | -5 |

-5.99 | ⇒ | -5 |

**Round down (floor):**

Rounding down, sometimes referred to as "taking the floor" of a number means rounding down towards the nearest integer. For example, when rounding to the ones place, any non-integer value will be rounded down to the next lowest integer, as shown below:

5.99 | ⇒ | 5 |

In the case of negative numbers, rounding down means rounding a non-integer negative number to its next nearest, more negative integer. For example:

-5.01 | ⇒ | -6 |

-5.50 | ⇒ | -6 |

-5.99 | ⇒ | -6 |

**Round half to even:**

Rounding half to even can be used as a tie-breaking rule since it does not have any biases based on positive or negative numbers or rounding towards or away from zero, as some of the other rounding methods do. For this method, half values are rounded to the nearest even integer. For example:

5.5 | ⇒ | 6 |

6.5 | ⇒ | 6 |

-7.5 | ⇒ | -8 |

-8.5 | ⇒ | 8 |

**Round half to odd:**

Rounding half to odd is similar to rounding half to even (above), and can be used as a tie-breaking rule. For this method, half values are rounded to the nearest odd integer. For example:

5.5 | ⇒ | 5 |

6.5 | ⇒ | 7 |

-7.5 | ⇒ | -7 |

-8.5 | ⇒ | -9 |

**Round half away from zero:**

Rounding half away from zero can be used as a tie-breaking rule, and means exactly as the phrase describes: rounding half values away from zero. It has no biases towards positive or negative numbers, but does have a bias away from zero. Another way to think about this rounding method is to round a half value towards the next integer closer to positive or negative infinity based on whether the value is positive or negative, respectively. For example:

5.5 | ⇒ | 6 |

-5.5 | ⇒ | -6 |

**Round half towards zero:**

Rounding half towards zero is similar to rounding half away from zero, except that it rounds in the opposite direction. It has no biases towards positive or negative numbers, but does have a bias towards zero. The method means that half values will be rounded towards the next integer that is closer to zero than it is to positive or negative infinity. For example:

5.5 | ⇒ | 5 |

-5.5 | ⇒ | -5 |

### Rounding to fractions

Rounding to fractions involves rounding a given value to the nearest multiple of the chosen fraction. For example, rounding to the nearest 1/8:

15.65 | ⇒ | 15 |
| =15.625 | |||

15.70 | ⇒ | 15 |
| =15.75 | |||

15.80 | ⇒ | 15 |
| =15.75 |

This can be particularly useful in the context of engineering, where fractions are widely used to describe the size of components such as pipes and bolts.