Rounding Calculator

Mastering Rounding: The Complete Guide

Rounding is the process of reducing the number of digits in a number while preserving its approximate value. This Professional Rounding Calculator offers comprehensive control: round to decimal places, significant figures, or nearest values (10, 100, 0.5, etc.), with six different rounding modes including the standard half‑up, Banker's rounding, ceiling, floor, and truncation. Each calculation includes a detailed explanation of the rounding decision.

Rounding to Decimal Places

To round to n decimal places, examine the digit at position n+1 after the decimal point. If this digit is 5 or greater, increase the n‑th digit by 1; otherwise, leave it unchanged. For example, rounding 3.14159 to 2 decimal places gives 3.14 because the third digit (1) is less than 5.

Significant Figures (Sig Figs)

Significant figures indicate the precision of a measurement. Rules: all non‑zero digits are significant; zeros between significant digits are significant; leading zeros are not; trailing zeros after a decimal are significant. Rounding to n significant figures identifies the n‑th significant digit and rounds based on the following digit. This is essential in scientific and engineering contexts.

Rounding Modes Explained

• Half Up (Standard): 5 or above rounds up; below 5 rounds down.
• Half Down: 5 rounds down; above 5 rounds up.
• Half Even (Banker's): If the digit is exactly 5, round to the nearest even number. Reduces cumulative bias.
• Ceiling: Always round toward positive infinity.
• Floor: Always round toward negative infinity.
• Truncate: Simply discard extra digits without rounding.

Rounding Negative Numbers

Different rounding modes treat negative numbers differently. Standard half‑up rounds away from zero (e.g., -2.5 → -3). Ceiling always moves toward positive infinity (-2.3 → -2), while floor moves toward negative infinity (-2.3 → -3). The calculator handles all cases correctly.