Rounding Calculator

Number
Precision	Tenths (1) Hundredths (2) Thousandths (3) Ten Thousandths (4) Hundred Thousandths (5) Millionths (6) Ones (0) Tens (-1) Hundreds (-2) Thousands (-3) Millions (-6) 1/2 1/4 1/8 1/16 1/32 1/64 Precision of -1000 to 1000 digits

Settings
Rounding Mode: Round to the nearest (default) Round half up Round half down Round up (ceiling) Round down (floor) Round half to even Round half to odd Round half away from zero Round half towards zero Rounding Precision: Select a precision level Input a precision level

Settings

Click "Settings" to set the rounding method or define your own precision level.

To round a value means to substitute it by a nearby estimate that yields a more concise or clearer form according to a chosen rounding rule. For instance, rounding 2.7 to the closest whole number gives 3.

Rounding Methods

Multiple rounding conventions exist for adjusting a number. By default the tool rounds to the nearest integer, though you can switch to alternative modes and specify different precision levels. Below you’ll find a rundown of every rounding option the calculator supports.

Round half up:

One of the most frequently applied techniques is the “round‑half‑up” rule. It directs that numbers exactly halfway between two increments are rounded upward. For example, when you round to the unit digit:

The interpretation becomes less clear for negative inputs. Some implementations turn –5.5 into –5, while others produce –6. In this context, up is taken to mean moving toward the larger, i.e., more positive, integer. For instance, rounding to the units place:

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:

With negative values the rule mirrors “round‑half‑down,” which is also a matter of definition. Here we treat down as moving toward the smaller, more negative integer. For example, when rounding to the ones digit:

Round up (ceiling):

The “round‑up” or ceiling operation pushes a number to the smallest integer that is not less than the original. For instance, when rounding to whole numbers, any fractional value is lifted to the next larger integer, as illustrated:

For negative inputs, rounding up translates a non‑integer negative number to the nearest integer that is greater (i.e., closer to zero). For example:

Round down (floor):

The “round‑down” or floor function moves a number to the greatest integer that does not exceed it. For example, when rounding to the unit place, any fractional component is discarded, yielding the next lower integer, as shown:

When dealing with negative numbers, rounding down sends a non‑integer value to the next integer that is smaller (i.e., further from zero). For instance:

Round half to even:

The “round‑half‑to‑even” strategy serves as a neutral tie‑breaker, avoiding bias toward positive or negative directions or away from zero. Under this rule, values exactly halfway are rounded to the nearest even integer. For example:

Round half to odd:

The ‘half‑to‑odd’ rounding approach works like the previously described ‘half‑to‑even’ technique and serves as a tie‑breaker. With this rule, any value that falls exactly halfway is rounded to the closest odd whole number. Illustrative example:

Round half away from zero:

The ‘half‑away‑from‑zero’ method acts as a tie‑breaker, doing precisely what its name suggests: a value that is exactly half is pushed away from zero. It treats positive and negative numbers without preference, yet consistently moves the result farther from zero. In other words, a half‑value is rounded to the next integer in the direction of positive infinity for positive numbers, and toward negative infinity for negative ones. Sample calculation:

Round half towards zero:

The ‘half‑toward‑zero’ rule mirrors the ‘half‑away‑from‑zero’ technique but in reverse, pulling half‑values back toward zero. It remains impartial to sign, yet always chooses the integer nearer to zero rather than to either infinity. Thus, a value exactly at .5 is rounded to the adjacent whole number that lies closer to zero. Example below:

Rounding to fractions

Fractional rounding means adjusting a number to the closest multiple of a specified fraction. For instance, snapping a value to the nearest one‑eighth increment:

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.