Rounding Calculator

Enter a number, select the precision and rounding mode, and get the rounded result instantly.

Number to round:

Round to nearest:

Rounding mode:

Result:

Enter a number

Understanding Rounding Modes & Precision

Rounding to Fractions (Precision)

Beyond standard decimal place rounding, this calculator also allows you to round numbers to the nearest common fraction, such as 1/2, 1/4, 1/8, 1/16, 1/32, or 1/64. When you select a fractional precision, the calculator determines which of these fractional increments your input number is closest to.

For example, if you round 3.3 to the nearest 1/4, it will result in 3 1/4 (which is 3.25), as 3.3 is closer to 3.25 than to 3.50 (3 2/4). The selected rounding mode (e.g., Round half up, Round half to even) is then applied if the number is exactly halfway between two such fractional steps, using the chosen mode's tie-breaking rule relative to those fractional increments.

Round to the nearest (default)

Introduction: This mode rounds numbers to the closest integer. When a number is exactly halfway between two integers (e.g., 2.5), this mode, mirroring JavaScript's `Math.round()`, typically rounds towards positive infinity. Thus, 2.5 becomes 3, and -2.5 becomes -2.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 2.3 (to 0 decimals) => Output: 2
Input: 2.7 (to 0 decimals) => Output: 3
Input: 2.5 (to 0 decimals) => Output: 3
Input: -2.5 (to 0 decimals) => Output: -2

Common Scenarios: General-purpose rounding, often the default behavior in many programming environments for basic rounding tasks. Suitable when a simple and consistent tie-breaking rule (halves towards positive infinity) is acceptable.

Round half up

Introduction: This mode rounds numbers to the closest integer. If a number is exactly halfway between two integers, it rounds up (towards positive infinity). For example, 2.5 rounds to 3, and -2.5 rounds to -2 (as 'up' here means towards positive infinity).

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 7.5 (to 0 decimals) => Output: 8
Input: 7.2 (to 0 decimals) => Output: 7
Input: -7.5 (to 0 decimals) => Output: -7

Common Scenarios: Frequently used in academic grading and general calculations where halves should consistently round towards a numerically larger value (or less negative value).

Round half down

Introduction: This mode rounds numbers to the closest integer. If a number is exactly halfway between two integers, it rounds down (towards negative infinity). For example, 2.5 rounds to 2, and -2.5 rounds to -3.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 3.5 (to 0 decimals) => Output: 3
Input: 3.7 (to 0 decimals) => Output: 4
Input: -3.5 (to 0 decimals) => Output: -4

Common Scenarios: Used in situations where a conservative rounding approach is needed for tie-breaking, ensuring that half-values resolve to the numerically lower value. It can be specified in particular standards or requirements.

Round up (ceiling)

Introduction: This mode always rounds the number to the next integer in the direction of positive infinity, unless it's already an integer. For example, 2.1 rounds to 3, and -2.9 rounds to -2.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 4.1 (to 0 decimals) => Output: 5
Input: -4.9 (to 0 decimals) => Output: -4
Input: 4.0 (to 0 decimals) => Output: 4

Common Scenarios: Ensuring a minimum quantity (e.g., number of buses, inventory levels) or in pricing items sold in discrete units where any fraction of a unit incurs the full unit cost.

Round down (floor)

Introduction: This mode always rounds the number to the previous integer in the direction of negative infinity, unless it's already an integer. For example, 2.9 rounds to 2, and -2.1 rounds to -3.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 5.9 (to 0 decimals) => Output: 5
Input: -5.1 (to 0 decimals) => Output: -6
Input: 5.0 (to 0 decimals) => Output: 5

Common Scenarios: Calculating completed units (e.g., age in full years), determining how many full items can be obtained within a budget, or in array indexing.

Round half to even (Banker's Rounding)

Introduction: This mode rounds numbers to the closest integer. If a number is exactly halfway between two integers, it rounds to the nearest even integer (e.g., 2.5 to 2, 3.5 to 4). This method minimizes long-term bias.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 2.5 (to 0 decimals) => Output: 2
Input: 3.5 (to 0 decimals) => Output: 4
Input: -2.5 (to 0 decimals) => Output: -2

Common Scenarios: Widely adopted in financial, statistical, and scientific calculations (e.g., IEEE 754 standard) to reduce cumulative rounding errors. Ideal for accounting and data analysis.

Round half to odd

Introduction: This mode rounds numbers to the closest integer. If a number is exactly halfway between two integers, it rounds to the nearest odd integer (e.g., 2.5 to 3, 3.5 to 3).

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 2.5 (to 0 decimals) => Output: 3
Input: 4.5 (to 0 decimals) => Output: 5
Input: -2.5 (to 0 decimals) => Output: -3

Common Scenarios: Less common in standard applications but can be employed in specific algorithms or custom numerical processes where this particular tie-breaking behavior is desired.

Round half away from zero

Introduction: This mode rounds to the closest integer. If a number is exactly halfway, it rounds away from zero (e.g., 2.5 to 3, -2.5 to -3). Positive halves round up; negative halves round down in value.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 2.5 (to 0 decimals) => Output: 3
Input: -2.5 (to 0 decimals) => Output: -3
Input: 2.3 (to 0 decimals) => Output: 2

Common Scenarios: Often taught in primary education due to its symmetrical handling of positive and negative halves. Used in some financial contexts when an intuitive 'larger magnitude for halves' rule is preferred.

Round half towards zero

Introduction: This mode rounds to the closest integer. If a number is exactly halfway, it rounds towards zero (e.g., 2.5 to 2, -2.5 to -2). Positive halves round down; negative halves round up in value.

Examples (typically at 0 decimal places for tie-breaking illustration):

Input: 2.5 (to 0 decimals) => Output: 2
Input: -2.5 (to 0 decimals) => Output: -2
Input: 2.8 (to 0 decimals) => Output: 3

Common Scenarios: Used when a bias towards zero is desired for tie-breaking situations. This is effectively truncation for values that are exact halves, while non-halves are rounded to the nearest.